Home

The COMSOL Multiphysics Physics Builder User's Guide

1. commonly contains most of the variables and equations that a specific physics interface requires In the Model Builder zero or more instances of a feature can exist as a child node to a physics interface instance or another feature instance Except for global features they always have a selection on a specific geometry dimension domains boundaries edges or points Typically the governing equations of a problem are defined for a feature at the domain level and constraints and flux conditions for features are defined at the boundary level In this section Feature Periodic Feature Pair Feature Feature Link Multiphysics Feature Contained Feature Device Model Feature Feature Attributes Feature The settings window for a Feature node _ has the following sections IDENTIFIERS The Type is a unique string that identifies a feature and it must be unique among all features supported by a physics interface The Default identifier and tag field is used to generate the tag of newly created instances in the Model Builder The text entered in the Description field is the text COMSOL displays for the feature in the Model Builder RESTRICTIONS From the Allowed space dimensions list define what space dimension this particular feature can be used with Same as parent the default means that the feature supports the same space dimensions as the parent instance which can either be a physics interface or anothe
2. User Input Group Options User Inputs and GUI Components The settings under the Declaration section often determines what GUI component you see when the user input is visible SINGLE ARRAY INPUTS The table below summarizes the behavior for single array inputs option Array type set to Single DIMENSION ALLOWED VALUES GUI COMPONENT Scalar or Ixl Any field text box Scalar or Ix From list Combo box Vector 3x1 Not applicable Table with 1 3 rows depending on the option Vector component to display Matrix 3x3 Not applicable Table with 1 3 rows and 1 3 columns depending on the option Matrix component to display You also get a combo box for matrix symmetry Boolean Not applicable Check box DESIGNING THE GUI LAYOUT 115 116 CHAPTER 3 DIMENSION ALLOWED VALUES GUI COMPONENT Custom Not applicable Table with rows and columns representing the specified dimension If it represents a square matrix you can specify a symmetry with the option Matrix symmetry for square matrix Changeable Not applicable Single column table with the possibility to add rows Depending on the dimension of the input you get different options in the GUI Options section You find the available options below Hide user input in GUI when inactive The the logic controlling the user input determines that it is inactive the input s GUI component disappears from the layout This is not necessary if the us
3. The settings window for the dependent variable declaration contains the following sections DEFINITION In the Dependent variable reference list you choose if you can use the physical quantity as the reference choose Use physical quantity which is the default or if you have to append an unique tag choose Use physical quantity tag and enter a tag in the Unique tag field The Physical quantity list defines what quantity the dependent variable represents including the unit As mentioned previously the physical quantity is also used to generate the unique reference tag for the dependent variable In addition to the PHYSICS BUILDER TOOLS predefined physical quantities you can use locally defined physical quantities or physical quantities imported from an external resource Select Locally defined from the top of the Physical quantity list to use one of the locally defined physical quantities which you choose from the Link list Click the Go to Source button to move to the Physical Quantity node for the selected local physical quantity Select Imported from external resource from the Physical quantity list to use physical quantities from another imported Physics Builder file which you choose from the Imported file list Click the Go to Source button to move to the Import node for the imported Physics Builder file It is also possible to choose None from the list of physical quantities This is not a physic
4. Exterior boundaries to the selection All boundaries that only has one of the upside domain or downside domain belonging to the domain selection PHYSICS BUILDER TOOLS Interior boundaries to the selection The boundaries where the upside domain and downside domain both belong to the domain selection Exterior boundaries whose upside is in the selection Include exterior boundaries that has the upside domain in the domain selection Exterior boundaries whose downside is in the selection Include exterior boundaries that has the downside domain in the domain selection Interior Exterior Exterior Interior Figure 3 2 A schematic of a domain selection with highlighted exterior and interior boundaries Note that some exterior boundaries are not highlighted Frame Shape Add a Frame Shape node usw to define the motion of the moving frame either as an expression or as degrees of freedom To add this node right click a node that can have it as a child node for example Component or Feature Then select Frame Shape from the Variables list SETTINGS Select a Frame motion from the list Free the default or Given by expression Choose Free to define degrees of freedom for the motion If you choose Given by expression enter an Expression to prescribe the motion CREATING VARIABLES 65 66 CHAPTER 3 Creating Equations You need a weak form equation a differential equation us
5. This is the default for non spatial tensors Use the option Specifying a template if you have a certain naming convention for the i th component For example assume that you want to the use following names and descriptions for a velocity vector NAME DESCRIPTION x vel x velocity y_vel y velocity z_vel z velocity Then you specify the following template for the variable name str append coord i vel and for the description coord i velocity If you have a tensor with up to 4 indices use the identifiers j m and n to access the other indices It is also possible to concatenate parts with str append operator The operator appends all its argument to generate the final component name Assume that a feature has a user input called Port that has the value 2 The following template str append phys R par Port par Port then generates the following component name root mod1 ph is the physics scope root mod1 ph R22 The final option is Specifying each component separately Here you type the name and description for each component in the table below the list You can use the dot and PHYSICS BUILDER TOOLS hash symbols to use the coordinate names You can implement the example above with the following component settings COMPONENT NAMES COMPONENT DESCRIPTIONS str append coord 1 vel coord 1 velocity str append coord 2 vel coord 2 velocity str append coord 3 vel coord 3 velocity ENTERING
6. Bibliography Table and Text In addition there are subnodes for creating a Reference List Item Table Heading Row or Table Row The following table lists all documentation components TABLE 3 1 DOCUMENTATION COMPONENTS DOCUMENTATION COMPONENT ICON DESCRIPTION Bibliography i Adds a reference or bibliography to the report or document Right click to add Reference nodes for each reference Code Adds a text block for code using a code monospace font You can also make part of the text using an italic or bold variant of the code font Equation fo Adds an equation to the report or document You can use LaTeX markup directly or import the equation as an image Under Equation preview you can see the equation that the LaTeX commands that you enter create ADDING COMMENTS AND DOCUMENTATION 137 TABLE 3 1 DOCUMENTATION COMPONENTS DOCUMENTATION COMPONENT ICON DESCRIPTION Heading E Adds a heading to the report or document with a text from the Text field and a layout for the level Level Level 6 from the Level list The default is to use the level where the Heading node appears Image ER Adds an image to the report or document Select the image source from the Source list Plot group to select the plot from available plots in the Plot group list or External to use any external image file in PNG Windows Bitmap BMP or JPEG format Add a Caption if desired List Adds a list By default the Numbered
7. Default Multi Scalar Plot Default Plot Parameters Default Scalar Plot For the Default Scalar Plot 4 enter the expression in the Expression field The expression follows the rules outlined in Entering Names and Expressions and is used in all new plots created by the user that requests a scalar value for example a surface plot Enter the description for the expression in the Description field PHYSICS BUILDER TOOLS Default Vector Plot For the Default Vector Plot 4 enter a valid vector variable name in the Variable name field The name follows the rules outlined in Entering Names and the components of the vector are used in all new plots created by the user that requires a vector quantity for example an arrow plot Default Deformation Plot For the Default Deformation Plot enter a valid vector variable name in the Variable name field The name follows the rules outlined in Entering Names and the components of the vector are used in all new deformation plots created by the user Deformation plots show a deformed shape typically using a displacement vector as the vector variable Default Multi Scalar Plot For the Default Multi Scalar Plot fill the table with expressions and descriptions in the Expression column and Description column The expressions follow the rules outlined in Entering Names and Expressions and are used in all new plots created by the user that requests several sca
8. Device Model The Device Model gt defines a set of variables and equations that corresponds to a certain device characteristic Typical examples from the field of electrical circuits are capacitors resistors voltages sources and bipolar transistors To a device model you can add modifiable inputs variables equations other devices and ports as child nodes There are various ways to add a Device Model node Go to Building Blocks gt Features gt and add any of these nodes Device Model Feature Feature or Periodic Feature Then right click these nodes to add a Device Model from the Devices list Or go to Building Blocks gt Components gt and add a Component node Then right click the node to add a Device Model from the Devices list The settings window for a device model contains the following sections DEVICE MODEL In the Type field you define a unique string that identifies the device model When you create a Device you must specify a type of a device model for that device The device then instantiate the device model A device model type should be unique but if you declare several device models with the same type the last one will be used In the Inherited type field you can enter a parent type that this device model inherits all inputs ports variables and equations from Leave this field empty to skip inheritance A device model can also be abstract meaning that you can only specify this type as an inherited type of anot
9. Right click the Physics Interface node and select Results Defaults 4 2 Right click Results Defaults 4 and select Plot Group 2D ji 3 Right click the Plot Group 2D a node and select Surface E 4 In the Surface L3 settings window type probdens in the Expression edit field 5 Right click the Surface Ld node and select Rename In the Rename Surface dialog box type Probability density in the New name edit field Click OK 6 Right click Results Defaults 4 and select Plot Defaults 4 7 Right click the Plot Defaults 4 node and select Default Scalar Plot 4 In the Expression edit field type probdens This makes the probability density function the default for all scalar plots MAKING A QUANTUM MECHANICS PHYSICS AREA To add the Schrodinger Equation to a new physics area for Quantum Mechanics under the Mathematics branch do the following steps Right click the Physics Areas node j and select Physics Area 13 2 In the settings window for the Physics Area node enter QuantumMechanics in the Name edit field Quantum mechanics in the Description edit field The default icon is physics png sh which is appropriate for this physics area Otherwise click SCHR DINGER EQUATION IMPLEMENTATION 179 Browse to use another icon Enter 10 in the Weight edit field to make the Quantum Mechanics area appear last in the list under Mathematics the higher the weight the lower position the physics are
10. Under the Shape Declaration section you choose what shape function to use for the constraint Similar to the Dependent Variable Definition you can choose to specify a reference to a Dependent Variable Declaration and the constraint then uses the same shape function as that dependent variable To use this option choose Field quantity from the Constraint shape function list With the option Use specific shape in this list you can specify an arbitrary shape function for the constraint ADVANCED The Use weak constraint check box lets you deactivate support for weak constraints which is selected by default When selected the constraint can potentially generate a weak form equation Therefore it is necessary to support a Base vector system list selection similar to the weak form equation see Weak Form Equation and Using Coordinate Systems Clearing the Use weak constraint check box means that it is not possible to activate weak constraints for an instance of the feature owning this constraint in the Model builder Constraint and Using Weak Constraints in the COMSOL Multiphysics e User s Guide See Also Group Members Define a Section CREATING CONSTRAINTS 73 74 Creating Device Systems CHAPTER 3 In this section About Device Systems Device Model Port Model Device Variables Device Equations Device Inputs Device Constants Dort Device Port Connections Input Modifier Abo
11. electron charge e and the permittivity of vacuum 9 are physical constants e const and epsilonO const respectively and r is a distance that you can formulate using the space coordinates in the space dimension of the model THE BOUNDARY CONDITIONS The Schrodinger Equation interface includes the following boundary conditions Typically you assume that the exterior boundary is such that there is zero probability for the particle to be outside the specified domain Such Zero Probability boundary 172 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES condition is equivalent to a Dirichlet condition 0 This is the default boundary condition There is also a Wave Function Value boundary condition Y for the case that you do not want to specify a zero probability This boundary condition defines one user input for Yo For axisymmetric models the cylinder axis r 0 is not a boundary in the original problem but here it becomes one For these boundaries the artificial Neumann boundary condition n V 0 serves as an Axial Symmetry condition This is the default boundary condition for axial symmetry boundaries and COMSOL Multiphysics adds these automatically All boundary conditions are exclusive that is only one of them can be active for any of the boundaries ADDITIONAL VARIABLES One variable to add is the quantity Iv 2 which corresponds to the unnormalized probability density function of the electron s pos
12. Any for an entry of a general scalar number Type 293 15 in the Default value edit field corresponding to room temperature in K Leave all other default values Right click the User Input node and select Variable Definition a This user input then becomes available as a variable tee TO in for example the predefined expressions for results evaluation You can also refer to TO directly in the weak equation Leave all other settings at their default values Now define a Section in the settings window for the boundary condition Right click the Feature 3 Temperature node and select Inputs gt User Input Group P In the settings window locate the Declaration section Type TemperatureSection in the Group name edit field Type Temperature in the Description edit field Add User Input TO to the Group members list Use the button to get a selection list of available user inputs I0 Locate the GUI Options section Change the GUI layout to Group members define a section Now define the constraint equation II Right click the Feature 3 Temperature node and select Constraint P In the settings window locate the Declaration section D In the Expression edit field type TO T I3 Locate the Shape Declaration section and select Temperature K from the Physical quantity list I4 Leave all other default values EXAMPLES OF CUSTOM PHYSICS INTERFACES The Electric Potential Boundary Condition Right c
13. Enable Physics Builder check box if not selected already From the File menu choose New gt Physics Builder A Physics Builder window then replaces the Model Builder window on the COMSOL Desktop Right click the root node Untitled mphdev and select Physics Interface This adds a Physics Interface node y Move to the settings window for the Physics Interface I node In the Identifiers section type ThermoelectricEffect in the Type edit field tee in the Default identifier and tag edit field and Thermoelectric Effect in the Description edit field If you have a custom icon for the interface you can click the Browse button to locate the icon file The default is to use the physics png icon Se The Thermoelectric Effect interface should support all space dimensions except 0D so leave the Allowed space dimensions list with the default contents which includes all space dimensions except 0D In the Allowed study types list select the default Time dependent study type and click the Delete button 9 underneath the list For this example only the Stationary study type is allowed In the Settings section verify that Domain is selected in the Top domain level list This means that the equations in the physics interface apply to the domains in the geometry which is the case for most physics interfaces Leave the setting in the Default frame list at the default value Material It is good practice to save the physics interface af
14. Equation 4 1 above you need to specify the following items The name and description for the physics interface The supported space dimension for the physics interface The study types stationary time dependent eigenvalue and so on that the physics interface supports The equation written using a weak formulation to solve and the input variables that it needs The boundary conditions that the physics interface needs including the default boundary condition and the inputs that they need Any additional variables that are relevant to define for use in for example results analysis and visualization Asuitable default plot to be displayed when the solver has finished and possibly custom quantities as default plot expressions for new plots NAME AND DESCRIPTION The name of this interface is Schrodinger Equation avoiding using the character 6 in the user interface The short name is scheq There is also an identifier SchrodingerEq which is used by the Java and MATLAB interfaces SUPPORTED SPACE DIMENSIONS The Schrodinger Equation interface is available in all space dimensions THE STUDY TYPES The Schr dinger equation is an eigenvalue equation so an eigenvalue study is the only applicable study type SCHR DINGER EQUATION IMPLEMENTATION 171 THE EQUATION With scalar coefficients in the equation and using C as a replacement for the coefficient 2 the weak formulation using the COMSOL te
15. Group Options Otherwise behaves as a single array vector with restrictions what you can enter in the table cells Matrix 3x3 Scalar Any Behaves as a single array matrix or Ixl Vector 3x1 Boolean Not applicable Several check boxes when the input is a member to a special input group see User Input Group Options Otherwise behaves as a single array vector with restrictions what you can enter in the table cells For double array inputs you might get an error when you try to use an unsupported combination In other situations especially when the inner dimension is a scalar you can get a component but with an unpractical behavior For example when the outer dimension is fixed but nonscalar Note the inner dimension is scalar and Allowed values is set to From list Then the input behaves as the single array version but with restrictions on what you can enter in the table cells There are fewer GUI options for double array inputs but those supported are identical to the options for single array inputs E User Input See Also DESIGNING THE GUI LAYOUT II7 118 CHAPTER 3 User Input Group Options You can use the user input group for two main purposes controlling GUI layout and putting the same activation conditions on several user inputs The latter is usually a consequence when implementing the first Grouping of user inputs also makes it possible to define the section name and to create hel
16. Interface Enter the settings available in the Physics Interface settings window initially in the Identifiers Restrictions and Settings sections 5 Add the dependent variable declarations for the variables to solve for 24 CHAPTER 3 PHYSICS BUILDER TOOLS 6 Add the features that the physics interface requires All features can be added directly under the physics interface Alternatively add them to Building Blocks gt Features C and then add a link to the feature in the physics interface By placing features in the Building Blocks branch 4 these features can be reused by linking from several physics interfaces 7 Add the properties to the physics interface in the same way as the features pon 8 Test the physics interface using the Preview toolbar button 55 This preview automatically sets up a simple modeling environment with a predefined geometry and an instance of the physics interface Experiment with the settings window for all features the GUI logic and investigate the generated equations in the equation view To test a physics interface more thoroughly use the The Physics Builder Manager Physics Interface Settings The settings window for the Physics Interface y contains the following sections PHYSICS AREA This section is initially collapsed It contains a tree view of all physics areas fluid flow heat transfer and so forth and sub areas available from built in resources areas defined in th
17. NAMES OF OPERATORS AND FUNCTIONS When you want to enter a name to an operator or function almost the same rules apply as for variable names The only difference is the default scope For variable names the default scope is always the physics scope represented by the phys prefix When you declare a new operator or function the default prefix is also phys but not when you use the operator or function in an expression Then the default is the mod prefix which is interpreted as model scope The reason is simply that it is most common that you declare new operators with physics scope but not when you use a function Then you often refer to functions that are unscoped for example sin cos exp gradient and normalize In the Model Builder all unscoped names are first interpreted using model scope then root scope so it is possible to change the meaning of the function name sin if you want Using Coordinate Systems When creating a feature or property you can define two coordinate systems THE BASE VECTOR SYSTEM This is the system a feature declare its variables in Typically this only has an effect if the variable is a spatial tensor for example a vector with length 3 It also has an effect for weak form equations where the base vector system can define the volume factor for the weak form integration The most common choice is to use the coordinate system represented by the current frame used by the feature In the Base vector sy
18. a dependent variable into an equation expression If the default name of a dependent variable is u then the following syntax can be used to access the current user defined name of that dependent variable symbref dep u CREATING COMPONENTS 87 88 Building Blocks CHAPTER 3 Under the root of the tree there is a branch called Building Blocks 4 Under this branch you can create a library of components features or properties that you can build physics interfaces with Components A list of Component and Selection Component nodes Properties ED A list of Property nodes Features C A list of Feature nodes These items are not used in any physics interface until the are referenced from a link node see Component Link Property Link and Feature Link In this section Components Properties Features Components The Components branch contains the following items e Component A collection of user inputs variables equations and constraints Items in this branch are available to any feature or property as component links Selection Component B A selection definition that can either be an explicit selection or a selection being the result of a Boolean operation Code Editor Opensa text editor window for Java code providing a possibility to enter coded methods in Java The components in this list are available to all Component Link nodes The selec
19. and right click Component Then select Coefficient Form Equation from the Equations list The settings window for a coefficient form equation contains the following sections EQUATION This section displays the equation that you define by defining the coefficients in the next section COEFFICIENTS There are eight coefficient in a coefficient form equation You define each coefficient by defining a tensor expression that requires a certain dimension The dimensions are defined by the dimension of the dependent variable N and the number of spatial dimension always 3 The table below lists the dimensions for all eight coefficients COEFFICIENT DESCRIPTION DIMENSION Y Conservative flux N by 3 a Absorption coefficient N by N a Conservative flux convection coefficient N by N by 3 B Convection coefficient N by N by 3 c Diffusion coefficient N by N by 3 by 3 f Source term N by 1 da Damping or mass coefficient N by N ea Mass coefficient N by N Ifthe dependent variable is a scalar you can simplify the tensor dimensions by skipping all singleton dimensions This simplifies the y a and B coefficients to be spatial vectors CREATING EQUATIONs 69 70 CHAPTER 3 length 3 The dependent variable can only be a tensor up to rank 1 a vector so use the weak form equation for dependent variables of higher ranks For information about writing expressions see Entering Names and Expressions You also specify t
20. brief explanation of the matching options below Always match If there is any matching announced variable always use the first one found PHYSICS BUILDER TOOLS Synchronized Match to a matching announced variable if the provider to that variable fulfills the following conditions It has a feature input of the quantity chosen in the Synchronized physical quantity list That feature input chooses an announced variable from the provider owning the synchronized feature input Always match within physics interface If there is any matching announced variable by the current physics interface use the first one found Model input match Also matches within the physics interface but you can disable the matching through an interface setting Never match Never do any automatic matching The default option is User defined but you can always manually choose among the found announced variables GUI OPTIONS If you want the feature input to disappear when it is inactive you select the Hide user input in GUI when inactive check box Select the Show no description check box to hide the text label containing the description above the GUI component of the input Similarly you can hide the symbol from the GUI by selecting the Show no symbol check box As a final option it is possible to add a divider above the GUI component and any description text label The divider is a horizontal line with an optional descriptive te
21. check box is selected giving a numbered list clear the check box for an unordered bullet list Right click the List node to add List Item nodes List Item 4E Right click the List node to add this node with a Text area for the list item s contents Right click to add Code Equation Image Table Text or other List nodes for inserted texts equations images or tables in the list or for creating nested lists Note Adds a Note node for adding one of the following note types which you select from the Type list Note the default Caution Important Model See also or Tip From the Show list select Icon the default to display the icon only Description the type or Icon and description Then add the text for the note Reference we Adds a reference to a bibliography or reference sections Select one of the following reference types from the Type list Journal article the default Book Conference paper Thesis or Web You can always add Authors and Title the other parts of the reference depends on the type For Web you add the URL web address to the web page Table Adds a table with a Title and a Number of columns default 3 columns Right click to add a Table Heading Row and Table Rows 138 CHAPTER 3 PHYSICS BUILDER TOOLS TABLE 3 1 DOCUMENTATION COMPONENTS DOCUMENTATION COMPONENT ICON DESCRIPTION Table Heading Row fin Right click the Table node to add this node and then define headings for
22. enter the variable fully scoped for example root lambda to access the eigenvalues from the solver You may also want to access the value of a user input in your equations without adding it as a variable The syntax for this is to add par before the input parameter name For example to access the input parameter sigma in an expression type par sigma The par prefix is part of a name generation syntax that the builder interprets This syntax is built up by a sequence of dot separated items where each position has a special meaning The full syntax description can be defined by the following rule lt prefix gt lt identifier gt lt input gt lt integer gt All items within brackets mean that you do not have to specify them and in some cases a default is used instead An asterisk means that you can write zero or several items The par prefix in the mentioned above is an example when the identifier position is a user input and the value of that user input replaces the entire sequence There are other similar reserved prefixes for accessing different scopes and specifying operators You find the complete list in the following table PREFIX DESCRIPTION EXAMPLE phys mod root coord item par mat Replaced by the physics interface scope Replaced by the model scope Used as is to define root scope Identifies the coordinate and is used together with number dot Replaced by a scope that represe
23. file mph that uses one of your new interfaces you must make sure that the same interface is available when you open the file Note again COMPILING AN ARCHIVE When your interface is finalized and you are ready to distribute it to others you can compile all development files into a builder archive The archive is a folder containing your source builder files the compiled builder files all files the builder files refer to icons for example the necessary Java code and a set of language files for translation The language files are ordinary text files where you can add a translation to all descriptions displayed for your interfaces A language file has the following format German language file THE PHYSICS BUILDER MANAGER 127 128 Original description Auto current calculation deployment1 phys1 description Automatische Stromberechnung Original description Current domain deployment1 phys1 feat1 description Stromf hrender Bereich All lines starting with a hash symbol are comments All files use the original description string by default but you replace them when translating The original description is always in the comment above the translation for reference Do not change the tag on the left side of the equal sign This is used by COMSOL to identify the description If you recompile an archive into to an existing archive the compilation replaces all files except the language files The compi
24. gt User Input Group P In the settings window locate the Declaration section I3 Type ElectricPotentialSection in the Group name edit field Type Electric Potential in the Description edit field I4 Add User Input V0 to the Group members list Use the button to get a selection list of available user inputs I5 Locate the GUI Options section Change the GUI layout to Group members define a section Now define the constraint equation l6 Right click the Feature 4 ElectricPotential node and select Constraint P In the settings window locate the Declaration section THERMOELECTRIC EFFECT IMPLEMENTATION I6l I7 In the Expression edit field type VO V I8 Locate the Shape Declaration section and select Electric Potential V from the Physical quantity list I9 Leave all other default values The Heat Flux Boundary Condition l 2 3 Right click the Physics Interface node and select Feature C In the Feature 5 settings window locate the Identifiers section Type HeatFlux in the Type edit field Type hf in the Default identifier and tag edit field Type Heat Flux in the Description edit field Change the Category for overwriting selections to Contributing Leave all other settings at their default values Right click the Feature 5 HeatFlux node and select Inputs gt User Input P In the settings window locate the Declaration section Type qin in the Input name edit field and Normal Heat Flu
25. in the previous section You use the option Export As Plugin to export the archive to a compressed archive jar when you want to include it into a COMSOL installation The next step is to PHYSICS BUILDER TOOLS copy the compressed archive into the plugins folder of the COMSOL installation Finally you have to restart COMSOL before you can use the new plug in THE PHYSICS BUILDER MANAGER 129 130 Migration CHAPTER 3 In this section About Backward Compatibility Version Physics Interface Feature Property Change Type Rename Inputs Migration Links License Settings About Backward Compatibility Migration or backward compatibility has to be considered in situations when you make changes to your physics interface design but still want users of this interface to use a COMSOL Multiphysics model files created in the old version of your interface If the migration is done properly the old model file is corrected when opened and the user can continue working with it without any problems Otherwise the user can get a series of error messages complaining about invalid names and values Another situation is if the users has saved his model as a Model Java file The change you made in the interface can then break that Model Java file so the user cannot execute it It is possible to define migration for this as well so generated files can execute although they contain Java code in an old s
26. interface If you want to control the space dimensions manually choose Customized from the list You can then select from a list of all space dimensions You can also impose a special restriction on study types for this property If you try to solve a problem for a property that does not support the current study type it does not add any contributions to the model Choose Customized from the Allowed study types list to control the supported study types manually by selecting from a list of study types The option Same as parent the default option means that the property supports the same study types as the physics interface CREATING PROPERTIES 4l Property Link The Property Link 5 refers to a common definition of a property typically under the Building Blocks branch The settings window has the following section SOURCE PROPERTY In the Links from list you choose where to look for a certain property Possible options are Building blocks Lets you choose among the properties listed under the Properties branch in the Building Blocks branch You choose the property from the Link list e Built in Lets you choose among COMSOT built in properties that are available to the Physics Builder In the Package list you choose the main resource to use properties from For each resource you have a list of properties in the Link list to choose from You can only choose among the currently published properties External resour
27. of features in the Link list to choose from You can only choose among the currently published features External resources Lets you choose among the features found in an imported builder file under the External Resources branch You choose the file from the Imported file list The Link list contains all features found in the Building Blocks gt Features branch of the selected file CREATING FEATURES 37 38 A feature link also has a Add as default feature check box see Feature io Information Sections for the Feature node See Also Multiphysics Feature A Multiphysics Feature is a combination of other features that behave like one feature The multiphysics feature inherits all variables and equations that all contained features has which you add through Contained Feature nodes The settings window of the multiphysics feature is very similar to a feature but with some settings removed as they are inherited from the contained features The entire Restrictions section is gone because the allowed space dimensions and allowed study types get their values from an intersection of the values in the contained features Identifiers section for the Feature node G See Also Variable Declarations section for the Physics Interface Settings node CHAPTER 3 SETTINGS Almost identical to the Settings section of the Feature node For a multiphysics feature you cannot change the supported geometric entity
28. options that you do not have to change in most cases In the Input base vector system list you can override the input base vector system specified by the parent for example a feature or property by choosing something else than the default option Same as parent See Using Coordinate Systems and Transformation Between Coordinate Systems for more information about selecting base vector systems GUI OPTIONS If you want the user input to disappear when it is inactive select the Hide user input in GUI when inactive check box Select the Show no description check box to hide the text label containing the description above the GUI component of the user input Similarly you can hide the symbol from the GUI by selecting the Show no symbol check box As a final option it is possible to add a divider above the GUI component and any description text label The divider is a horizontal line with an optional descriptive text Select the Add divider above the user input check box to add the divider When selected you can enter the divider text in the Text field CREATING USER INPUTS 45 46 CHAPTER 3 See Designing the GUI Layout for more information about GUI options User Input Group The User Input Group node is a collection of other user inputs user input groups and material parameters Use it to organize the GUI layout of the feature and property This can be a complex task and you can read more about the details of this p
29. same way as ordinary model files mph except that they have the extension mphdev Opening a file is also similar to opening MPH files just make sure that Physics Builder File mphdev is selected from the Files of type list in the Open dialog box TESTING CUSTOM PHYSICS INTERFACES Physics Builder files may contain several physics interface declarations that you can access from the Model Wizard These physics interfaces are identical to built in physics interface the physics interfaces shipped with COMSOL with the difference that their functionality is specified by your Physics Builder file COMSOL searches and uses the Physics Builder files that are located under the Development Files branch Z7 Select View gt Physics Builder Area to open the settings window Right click the Development Files node to add new Physics Builder PHYSICS BUILDER TOOLS files to the list To remove a builder file from the list select it and then right click it and choose Remove Selected 9 from the context menu COMSOL loads all physics interfaces listed in the Development Files node when a new session is started If a Physics Builder file is added during a session COMSOL loads it and updates the list of physics interfaces If the Physics Builder file is changed on the file system by another session you have to manually reload it to activate these changes Click the Update Builder Files toolbar button in the Physics Builder Manage
30. selected cell means that the row category overwrites the column category You can add new categories by clicking the Add a button PHYSICS BUILDER TOOLS The Definitions Library The Definitions Library branch II contains definitions of material property groups physical quantities and other definitions that are used by but are not part of a physics interface Domain Type Conditions The Domain Type Condition node defines a domain type condition that a feature can link to by choosing From condition in the Allowed domain types list in the Settings section of a feature s window see Feature The conditions are defined in the Domain Condition subnodes see Domain Condition Right click the Definitions Library node am to add a Domain Type Conditions node d Right click to add a Domain Condition subnode The settings window for a Domain Type Conditions node 4f contains the following section SETTINGS The table displays a list of all Domain Condition nodes under this Domain Type Condition node For each row domain condition select Take complement and choose Operation to use with the next condition The choices in this table produce a complete condition sequence without precedence between operations For example if the table has the following three rows CONDITIONS TAKE COMPLEMENT OPERATION WITH NEXT Condition X Intersection Condition2 VN Union Condition3 X Intersection The contents of this tab
31. sequence but it is then not allowed to link to this component from an interface that does not support the study steps in the list The Study Sequence node s settings window contains the following sections IDENTIFIERS Enter the Name Description and Icon for the study sequence in the corresponding text fields RESTRICTIONS Select the Restrict to space dimensions check box to only allow the study sequence for the chosen space dimensions CREATING STUDY AND SOLVER DEFAULTS 101 102 Creating Result Defaults To define results defaults for a physics interface you create plot groups as you want them to look after you solve a model in the Model Builder You can vary the result defaults using the Usage Condition node It is common to specify one default for 3D and another for 2D because you usually use different plot groups and different plot types Most of the nodes in a result defaults setting work in exactly the same way as in the Model Builder This chapter only describes the nodes that differ significantly or do not have a counterpart in the Model Builder CHAPTER 3 Q Results Analysis and Plots in the COMSOL Multiphysics Reference See Also Cnag Plot Defaults All child nodes to the Plot Defaults branch 4 defines the default expression of variables to use for newly created plots of certain types The supported types are Default Scalar Plot Default Vector Plot Default Deformation Plot
32. settings see Model Couplings in the COMSOL Multiphysics Reference Guide Not all model couplings are supported as operations in the Physics Builder and the following sections list the ones supported Average The average operator is almost identical to the average operator you can add in the Model Builder see About Model Couplings and Coupling Operators in the COMSOL Multiphysics Reference Guide The main differences is how you specify the operator name and selections which is described in the Introduction to Operators and Functions of this chapter Integration The Integration operator is almost identical to the integration model coupling you can add in the Model Builder see About Model Couplings and Coupling Operators in the PHYSICS BUILDER TOOLS COMSOL Multiphysics Reference Guide The main differences is how you specify the operator name and selections which is described in the Introduction to Operators and Functions of this chapter Maximum The Maximum operator is almost identical to the Maximum model coupling you can add in the Model Builder see About Model Couplings and Coupling Operators in the COMSOL Multiphysics Reference Guide The main differences is how you specify the operator name and selections which is described in the Introduction to Operators and Functions of this chapter Minimum The Minimum operator is almost identical to the Minimum model coupling you can add in the Model Builder s
33. the Preferences dialog box PHYSICS BUILDER TOOLS Enter the plug in s name and title in the Plug in name and Plug in title fields respectively The complete plug in name will be formed from the plug in prefix and plug in name The plug in title is the title that will appear in the Contents tree on the left side of the standalone Help window or on the Contents page of the Help window for Dynamic help integrated in the COMSOL Desktop From the Add to list select None the default to not link the plug in to the contents of any COMSOL product or select COMSOL Multiphysics or any of its modules or LiveLink products to add the documentation to one of the products As an advanced option you can select Custom to link to a custom plug in that you specify in the Link to plug in named field and the Link to anchor ID field The custom plug in must extend the org eclipse help toc extension point and contain the specified anchor for your documentation plug in to link to n the Vendor field you can enter the name of your organization This name will appear in the manifest file inside the generated plug in Enter the version of the plug in in the Plug in version field The default version is 1 0 0 Like the vendor name this number is written to the plug in s manifest file Documentation Text Components Right click Section nodes to select and add these documentation nodes Bibliography Code Equation Heading Image List Note
34. the boundary geometric entity level PREFERENCES A feature instance in the Model Builder can have a section called Model Inputs which shows up when you select the Include model inputs check box A model input is an input argument to material parameters when they depend on a quantity for example if the density depends on temperature Select the Singleton feature check box if the physics interface only allows a single instance of the feature For features under a physics interface there is an Add as default feature check box Select this check box if you want the feature to be a default feature When you specify default features specify the geometric entity level in the Default domain level list Newly created interfaces then add the feature on this level The Default domain type specify the domain type the default feature is added on In the Advanced preferences table you can specify special options for the default feature By default all default features have a selection over all domains it cannot be changed and you can neither remove or disable the feature Select the check box columns to alter this default behavior GUI OPTIONS Select the Hide feature from context menus to remove the possibility to add new features of this type This can be useful when a feature must be kept for backward compatibility reasons but a user cannot add them in new models PHYSICS BUILDER TOOLS INFORMATION SECTIONS This is a group of section
35. true for the domain type setting because all pairs belong to a special domain type called Pair Ordinary features that support this domain type also appear in a pair version among the physics interface s pair conditions All pair features also has a special type of rule for overriding selections They are always exclusive to all non pair features preceding the pair in the list For all features pairs and non pairs that lies below the pair in the list contributes with the pair condition As a result you cannot set the category for overriding selection for pair features PREFERENCES Identical to the same section for the Feature node see Preferences It is not possible to add a pair feature as a default feature to a physics interface GUI OPTIONS Identical to the same section for the Feature node see GUI Options Feature Link The Feature Link amp refers to a common definition of a feature for example under the Building Blocks branch SOURCE FEATURE In the Links from list you choose where to look for a certain feature Possible options are Building blocks Lets you choose among the features listed under the Features branch in the Building Blocks branch You choose the feature from the Link list Built in Lets you choose among COMSOL s built in features that are available to the Physics Builder In the Package list you choose the main resource to use features from For each resource you have a list
36. understand what you can expect to see on the Graphical User Interface GUI and know which data must be entered into various data entry fields In particular these conventions are used throughout the documentation Click text highlighted in blue to go to other information in the PDF When you are using the online help deskin COMSOL Multiphysics these links also work to other modules model examples and documentation sets ABOUT THE PHYSICS BUILDER 13 A boldface font indicates that the given word s appear exactly that way on the COMSOL Desktop or for toolbar buttons in the corresponding tooltip For example the Model Builder window ep is often referred to and this is the window that contains the model tree As another example the instructions might say to click the Zoom Extents button 459 and this means that when you hover over the button with your mouse the same label displays on the COMSOL Desktop The names of other items on the COMSOL Desktop that do not have direct labels contain a leading uppercase letter For instance the Main toolbar is often referred to the horizontal bar containing several icons that are displayed on top of the user interface However nowhere on the COMSOL Desktop nor the toolbar itself includes the word main The forward arrow symbol gt is instructing you to select a series of menu items in a specific order For example Options gt Preferences is equivalent to From the Opt
37. weak form equation In axial PHYSICS BUILDER TOOLS symmetry this means that you do not get the factor 2zr For more information on non orthonormal systems see Using Coordinate Systems ADVANCED If you want to use a different base vector system than the parent feature or property you can choose a different system in the Base vector system list See Using Coordinate Systems for more information about choosing coordinate systems Weak Form Modeling in the COMSOL Multiphysics User s Guide G Weak Form Theory Background and The Finite Element Method in See Also the COMSOL Multiphysics Reference Guide General Form Equation As an alternative to the weak form you can enter the equation using the General Form Equation node fau To add this node go to Building Blocks Components and right click Component Then select General Form Equation from the Equations list The settings window for a general form equation contains the following sections EQUATION This section displays the equation that you define by defining the coefficients in the next section COEFFICIENTS There are four coefficient in a general form equation You define each coefficient by defining a tensor expression that requires a certain dimension The dimensions are defined by the dimension of the dependent variable N and the number of spatial dimension always 3 The table below lists the dimensions for all four coefficients COEFFICI
38. 83 83 84 86 88 88 89 89 89 90 90 91 9l CONTENTS 5 6 CONTENTS Creating Material Property Groups Material Property Group Material Property Adding Physical Quantities Physical Quantity Creating Override Rules Override Rule The Definitions Library Domain Type Conditions Domain Condition Plot Menu Categories Creating Study and Solver Defaults Field Absolute Tolerance Outer Job Parameters Eigenvalue Transform Study Sequence Creating Result Defaults Plot Defaults Default Scalar Plot Default Vector Plot Default Deformation Plot Default Multi Scalar Plot Default Plot Parameters Creating Mesh Defaults Mesh Size Entering Names and Expressions Tensor Parser Entering Names Using Coordinate Systems Transformation Between Coordinate Systems 93 93 94 95 95 96 96 97 97 97 98 99 99 100 100 100 101 102 102 102 103 103 103 103 104 104 106 106 108 Ml 113 Designing the GUI Layout User Inputs and GUI Components User Input Group Options Creating Elements Element GeomDim Srce Array Record String Elinv Elpric Event Degree of Freedom Re Initialization The Physics Builder Manager Migration About Backward Compatibility Version Physics Interface Feature Property Change Type Rename Inputs Migration Links License Set
39. COMSOL Multiphysics Physics Builder Users Guide VERSION 4 3 BETA Ng COMSOL Physics Builder User s Guide 1998 2012 COMSOL Protected by U S Patents 7 519 518 7 596 474 and 7 623 991 Patents pending This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement www comsol com sla and may be used or copied only under the terms of the license agree ment COMSOL COMSOL Desktop COMSOL Multiphysics and LiveLink are registered trademarks or trade marks of COMSOL AB Other product or brand names are trademarks or registered trademarks of their respective holders Version May 2012 COMSOL 4 3 Contact Information Visit www comsol com contact for a searchable list of all COMSOL offices and local representatives From this web page search the contacts and find a local sales representative go to other COMSOL websites request information and pricing submit technical support queries subscribe to the monthly eNews email newsletter and much more If you need to contact Technical Support an online request form is located at www comsol com support contact Other useful links include Technical Support www comsol com support Software updates www comsol com support updates Online community www comsol com community Events conferences and training www comsol com events Tutorials www comsol com products tutorials Knowledge Base www comsol com support kno
40. COMSOL Multiphysics User s Guide See Also CREATING MESH DEFAULTS 105 106 Entering Names and Expressions CHAPTER 3 In this section Tensor Parser Entering Names Using Coordinate Systems Transformation Between Coordinate Systems Tensor Parser All Expression fields supports tensor variables and operators for tensors If you for example want the cross product between two vectors simply type AxB directly in the Expression field The symbol for the cross product is among the standard mathematical symbols defined by the Unicode standard The other special symbols used by expressions are the inner dot product A B and the nabla operator VA You can use predefined key bindings to type them into an expression see the following table SYMBOL KEY BINDING UNICODE HEXADECIMAL x Ctrl Alt Keypad 00D7 Ctrl AlctPeriod 00B7 V Ctrl Alc Comma 2207 The system font must support the special symbols to display them properly otherwise the expression might not look correct You can also press Ctrl Space to get a list of the supported operations that includes any special characters As a last resort it is always possible to copy paste them from an editor that supports Unicode input or directly from a Unicode character map PHYSICS BUILDER TOOLS There are also some function that you can use to perform tensor operations for example the transpose of a matrix or the inverse of a matrix The follo
41. Degree of Freedom Re Initialization nodes In the Event type list choose the Explicit or Implicit event type For explicit events specify a Start time and optionally a Period for cyclic events The implicit event requires a Condition that triggers the event when the value of the condition goes from 0 to 1 The condition must contain a degree of freedom with the Solver field type set to Quadrature in the Advanced section of either a Variable Definition node or a Dependent Variable Definition node Note that this option is currently only supported for global states Set the Solver field type to Discrete for global states that are discontinuous in time Such states are typically used as logical help variables in if statements to turn on and off equations Degree of Freedom Re Initialization The Degree of Freedom Re Initialization node uw is identical to the Degree of Freedom Initialization node that initializes degrees of freedom dependent variables shape variables and global states There is only one extra section for needed for reinitialization after triggered solver events REFERENCE Enter the unique tag in the Event tag field that points to the Event node that triggers this reinitialization step io See Degree of Freedom Initialization for the rest of the settings See Also CHAPTER 3 To add this node go to Building Blocks Right click Components to add a Component node Then select Degree of Freedom Re Initializ
42. E SYSTEMS 78 CHAPTER 3 Port A Port sis is a port model instance that you add to a device model to define the connections that devices uses to communicate with each other In the Name edit field you enter the name of the port This name defines the variable names that you use to access the variables declared in the port model that you refer to in the Type edit field Ifa port model declares a variable named v and you typed a in the Name edit field you access the variable v by typing a v Device A Device i is a device model instance that you can add under a feature or under a device model If you add it under a feature the program creates one device per feature instance To make this work properly ensure that the device gets a unique name typically by specifying the name to entity tag The device then gets the same name as the parent feature You enter the name in the Name edit field and in the Type edit field you enter the device model that the device is an instance of If the device is under a device model you can access the variables defined by the device s device model by pre pending the name of the device to the name of the variable Assume that the device model declares a variable named R and the device has the name R1 To use this variable in the device model that the device belongs to you then type R1 R There are various places where you can add a Device node For example go to Building Blocks gt Feat
43. ENT DESCRIPTION DIMENSION r Conservative flux N by 3 f Source term N by 1 da Damping or mass coefficient N by N ea Mass coefficient N by N If the dependent variable is a scalar you can simplify the tensor dimensions by skipping all singleton dimensions This simplifies the y coefficient to be a spatial vector length CREATING EQUATIONS 67 68 CHAPTER 3 3 The dependent variable can only be a tensor up to rank 1 a vector so use the weak form equation for dependent variables of higher ranks For information about writing expressions see Entering Names and Expressions You also specify these coefficients for boundary conditions which differs slightly from the General from PDE interface in the Model builder It is straightforward to convert a Flux Source boundary condition from this interface to an equivalent representation using only the f coefficient f 8 qu where g and q are the coefficients in the Flux Source boundary condition and u is the dependent variable name DEPENDENT VARIABLE In the Variable name edit field write the name of the dependent variable you enter the general form equation for The variable name can also be a variable that you have defined as a shape function SELECTION The options in the Selection list and Output entities list define the selection where this variable definition is valid See Specifying Selections for more information about using these lists PREFERENCES Clear the U
44. Equations sits You can use any device variable device input or device constant in these equations If you wish to use non device variables add a scope specifier to the variable Assume for example that you want to use the variable A declared by a variable declaration in a device equation In an ordinary expression you just type A but in a device equation the parser assumes that this is a device variable named A Instead you type phys A to specify that this is a variable outside the device context Device Inputs Declares the inputs of a device model Fill the table in this section with the Device Inputs P that the device model supports Each device input also needs a default value These inputs can be used in the equations of the device model A device instantiating a device model can modify the default values through the Input Modifier As an alternative to specify the inputs in this node you can add them directly in the Device inputs section of a device model Device Constants Fill the table with the constants you need for a device model You can use these Device Constants a in the equations of the same device model or any device model that inherits from it Enter the name of the constant in the right column and the constant expression in the left The expression must be a constant with respect to device variables but they can depend on ordinary variables declared outside the device context CREATING DEVIC
45. ING AN ADDITIONAL VARIABLE Add the probability density function as a variable that is available in the model and for plotting when the Show in plot menu check box is selected in the Preferences section which is the default setting or evaluating Right click the Physics Interface node and select Variable Variable Declaration a 2 In the Variable Declaration settings window locate the Declaration section EXAMPLES OF CUSTOM PHYSICS INTERFACES 3 Type probdens in the Variable name edit field type Probability density function in the Description edit field and type mid psi mid 2 in the Symbol LaTeX encoded edit field 4 Select Dimensionless 1 from the Physical quantity list 5 Leave the settings in the Preferences section at their default values The Show in plot menu check box must be selected for this variable to appear as a predefined expression in plots 6 Right click the Variable Declaration node and select Variables Variable Definition a 7 In the Variable Definition settings window locate the Definition section 8 Type abs psi 2 in the Expression edit field Notice that the variable probdens now appears in the Variable Declarations list in the Physics Interface settings window DEFINING DEFAULT PLOTS AND DEFAULT PLOT QUANTITIES Define a default 2D plot group for plotting the probability density function and make the probability density function the default scalar quantity for user defined plots
46. K Leave Active in the Allowed domain types list THERMOELECTRIC EFFECT IMPLEMENTATION 153 154 CHAPTER 4 7 Leave the Category for overwriting selections at the default setting Exclusive 8 From the Material type list select Solid 9 Leave the rest of the settings in the Feature settings window at their default values 10 Right click the Feature HeatTransferModel node and select Variables gt Dependent Variable Definition P In the settings window locate the Definition section II Select Temperature K from the Physical quantity list 12 Leave the other settings at their default values I3 Right click the Feature HeatTransferModel node and select Inputs gt User Input Pj In the settings window locate the Declaration section I4 Type k in the Input name edit field and Thermal conductivity in the Description edit field Type k in the Symbol LaTeX encoded edit field Select Thermal conductivity W m K from the Physical quantity list I5 Keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Type 1 6 typical value for Bismuth telluride in the Default value edit field l6 Leave all other default values I7 Right click the User Input node and select Variable Definition a This user input then becomes available as a variable tee k in for example the predefined expre
47. Link list External resources Lets you choose among the components listed in an imported builder file under the External Resources branch You choose the file from the Imported file list The Link list contains all components found in the Building Blocks Component branch of the selected file When the source component has parameters declared these show up in the Component parameters table The value in the Expression column changes the parameter value for this particular instance of the link Other links to the same source component can use a different expression If the source component uses a loop parameter the Loop parameter table appears Enter the name of the dependent variable in the Expression column Usage Condition The Usage Condition 7 node puts a condition that enables or disables its children You can use the condition in a variety of contexts for example for variable definitions under a feature or for solver defaults What kind of conditions you can use differ among contexts because some conditions cannot be evaluated in all contexts The section description below covers all possible conditions although some might not be visible depending on the context The settings window for the Usage Condition node contains one section USAGE CONDITION For usage conditions under features or properties you choose the Explicit condition in the Condition list to get access to the settings described below With the And con
48. Normal The option Control is used for optimization and sensitivity problems whereas the Discrete and Quadrature options are used for solver events see Event Dependent Variable Declaration A Dependent Variable Declaration node uw declares a dependent variable used by the interface This node does not make the interface add any shape functions for this variable it just declares that a dependent variable exists All dependent variables in a physics interface must have an unique identifier or reference tag within an interface In most cases you only solve for one type of physical quantity per interface so the physical quantity works fine as a reference tag If you need two or more dependent variables for the same physical quantity it is necessary to append a unique tag to the reference tag To add this node right click Physics Interface or Multiphysics Interface and select Dependent Variable Declaration from the Variables list You must use this reference tag when defining the actual shape functions for the variable which you do under a feature or a property see Dependent Variable Definition You can also use the same shapes as a dependent variable for constraints and then you need the reference tag to point to the correct variable The reason for using an reference tag instead of a variable name is that the dependent variable name can be changed in the Model Builder In the Physics Builder you can only declare a default name
49. S 5l w Untitled mphdev F External Resources d Building Blocks Components f Componenti reo Constraint 1 Pj UserInput1 Pi Material Property 2 a Variable Definition 1 2 Activation Condition 1 User Input Group 1 2 Activation Condition 1 lt Additional Requirement 1 Pi Material List 1 2 Activation Condition 1 Pj Feature Input 1 a Variable Definition 1 lt Activation Condition 1 a Selection Component 1 Properties G Features Periodic Feature1 g Pair Feature1 V Physics Interface 1 v Multiphysics Interface 2 P Physics Areas I Material Groups Migration Figure 3 1 A subnode of the Activation Condition node for additional requirements 52 CHAPTER 3 PHYSICS BUILDER TOOLS Creating Variables In this section About Creating Variables Variable Declaration Variable Definition Dependent Variable Declaration Dependent Variable Definition Initial Value Degree of Freedom Initialization Component Settings Specifying Selections Frame Shape About Creating Variables A variable is essentially defined by an expression of other variables dependent variables user input parameters or entered values You can use variables for many important purposes including the following examples To add a quantity for plotting and results evaluation To simplify the writing and readability of expressions To make evaluation of long expressions more efficient espec
50. SULTS AND VISUALIZATION By default COMSOL Multiphysics shows a surface plot of the probability density function V for the first eigenmode In the settings window for the 2D Plot Group I you can select which eigenmode to plot by selecting the corresponding eigenvalue from the Eigenvalue list You can also verify that the eigenvalues correspond to the first energy eigenvalues listed in Results 186 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES In the settings window for the Surface plot you can click the Replace Expression button and select Schrodinger Equation Wave function to plot the variable psi which is the complex valued wave function for the electron position EXAMPLE MODEL HYDROGEN ATOM 187 188 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Index A allowed values for inputs 44 announcing variables 55 B backward compatibility 130 Bohr radius 183 Boolean inputs 44 builder archive compiling 127 Building Blocks 88 built in physics interfaces 24 C cards 118 cards for GUI layout 118 code editor 89 compiling builder archive 127 compiling builder files 127 component links 83 component settings 62 components 88 creating 82 components for GUI design 115 conditions adding 84 constraints 72 contained features 39 contravariant 13 contributing boundary condition 150 contributing features 33 covariant 113 cross product 106 D del operator 148 documentation finding 12 dot produc
51. THE PHYSICS INTERFACE At any time during the implementation ofa physics interface using the Physics Builder you can launch an updated preview of the physics interface so that you can add feature nodes and check that the contents and behavior ofthe associated settings windows and other functionality is as expected To do so select the main node for the physics interface implementation for example Physics Interface 1 and then click the Show Preview button 53 on the settings window toolbar or press F8 An instance of the physics interface then appears at the bottom of the Physics Builder tree When you are finished update COMSOL Multiphysics to check that the new physics interface appears in the Model Wizard and that the functionality and settings appear as expected From the View menu choose Physics Builder Area 2 Under Builder Files right click the Development Files node and select Add Builder File Browse to locate ThermoelectricEffect mphdev select it and click Open 3 Click the New Model button on the main toolbar 4 Select any space dimension In the Model Wizard s Add Physics page select Heat Transfer gt Thermoelectric Devices Thermoelectric Effect tee 164 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES 9 Click Next Om the Study Type page verify that Stationary is the only available study type under Preset Studies Select it and click Finish s In the Model Builder verify tha
52. Variable Definition P In the settings window locate the Definition section 9 In the Expression edit field type sigma VV S VT 10 Leave all other settings at their default values Il Right click the Feature 2 ThermoelectricModel node and select Variables gt Variable Declaration P In the settings window locate the Declaration section 12 Type P in the Variable name edit field and Peltier coefficient in the Description edit field Type P in the Symbol LaTeX encoded As Size select Scalar Select Electric Potential V from the Physical quantity list I3 Right click the Feature 2 ThermoelectricModel node and select Variables Variable Definition P In the settings window locate the Definition section 14 In the Expression edit field type S T I5 Leave all other settings at their default values l6 Right click the Feature 2 ThermoelectricModel node and select Variables Variable Declaration P In the settings window locate the Declaration section I7 Type E in the Variable name edit field and Electric field in the Description edit field Type E in the Symbol LaTeX encoded As Size select Vector 3x1 Select Electric field V m from the Physical quantity list I8 Right click the Feature 2 ThermoelectricModel node and select Variables Variable Definition P In the settings window locate the Definition section I9 In the Expression edit field type VV 20 Leave all other setting
53. YOUT 12l The table columns get their headers from each user input if the Table headers list has the option Use user input descriptions Choose Specify to enter them manually in the table that pops up below the list The last table controls the settings for each column where you specify the column settings in the corresponding row The table below summarizes the available options OPTION DESCRIPTION Widths The initial width of the column Editable Selected means that the user can edit the column Variable The column must represent unique and valid variable names Expression The values must be an expression without syntax errors Synchronized You get fields below the table for easier typing S uu User Input Group See Also 122 CHAPTER 3 PHYSICS BUILDER TOOLS Creating Elements You can create low level elements that are not supported by any other standard node A variable definition is actually an element but it is much easier to use the Variable Definition node than creating the low level element from scratch Using these elements requires in depth knowledge about the element syntax and is considered as very advanced usage There is also limited documentation on the low level element syntax In this section Element GeomDim e Src e Array Record String Elinv Elpric Event Degree of Freedom Re Initialization Element Creates a new element of the type entered in the Element typ
54. a gets in the tree of physics areas This completes the definition of this Schrodinger Equation interface Save the file that contains the physics interface SchrodingerEquation mphdev 3 Locate the Physics Area section and select the Mathematics node Beneath the tree of physics areas click the Set As Parent button f This moves the new physics area to the Mathematics node 4 Select the Physics Interface node 5 Locate the Physics Area section expand it and select the Mathematics gt Quantum mechanics node Beneath the tree of physics areas click the Set As Parent button d This places the Schrodinger Equation interface under the Quantum mechanics physics area TESTING THE PHYSICS INTERFACE At any time during the implementation ofa physics interface using the Physics Builder you can launch an updated preview of the interface so that you can add feature nodes and check that the contents and behavior of the associated settings windows and other functionality is as expected To do so select the main node for the physics interface implementation for example Physics Interface 1 and then click the Show Preview button 5 on the settings window toolbar or press F8 An instance of the physics interface then appears at the bottom of the Physics Builder tree When you are finished update COMSOL Multiphysics to check that the Schrodinger Equation interface appears in the Model Wizard and that the functionality and settings appe
55. a link node very similar to the Feature Link and Property Link nodes The difference is that you do not choose an item from the Building Blocks branch but among the available physics interfaces The settings window has the following sections PHYSICS BUILDER TOOLS SOURCE INTERFACE In the Links from list choose where to look for a certain interface Options are Local interfaces Choose from the interfaces defined in the same file Choose the interface from the Link list Built in Choose from COMSOL s built in interfaces that are available to the Physics Builder Select the main resource from the Package list For each resource choose an interface from the Link list Only the currently published interfaces are available External resources Choose from the interfaces found in an imported builder file under the External Resources branch Choose the file from the Imported file list The Link list contains all interfaces found in the selected file INTERFACE FEATURES In the Add default features from interface list choose Use default features to add the same default features as the contained interface If Customized is selected choose the default features manually using the buttons under the list The list can be empty if you do not want to use any default features from this interface In the Remove features list add features from the contained interface that you do not want in the multiphysics interface Make sure th
56. about GUI options a Materials in the COMSOL Multiphysics Reference Guide CHAPTER 3 Feature Input The Feature Input node P is a special case of a User Input that also supports linking with any announced variable in the Model Builder A feature input is matched against an announced variable by matching against a physical quantity that you have to set for both items See Variable Declaration for information about how to set the physical quantity and the announce preference for variables Similar to the Material Property the feature input is a collection of two GUI components one list with the matching variables plus a User defined option and one field for the user defined value DECLARATION The declaration of a feature input is similar to that of a material property where you specify the name description symbol physical quantity and dimension see Material Property for further details An announced quantity has a certain dimension but it is possible to use a smaller dimension for a feature input in a feature You set this dimension with the Dimension list which can only contain Scalar and Custom for a scalar feature input OPTIONS In addition to the announced variables and User defined you can add extra items to the list in the feature instance by adding them to the Extra list items table A feature input supports several levels of matching that you choose from the Feature input match type list You can find a
57. ace a GUI component sequentially for each component of a vector valued user input The user input can either be a single array vector or an double array vector with a scalar or boolean inner type A typical example is if you want to activate each vector component value with a check box Then you create one double array user input with the outer dimension set to vector and the inner dimension set to Boolean and one single array user input as a vector Put both these DESIGNING THE GUI LAYOUT I19 120 CHAPTER 3 user inputs as member to a group using this layout and you get a layout like the screen shot below Description Boundary Selection Selection All boundarie 1 not applicable O0 4 O Un amp UJ F9 gt Override and Contribution v Section Check box Vector 0 Check box Vector 0 Check box Vector 0 Figure 3 5 A screen shot of a window created with the layout option Create a widget for each vector component RADIO BUTTONS FROM FIRST USER INPUT OTHERS INTERLEAVED Use this option when you want two or more radio buttons option buttons that control the visibility of other user inputs or groups The first user input must have a set of valid values each one representing one radio button The number of group members except the first one has to be equal to the number of allowed values in the first user input Similar to the previous GUI layout you get the GUI components of a group member a
58. ace dimensions list to restrict the space dimensions by intersecting the allowed space dimensions from the contained interfaces With the Custom dimensions and interfaces option you can add extra restrictions to the space dimensions From the Allowed study types list choose Intersection of interface types or Union of interface types to control how to combine the study type restrictions from the contained interfaces Select Customized to set the study types manually SETTINGS Choose the Default frame Material Spatial Geometry frame or Mesh These have the same meaning as for the Physics Interface Settings node The top geometric entity level for the multiphysics interface is the maximum level among the contained interfaces GUI OPTIONS Identical to the GUI Options section of the Physics Interface Settings node OVERRIDE RULE Identical to the Override Rule section of the Physics Interface Settings node DEFAULT FEATURES Similar to the Default Features section of the Physics Interface Settings node this section only lists the features flagged as default features for the multiphysics interface In this list you do not see any default features added by the Contained Interface node only the default features added directly under the multiphysics interface VARIABLE DECLARATIONS Identical to the Variable Declarations section of the Physics Interface Settings node Contained Interface The Contained Interface y is actually
59. al quantity so you have to enter an explicit unit in the SI unit field With the None option it is recommended to use the option Use physical quantity tag in the Dependent variable reference list The Default variable name field declares the default name for the dependent variable and the Description field provides a descriptive text for the variable shown in analysis and variable listings It is also possible to declare a symbol that can be used in equation displays and other tools Enter a LaTeX encoded string in the Symbol LaTeX encoded field to define a symbol mu for example to display the Greek letter u The Dimension list contains the choices Scalar Vector 3x1 Matrix 3x3 and Custom If you choose Custom you can specify a nonstandard dimension for example 3x3x3 if you need a tensor of rank 3 with indices of dimension 3 Do not use tensors of rank higher than 4 due to the rapid increase in memory usage PREFERENCES In this section you can select or clear the options Show in plot menu and Announce variable to feature inputs The Variable Declaration also uses these options so you can find a more detailed description under the Preferences section for that item ADVANCED This section contains advanced options that you do not have to change in most cases In the Base vector system list you can override the base vector system specified by the parent for example a feature or property by choosing something other
60. an old version unusable unless you handle the migration properly The settings window has the following sections CHANGE TYPE In the Old type label you see the old type and you can adjust the new type in the New type field The automatic logging of changes should prepare new Change Type nodes with the a correct new type COMPATIBILITY This section contains two check boxes One for activating migration or backward compatibility when opening COMSOL Multiphysics files and the other for activating compatibility for the model object API The default is to use both types of compatibility but you can clear any of the check boxes to deactivate the particular compatibility Rename Inputs The following nodes are used to rename the associated node User Input Material Parameter PHYSICS BUILDER TOOLS Feature Input Material List You can rename a user input which makes a file saved in an old version unaware of the fact that the old user input value is the value ofthe new input Nothing actually breaks but the input gets its default value so you should handle migration The situation can be worse for API migration because a Model Java file cannot execute if you try to access the old input The settings window has the following sections CHANGE NAME In the Old name label you see the old name and you can adjust the new name in the New name field The automatic logging of changes should prepare new Rename User Inpu
61. ar as expected From the View menu choose Physics Builder Manager 2 Under Builder Files right click the Development Files node Z7 and select Add Builder File Browse to locate SchrodingerEquation mphdev select it and click Open 3 Click the New button on the main toolbar 4 Select any space dimension In the Model Wizard s Add Physics page select Mathematics Quantum Mechanics gt Schrodinger Equation scheq 5 Click Next 6 Om the Study Type page verify that Eigenvalue is the only available study type under Preset Studies Select it and click Finish s 180 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES 7 Inthe Model Builder verify that the default nodes appear as expected and that their settings windows contain the user inputs that you specified Also right click the Schrodinger Equation node to add the Wave Function Value boundary condition which is not available by default 8 Proceed by building an example model see the Hydrogen Atom model below to verify that the Schrodinger Equation interface solves the correct equation using the correct boundary conditions and that you can plot the probability density function as a predefined expression 9 Correct any errors or problems that you find and save the physics interface again When you have successfully created a first instance of a physics interface you can consider improvements or additions for future development Typically you can save a
62. ard can contain several GUI components and other cards depending on the type of member it corresponds to In this way you can create an PHYSICS BUILDER TOOLS advanced nested dynamic GUI See below for a schematic drawing of this type of layout Section GUI component s from member 3 Figure 3 4 A schematic of the layout of the option Group members placed in a stack GROUP MEMBERS DEFINE A SECTION The simplest and one of the most important GUI layouts is the section layout You use it when you want specify what members that belong to a certain section You specify the title of the section in the Description field If you do not specify a section there is a default section that may be good enough for very simple layouts There are several situations when the default section is never generated When you want more than one section you must specify all sections When you have at least one Constraint node in your feature The constraint usually adds a special section for weak constraints and constraint type selection so you must specify all other sections as a section group As rule of thumb always add a section if you do not see the user inputs you expect EI The section that constraint nodes usually adds is not always shown You must show advanced physics options to see it Note CREATE A WIDGET FOR EACH VECTOR COMPONENT You can use this layout if you wish to pl
63. ariable When you make a connection between two or more devices the connection sets all non flow variables equal For the flow variables on the other hand the connection sets the sum of all flow variables equal to zero The settings view of the port model contains one section In the Type edit field you enter the port type that a port instance refers to It is also possible to let a port model inherit from another port model To do so enter the type of that port model in the Inherited type cdit field There are various ways to add a Port Model node Go to Building Blocks gt Features gt and add any of these nodes Device Model Feature Feature or Periodic Feature Then right click these nodes to add a Port Model from the Devices list Or go to Building PHYSICS BUILDER TOOLS Blocks gt Components gt and add a Component node Then right click the node to add a Port Model from the Devices list Device Variables Fill the table with the variables you need for a Device Model You can use these Device Variables a in the equations of the same device model or any device model that inherits from it By specifying an expression for a variable you directly define an equation for the variable This is equivalent to define an equation with the right hand side set to the variable name and the expression as the left hand side Device Equations Fill the table with right hand sides and left hand sides of an arbitrary number of Device
64. as for future extensions You can add a Comment node to each individual node in a physics interface including the components that you use to create a physics interface feature such as User Input and Variable Declaration nodes Documentation nodes for creating end user documentation including context help for the physics interface and its features In the main Documentation nodes you can add the topic description which is the concise description that the Help window displays when you click a node For the in depth documentation you can various sections that add plain text equations images lists tables references and other documentation items to build a full documentation of the functionality use and theory behind the physics interface and its features The following sections provide details about how to add documentation to physics interfaces in the Physics Builder Physics Interface Documentation By default the preferences are set up so that Developer Comment and User Documentation nodes appear under the nodes in the interface that needs comments and documentation You can change this in the Preferences dialog box under Comments and documentation in the Builder Tools section For the user documentation a default User Documentation text node is added automatically under the main User Documentation node but you can add any other documentation components such as equations images notes and tables The main User D
65. at you do not remove a feature that you use as a default feature Physics Interface Component Link Use a Physics Interface Component Link E to include all items defined within a component under the Building Blocks Components branch as if they were part of the physics interface containing the link see Creating Components The settings window of the physics interface component link contains the following additional section SOURCE COMPONENT In the Links from list you choose where to look for a certain component Possible options are Building blocks Lets you choose among the components listed under the Components branch in the Building Blocks branch You choose the component from the Link list Built in Lets you choose among COMSOL s built in features that are available to the Physics Builder In the Package list you choose the main resource to use features CREATING A PHYSICS INTERFACE 29 from For each resource you have a list of features in the Link list to choose from You can only choose among the currently published features External resources Lets you choose among the physics interface components listed in an imported builder file under the External Resources branch You choose the file from the Imported file list The Link list contains all components found in the Building Blocks Component branch of the selected file 30 CHAPTER 3 PHYSICS BUILDER TOOLS Creating Features A Feature
66. ated by 0D 1D 1D axial symmetry 4 2D ff 2D axial symmetry i and 3D icons These icons are also used in the documentation to clearly list INTRODUCTION the differences to an interface feature node or theory section which are based on space dimension The following tables are examples of these space dimension icons 3D models often require more computer power memory and time to a IB NDA LY solve The extra time spent on simplifying a model is time well spent when 3D solving it Remember that modeling in 2D usually represents some 3D geometry under the assumption that nothing changes in the third dimension 2D ABOUT THE PHYSICS BUILDER 17 18 Overview of the User s Guide This Physics Builder User s Guide contains information that helps you to get started with creating custom interfaces using the Physics Builder in the COMSOL Multiphysics product The information in this guide is specific to this functionality Instructions on how to use COMSOL in general are included with the COMSOL Multiphysics User s Guide As detailed in the section Where Do I Access the Documentation and Model Library this information is also searchable from the COMSOL Tip Multiphysics software Help menu CHAPTER 2 TABLE OF CONTENTS AND INDEX To help you navigate through this guide see the Contents and Index TOOLS The Physics Builder Tools chapter provides an overview and a description of eac
67. ation from the Elements menu PHYSICS BUILDER TOOLS The Physics Builder Manager With the Physics Builder Manager window you manage testing and compilation of your Physics Builder files Testing is when you temporarily include one or more development files mphdev in your COMSOL session to fully test their physics interfaces in a real modeling environment When you are satisfied with a collection of builder files you can compile them into a builder archive To open this window from the main menu select View gt Physics Builder Manager THE DEVELOPMENT FILES The files listed are included in your COMSOL session This means that your interfaces pops up in the Model Wizard so you can add them to your model and work with them like any other physics interface You can also save model files mph that use your new interface To add a development file you right click the Development Files node Z7 and choose Add Builder File If you right click on any added development file you can choose to remove it from the list or to open it There is also an option to compact the archive The compact operation removes all unnecessary data in the file to save space and simplify textual comparisons between different versions of a file Whenever you make changes to a builder file listed as a development files you must click the Update Builder Files toolbar button to re read all files into the current session If you save a model
68. ature 3 Electricinsulation uxw Dependent Variable 1 H Instance Global Definitions 4 V Model mod1 4 she Magnetic Field Formulation mff Faraday s Law 5 Perfect Magnetic Conductor Initial Values 5 Perfect Magnetic Conductor 5 Electric Insulation Figure 2 1 The definition of a new physics interface Magnetic Field Formulation in the Physics Builder left and the result in the Model Builder right The Physics Builder window contains a tree that represents a physics interface design project Such a project can define anything from a single physics interface to an entire product with a collection of physics interfaces The following chapters describe the tools that you use in the Physics Builder and provide detailed examples of how to create custom physics interfaces Where Do I Access the Documentation and Model Library A number of Internet resources provide more information about COMSOL Multiphysics including licensing and technical information The electronic ABOUT THE PHYSICS BUILDER 12 documentation Dynamic Help and the Model Library are all accessed through the COMSOL Desktop Ifyou are reading the documentation as a PDF file on your computer the blue links do not work to open a model or content referenced in a o different user s guide However if you are using the online help in Important COMSOL Multiphysics these lin
69. better overview if you have a feature containing a lot of variables You can for example collect all user inputs and groups used in a section and simply use a Component Link in the feature or property that need this section A component can contain the same items that Feature and Property can with a few exceptions Here are some examples Dependent Variable Definition Variable Declaration Variable Definition User Input User Input Group Material Property Feature Input Weak Form Equation Constraint 82 CHAPTER 3 PHYSICS BUILDER TOOLS Component In the Component node 4 you can collect nodes that define something specific that you need in several places or to group nodes together to avoid long lists of nodes under a feature or property The settings window contains one section for specifying parameters All other sections contain only read only information These sections are identical to these sections for features see Information Sections PARAMETERS Specify parameters by filling in the columns Name Description and Default expression A parameter expression can be changed for each component link that uses this component Select the Loop parameter check box to activate looping over the elements of a dependent variable Enter the Name Description and Default expression in the corresponding columns of the table Physics Interface Component In the Physics Interface Component node 4
70. c Model select left click right click the copper electrodes domains 1 and 3 For the Thermal conductivity enter 350 For the Electric conductivity enter 5 9e8 For the Seebeck coefficient enter 6 5e 6 OC uU A WwW The default Thermoelectric Model already has the correct values for Bismuth telluride and is now assigned to domain 2 7 Right click the Thermoelectric Effect node and select Electric Potential 8 Select boundary 3 bottom surface and keep the default 0 V 9 Right click the Thermoelectric Effect node and select Temperature I0 Select boundary 3 again and set the temperature to 273 15 K 0 degrees C II Right click the Thermoelectric Effect node and select Electric Potential 12 Select boundary 10 top surface and set the electric potential to 0 05 V EXAMPLES OF CUSTOM PHYSICS INTERFACES MESH GENERATION AND COMPUTING THE SOLUTION A mesh with default parameters is good enough for this very simple model The default mesh is automatically created if nothing else is specified when solving 2 Right click the Study node and select Compute RESULTS AND VISUALIZATION The default plot is for the temperature T Change the unit to degC to verify the 61 degree C temperature drop Also try visualizing some of the other predefined expressions such as the Electric potential V and Peltier coefficient P see the following figure 4 3 u s wwma d EXAMPLE MODEL THERMOELECTRIC LEG 169 The Schrodinge
71. cal quantity from the Link list ADDING PHYSICAL QUANTITIES 95 96 Creating Override Rules CHAPTER 3 When creating a model in the Model builder you add several feature instances as children to a physics interface If these features supports selections they obey certain rules about how a feature of one types overrides ore gets overridden by another feature This is not to be confused with features being applicable to a certain entity for i i d i example some features only apply on interior boundaries The overriding of selections is based on grouping features into categories and the rules apply between categories The two standard built in categories are exclusive and contributing Exclusive means that a feature in this category override all other categories Contributing on the other hand does not override any other feature with one exception The exception is for entity levels below the top entity level where all categories overrides all default features You add an override rule by right click the Definitions Library node add an Override Rule node You can access all added rules from any feature in the same file or in any other file that has the former file added as an Import node under the External Resources branch Override Rule The Override Rule node 4f settings window has a table that displays all categories as a matrix with the type identifiers as rows and what category they overwrite as columns A
72. ce dimensions except 0D In the Allowed study types list select the default study types Stationary and Transient and click the Delete button 59 underneath the list Then click the Add button ep and select Eigenvalue from the Allowed study types list then click OK 7 In the Settings section verify that Domain is selected in the Top geometric entity level list This means that the equations in the physics interface apply to the domains in the geometry which is the case for most physics interfaces Leave the setting in the Default frame list at the default value Material 8 It is good practice to save the physics interface after completing some steps From the File menu choose Save and create a physics interface file SchrodingerEquation mphdev in the default location Click Save This concludes the initial steps that set up the fundamentals for the physics interface The next steps adds equations boundary conditions and variables ADDING FEATURES First declare the dependent variable Y Right click the Physics Interface node and select Variables Dependent Variable Declaration uw 2 In the Dependent Variable Declaration settings window locate the Declaration section 3 Leave the setting in the Dependent variable ID list as Use physical quantity Type psi in the Default variable name edit field Type Wave function in the Description edit field Type psi the LaTeX syntax for the Greek letter y in the Symbol LaTeX en
73. ces Lets you choose among the properties listed in an imported builder file under the External Resources branch You choose the file from the Imported file list The Link list contains all properties found in the Building Blocks gt Properties branch of the selected file 42 CHAPTER 3 PHYSICS BUILDER TOOLS Creating User Inputs In this section Introduction to Creating User Inputs User Input User Input Group Material Property Feature Input Material List Activation Condition Additional Requirement Introduction to Creating User Inputs A User Input P is a parameter that shows up in the settings window of the feature instance in the Model Builder A user input always represent a data storage in a COMSOL Multiphysics model MPH file built with the Model Builder You can choose to hide a user input from the settings window and then the user input only represents a data storage One important difference between user inputs and variables is that all variables created by the Physics Builder are not saved in the MPH file but they can be recreated from the stored data essentially user inputs in an MPH file together with the Physics Builder file extension MPHDEV The value of a variable on the other hand can be read when solving or from result features in the Model Builder This is not possible with user inputs If you want to access a value of a user input you must first declare a variable and defi
74. choose a file from the system With the Import button you can re import the file This is necessary if you have changed the selected file from another COMSOL session PHYSICS BUILDER TOOLS Creating Physics Areas In the Model Builder you create a model with the Model Wizard After choosing geometry you select physics interfaces from a tree view This tree view contains categories representing physics areas at the top level and possible subcategories in each Physics Area When you create your own physics interface you can always put it in an existing category see Physics Interface Settings for more information how you do this Physics Area A Physics Area 3 contains a group of physics interfaces for more intuitive and quick access The settings window of the physics area node contains the following sections PHYSICS AREA This section contains a tree view of all physics areas and subcategories available from built in resources other areas defined in the current builder file and areas defined in any imported file under the External Resources branch To put your new physics area under a specific category in the tree you first select that item Then you click the Set as parent button ep below the tree As an alternative you can also right click the selected item and choose Set as parent from the submenu You find the currently selected category under the Parent area divider If you do not specify a parent area the area
75. cking any node in the documentation Selecting Write from any documentation node s context menu generates the entire document FORMAT You can select to create a document in one of the following formats which you choose from the Output format list HTML the default format for creating the document as an HTML file for display in a web browser Help plug in for creating the document as a plug in of Eclipse Help format that can become an integral part of the COMSOL documentation and help system Settings for Documentation in HTML Format When generating documentation you need to specify its name and title where to store the file Enter the output directory for the HTML files in the HTML output directory field or click Browse to open the Specify HTML Output Directory dialog box and browse to the desired location Also specify the document s name a title in the Document name and Document title fields respectively Settings for Documentation as Help Plug in When creating a help plug in you need to specify the following plug in location details and properties Enter the output directory for the help plug in in the Plug in output directory ficld or click Browse to open the Specify Plug in Output Directory dialog box and browse to the desired location Enter a Plug in prefix to use a common name space for your help plug ins You can specify a standard plug in prefix for your organization on the Builder Tools page in
76. coded edit field Leave the Size list s default setting Scalar because is a scalar field Select Dimensionless 1 from the Physical quantity list 4 In the Preferences section leave the default settings that makes the dependent variable available for plotting Plot and for use as an input in other physics interfaces Announce variable to feature inputs You also need to add a Dependent Variable node in the Schr dinger equation domain feature to create the shape function element type for the dependent variable in the domain see Step 24 below Next add the Schr dinger equation in a domain feature Right click the Physics Interface node and select Feature C 2 In the Feature settings window locate the Identifiers section EXAMPLES OF CUSTOM PHYSICS INTERFACES 3 Type SchrodingerEqu in the Type edit field Type schequ in the Default identifier and tag edit field Type Schrodinger equation model in the Description edit field 4 In the Restrictions section leave the default setting Same as parent for the Allowed space dimensions and Allow study types lists By selecting Customized you can restrict the feature to a subset of the allowed space dimensions or study types for the physics interface 5 In the Settings section select the default One level below top level Boundary condition geometry level in the Supported geometric entity levels relative to top geometric entity level list and click the Delete button me u
77. coded methods in Java to perform tasks that you cannot accomplish with the nodes in the Physics Builder trec Use of the code editor requires knowledge of the Java programming language and the COMSOL Java API Note that adding Java code usually makes it much harder to find and solve problems with your physics interface so only use it when really necessary The following Java interfaces are supported by the Code Editor node VariableDefinitionsProvider Defines expressions and selections for a set of declared variables UserInputProvider Defines dynamic allowed values and default values for lists A Code Editor node works exactly like a Component node so you include it through a Component Link node Contact COMSOL support to learn more about the supported interfaces BUILDING BLOCKs 89 90 CHAPTER 3 External Resources To avoid reimplementing features properties or components you can use items stored in a different builder file All items that you implement under the Building Blocks branch in a builder file can be used by any other builder file that imports it Under External Resources j you can add Import nodes T for importing other builder files Import Use the Import node T to import other builder files The settings window contains the following section IMPORT FILE In the File field you enter the path to the builder file you want to import As an alternative you can also click Browse and
78. condition can depend on user inputs in the parent feature parent property or some property If the user input is under a feature or property which may contain other user inputs you can directly refer to any of those user inputs by choosing PHYSICS BUILDER TOOLS By reference in the Specify user input list You then choose the user input from the User input list and finally add or enter the values that activates the user input in the Activating values list This list differs depending on the type of user input you refer to The other option in the Specify user input list is By name which means that you enter the name in the User input field The name is entered in the Input name field of the user input you want to refer to For the By name option you also have the list User input from where you can choose if the user input is under the parent feature This feature option or under a property in the physics interface Property option With the Property option you must also enter the type of the property that contains the user input in the Property field For boolean user inputs the values Selected and Not selected you enter as 0 and 1 As a final option you can select the Invert condition check box to invert the entire condition Additional Requirement An additional requirement to an activation condition is a requirement that has to be fulfilled otherwise the activation condition cannot be fulfilled CREATING USER INPUT
79. des settings windows e A Topic description which is the concise description of the node that appears in the context help in the Help window when you click the node You can use the Label font above and the characters and dashes below the text field to format parts of the text for the topic description The same references as for the Heading appears in the default text Developer Comments The Comments node contains developer comments about the implemented feature or other builder component These comments can include known capabilities and limitations ideas for further development and implementation detail that can be useful for maintaining and extending the functionality In the Text section you add this information You can use the character formatting tools above and below the text field to format parts of the text The reference that is ADDING COMMENTS AND DOCUMENTATION 135 136 CHAPTER 3 included by default ref entity doc entity gt isa general reference to the entity that the comment is about The Documentation Node The main Documentation node BA contains information about the formatting and defaults for a documentation Click the Preview Selected E or Preview All button to show a preview of the document in the Preview window Click the Write button _ in the toolbar for the Documentation settings window to create a document The Write option is also available by right cli
80. dition and Or condition choices you can define a usage condition that evaluates as a Boolean operation between other usage conditions You add those conditions to the Input condition list For usage conditions under Study Solver Defaults Result Defaults 9 and Mesh Suggestions 4 you always define an explicit condition Select the Restrict to space dimension check box to enable a condition on the geometry dimension used by the model in the Model Builder When selected you can add any of the following types 3D 2D ID Axial symmetry 2D Axial symmetry ID and 0D PHYSICS BUILDER TOOLS Select the Restrict to geometric entity levels check box to enable a condition on the geometric entity level of the context which can be the entity level of a feature The allowed levels are Global Domain Boundary Edge and Point For result defaults and mesh suggestions the check box is called Restrict to entity dimensions This essentially means the same thing but the allowed values are instead a subset of the dimensions 3D 2D ID and OD The plot and mesh settings are the same for Cartesian geometries and axial symmetry so these are left out When you select the Restrict to study types check box you enable a condition on the study type currently solved for This is applicable for usage conditions under features properties and study solver defaults A common example is when you want to define the result of a time derivative whic
81. e Rename Surface dialog box type Temperature in the New name edit field Click OK to confirm 7 Right click Results Defaults I 4 and select Plot Defaults 4 THERMOELECTRIC EFFECT IMPLEMENTATION 163 8 Right click the Plot Defaults node and select Default Scalar Plot In the Expression edit field type T In the Description edit field type Temperature This makes temperature the default for all scalar plots MAKING A THERMOELECTRIC DEVICES PHYSICS AREA To add the Thermoelectric Effect physics interface to a new physics area for Thermoelectric Devices under the Heat Transfer branch do the following steps Right click the Physics Areas node 9 and select Physics Area 13 2 In the Parent Area window for the Physics Area node select the Heat Transfer folder 3 In the Physics Area Settings section enter ThermoelectricDevices in the Name edit field Thermoelectric Devices in the Description edit field The default icon is physics png which is appropriate for this physics interface Otherwise click Browse to use another icon Enter 10 in the Weight edit field to make the Thermoelectric Devices area appear last in the list under Heat Transfer the higher the weight the lower position the physics area gets in the tree of physics interfaces This completes the definition of this Thermoelectric Effect physics interface Save the file that contains the physics interface as ThermoelectricEffect mphdev TESTING
82. e User Input node and select Variable Definition a This user input then becomes available as a variable tee S in for example the predefined expressions for results evaluation You can also refer to S directly in the weak equation I8 Leave all other settings at their default values ADDING VARIABLES Right click the Feature 2 ThermoelectricModel node and select Variables Variable Declaration P In the settings window locate the Declaration section 2 Type q in the Variable name edit field and Heat flux in the Description edit field Type q in the Symbol LaTeX encoded As Size sclect Vector 3x1 Select Inward heat flux Alm from the Physical quantity list 3 Right click the Feature 2 ThermoelectricModel node and select Variables gt Variable Definition P In the settings window locate the Definition section 4 In the Expression edit field type P J k VT THERMOELECTRIC EFFECT IMPLEMENTATION 157 5 Leave all other settings at their default values 6 Right click the Feature 2 ThermoelectricModel node and select Variables gt Variable Declaration P In the settings window locate the Declaration section 7 Type J in the Variable name edit field and Current density in the Description edit field Type J in the Symbol LaTeX encoded As Size select Vector 3x1 Select Current density A m from the Physical quantity list 8 Right click the Feature 2 ThermoelectricModel node and select Variables
83. e current builder file and areas defined in any imported file under the External Resources branch j See Creating Physics Areas to learn about adding physics areas To put a physics interface under a physics area in the tree select the relevant physics area node and then click the Set as parent button fs below the tree Or right click the physics node and choose Set as parent from the submenu You can find the currently selected category under the Parent area divider IDENTIFIERS In the Type field define a unique string to identify the physics interface The string should not conflict with other identifiers for the physics interfaces present in the Model Wizard The entry in the Default identifier and tag field is used to generate the scope of all variables that the physics interface adds in the Model Builder It also defines the prefix for the tag of all newly created physics interfaces in the Model Builder The tag of a physics interface is only important for references to a created interface in Model Java files The text written in the Description field is the text COMSOL Multiphysics displays for the physics interface in the Model Wizard CREATING A PHYSICS INTERFACE 26 CHAPTER 3 In the Model Wizard and for the physics instance in the Model Builder there is an icon displayed for the particular physics interface Using the Icon field you can Browse to an icon to display for the physics interface if the default is not appl
84. e field This node is a special type of Record node that represents the top level of an element To add this node go to Building Blocks Right click Components to add a Component node Then select Event from the Elements menu Geom Dim The GeomDim node 9 is a selection specification of the geomdim type See Specifying Selections for more information about specifying selections To add this node go to Building Blocks Right click Components to add both a Component and Element node Then select GeomDim CREATING ELEMENTS 123 124 CHAPTER 3 Src An SRC node 9 isa selection specification of the src type See Specifying Selections for more information about specifying selections To add this node go to Building Blocks gt Right click Components to add both a Component and Element node Then select SRC Array The Array node eff is a container for other nodes of the types Array String and Record If this node is a child to a Record node you specify the name of this record in the Name field To add this node go to Building Blocks Right click Components to add both a Component and Element node Then select Array Or add it as a child node to an Array Record or String node Record The Record node 9 is a container for other named nodes of the types Array String and Record All childs to this node have to specify a unique record name to identity the record If this node is a chi
85. e settings window of the variable you specify the initial value in the Default initial expression field The expression you enter here follow the rules outlined in Entering Names and Expressions but with an exception If you use a variable name here you must specify the scope it uses As an example assume that you want to use the interface variable init as initial condition then enter phys init in the expression field Otherwise the initial value expression just becomes init and at solution time this gets model scope Select the Set initial value on time derivatives check box to activate the initial values for the first time derivative In the Geometric entity level list you choose the entity level that the initial value is placed on This must match the entity level you put the dependent variable definition on PREFERENCES The options in this section are identical to the ones in the Preferences section of the Variable Definition Degree of Freedom Initialization A variable that has a shape function definition needs an initial value for nonlinear and transient simulations In the Degree of Freedom Initialization node iw you define the initial value for such variable definitions You can also use this to set the initial condition for dependent variables but it is recommended that you use the Initial Value node instead In situations where you do not want the Initial value feature in the Model Builder you can customize the initial va
86. each column Table Row sii Right click the Table node to add this node and then add the contents for each column in a row of a table Text Provides a Text area where text can be added including HTML tags for formatting and links For all Text List Item and Note nodes settings a set of tools above and beyond the text field provides a quick way to add formatting to the text The formatting tools above the text provide character formats for user interface labels emphasis code standard bold and italic equation components bold variables and constants subscript and superscript To convert a part of the text to any of these character formats highlight the text that you want to format and then click L for example to mark the text as a user interface label a sans serif boldface font using the HTML tags 1 and lt 1 gt before and after the text From the character tools below the text click the character that you want to insert for example click to insert an uppercase omega as VOmega in the text The character tools include lowercase and uppercase Greek letters and the en dash and em dash punctuation symbols For creating equations and text that includes mathematical symbols as part of the documentation COMSOL supports a subset of the LaTeX language Commands include Greek and other characters mathematical symbols and operators arrows text and font formats and environments for text and
87. ection I2 In the Expression edit field type qin test T For a theoretical explanation of this expression see the earlier theory section I3 Leave all other default values The Insulation Condition Right click the Physics Interface node and select Feature C3 2 In the Feature 6 settings window locate the Identifiers section 3 Enter Insulation in the Type edit field Enter in in the Default identifier and tag edit field Enter Insulation in the Description edit field 4 This time keep the Category for overwriting selections as Exclusive 5 In the Preferences section select the Add as default feature check box Keep the settings in the Default domain level and Default domain type lists to make this a default boundary condition on exterior boundaries only 6 Leave all other settings at their default values DEFINING DEFAULT PLOTS AND DEFAULT PLOT QUANTITIES Define a default 3D plot group for plotting the temperature and make the temperature the default scalar quantity for user defined plots Right click Physics Interface ThermoelectricEffect select Results Defaults 2 Right click Results Defaults 4 and select Plot Group 3D I 3 Right click the Plot Group 3D ap node and select Surface mp 4 In the Surface mp settings window type T in the Expression edit field Type K in the Unit edit field 5 Leave all other settings at their default values 6 Right click the Surface mp node and select Rename In th
88. ectrically insulating but thermally conductive first create a heat transfer equation 144 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES interface and then define the full thermoelectric equations a as a second step The weak form integrand for pure heat transfer is q test VT In this way you only need to solve for one degree of freedom T in the electrically insulating domains In addition to the domain weak form equations a number of different boundary conditions are implemented T T V V qo 0 Jg 0 do Gin The first condition sets a temperature T on a boundary The second condition sets a voltage Vo on a boundary The two conditions that set the heat flux and current density on the boundary to Zero are so called natural boundary conditions They are called natural because they arrive naturally as part of the weak form partial integration The natural boundary conditions represent thermal and electrical insulation This implementation in this example bundles these two conditions into one single insulation boundary condition As a matter of fact it is not even necessary to define this bundled boundary condition because that would anyway have been available any boundaries not explicitly set to a certain condition automatically obey the natural conditions However for better usability of the thermoelectric physics interface the natural boundary condition is available as one of the choices This wa
89. edefined parameters that must be in an outer sweep add these to the Outer Job Parameters node 3 Enter those parameters in the Parameter names column Eigenvalue Transform Use the Eigenvalue Transform node to define a transform between the internal eigenvalue computed by the eigenvalue solver and a more user friendly quantity The settings window has the following sections DECLARATION In the Study types list choose among the study types that uses the eigenvalue solver Enter a unique name and description for the transform in the Name and Description edit fields RELATION BETWEEN EIGENVALUES Enter the name of the variable name in the Eigenvalue name edit field This name is used in the following transform definitions In the Transform to lambda edit field enter the expression that computes the internal eigenvalue lambda when the transform s PHYSICS BUILDER TOOLS eigenvalue is known Enter the inverse transform in the Transform from lambda edit field Study Sequence A study sequence is a sequence of study steps that a user can choose in the last step of the Model Wizard Use the Study Sequence node to define such predefined study sequences Right click the node to add the study steps that are part of the sequence Note that it is only possible to add the study steps that the physics interface supports Ifyou add a sequence under a physics interface component all available study steps can be added to the
90. ee About Model Couplings and Coupling Operators in the COMSOL Multiphysics Reference Guide The main differences is how you specify the operator name and selections which is described in the Introduction to Operators and Functions of this chapter Function Nodes You can add a function to a feature property or component The function names follow the same rules as variables see Entering Names You usually have to use feature scope for any function defined by a feature otherwise you get a duplicate definition if you have more than one feature of that type Apart from the name syntax defining a function works in exactly the same way as in the Model Builder see Functions in the COMSOL Multiphysics Reference Guide CREATING OPERATORS AND FUNCTIONS 8l Creating Components In this section About Creating Components Component Physics Interface Component Selection Component Component Link Usage Condition Equation Display About Creating Components As an alternative to define variables user inputs and so forth directly under a feature or property it is possible to create a collection of such items These collections are called components and you find them under the Components branch under Building Blocks in the Physics Builder tree It is convenient to use components when you want to reuse user inputs for example in several different features Grouping variables into components can also give a
91. ee of freedom automatically sets a natural boundary condition for the other Results The results agree with that of Ref 1 and shows a 61 degree C cooling of the top part of the thermoelectric leg Reference 1 M Jaegle Multiphysics Simulation of Thermoelectric Systems Modeling of Peltier Cooling and Thermoelectric Generation in Proceedings of the COMSOL Conference 2008 Hannover ISBN 978 0 9766792 8 8 EXAMPLE MODEL THERMOELECTRIC LEG 167 168 CHAPTER 4 Modeling Instructions The following steps show how to build this model using the Thermoelectric Effect physics interface MODEL WIZARD Start COMSOL Multiphysics 2 In the Model Wizard click the 3D button on the Select Space Dimension page Then click the Next button 3 On the Add Physics page select Heat Transfer Thermoelectric Devices Thermoelectric Effect Click the Next button 4 On the Select Study Type page select Preset Studies gt Stationary Click the Finish button s GEOMETRY MODELING In the settings window of the Geometry node change the Length unit to mm 2 Add a block of width 1 mm depth 1 mm and height 6 mm 3 Still in the Block Settings page locate the Layers section and add two layers Layer 1 with Thickness 0 1 mm and Layer 2 with Thickness 5 8 mm PHYSICS SETTINGS Right click the Thermoelectric Effect node and select Thermoelectric Model 2 For this second Thermoelectri
92. ensity and temperature gradients These three effects are thermodynamically related by the Thomson relations P ST _ dS h TR where P is the Peltier coefficient SI unit V S is the Seebeck coefficient SI unit V K T is the temperature SI unit K and y is the Thomson coefficient SI unit V K These relations show that all three effects can be considered as one and the same effect This example primarily uses the Seebeck coefficient and also merely as an intermediate variable the Peltier coefficient The Thomson coefficient is not used The flux quantities of interest when simulating the thermoelectric effect are the heat flux q and the flux of electric current J q RVT PJ J oVV oSVT Some other quantities of relevance are 142 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES E vV Q J E where E is the electric field and Q is the Joule heating Conservation of heat energy and current gives oT PC V q Q Op Vis m J t where p is the density C is the heat capacity and p is the space charge density In this example consider the stationary case only V q Q V J 0 More explicitly the thermoelectric equations become V kVT P oVV oSVT oVV oSVT VV V oVV oSVT 0 It is pretty clear that the explicit form of the equations are cumbersome to work with and this example makes use of a series of intermediate variables to simplify entering them in the Physics Builder Equati
93. ent variable ID list as Use physical quantity Type V in the Default variable name edit field Type Electric Potential in the Description edit field Type V in the Symbol LaTeX encoded edit field Leave the Size list s default setting Scalar because V is a scalar field Select Electric Potential V from the Physical quantity list In the Preferences section leave the default settings ADDING THE HEAT TRANSFER MODEL Next add the Heat Transfer Model as a domain feature I 2 Right click the Physics Interface node and select Feature C3 In the Feature I settings window locate the Identifiers section Type HeatTransferModel in the Type edit field Type htm in the Default identifier and tag edit field Type Heat Transfer Model in the Description edit field In the Restrictions section leave the default setting Same as parent for the Allowed space dimensions and Allow study types lists By selecting Customized you can restrict the feature to a subset of the allowed space dimensions or study types for the physics interface In the Settings section select the default One level below top level Boundary condition geometry level in the Supported geometric entity level relative to top geometric entity level list and click the Delete button 9 underneath the list Then click the Add button f and select Same as top level Domain condition from the Supported domain levels relative to top domain level list then click O
94. equations and constraints declared by the feature If necessary it is possible to override this default by changing the setting in the Base vector system list under the Advanced section of any of these nodes Under the same Advanced section for variables you can also set the Base vector type to Covariant or Contravariant in a table where each row corresponds to a tensor index By default all tensor indices are contravariant and this setting is only important for non scalar spatial tensors in non orthonormal coordinate Note systems CHAPTER 3 THE INPUT BASE VECTOR SYSTEM This is the system used by all spatial length 3 vector valued and tensor valued user inputs The options in the Input base vector system list are the same as the Base vector system list see The Base Vector System When the settings differ between these two PHYSICS BUILDER TOOLS lists everything a user enters for a user input is automatically transformed to the system defined by the Base vector system list Transformation Between Coordinate Systems All spatial vectors and matrices can transform as tensors when an operation involves two tensors defined in different coordinate systems Consider the following example D n D n or in Einstein summation notation D n D n l where subscripts indicate covariant indices and superscripts indicate contravariant indices The type of index determines how a tensor transforms to a different coord
95. er input is a member of a user input group that can disappear Show no description Removes the label above the GUI component Show no symbol Removes the symbol to the left of the GUI component Add divider above the user input Places a horizontal line above the GUI component possibly with a descriptive text Show no coordinate labels For spatial vectors by default you get the coordinate labels in the left most column Selecting this option removes that column Vector components to display Controls what components of a spatial vector you want to display in non 3D geometries You can choose between All In plane and Out of plane Matrix components to display Same as above but for spatial matrices Matrix symmetry for square matrix For non spatial square matrices you can force a matrix symmetry with this option The choices are Diagonal Symmetric and Anisotropic and controls the cells that the user can edit PHYSICS BUILDER TOOLS DOUBLE ARRAY INPUTS Double array inputs are far more complex to design GUI components for and some combinations are not supported The table below summarizes the behavior for the supported double array inputs option Array type set to Double OUTER DIM INNER DIM ALLOWED VALUES GUI COMPONENT Vector 3x1 Scalar Any Behaves as a single array vector or Ixl Vector 3x1 Scalar From list Several combo boxes when the input is a or Ixl member to a special input group see User Input
96. esented by the following weak equation q test VT The weak formulation using the COMSOL tensor syntax becomes q test VT In this expression V is the de vector differential operator and represents the dot product scalar product The second equation is called the Thermoelectric Model and is represented by the following weak equation q test VT Qtest T J test VV The weak formulation using the COMSOL tensor syntax becomes q test VT Q test T J test VV where is ordinary multiplication between scalars A number of parameters is defined in order to efficiently use the COMSOL tensor syntax for defining the weak equations and also variables available for results and visualization The thermal conductivity k is a user input to both the Heat Transfer Model and the Thermoelectric Model The default value is set equal to 1 6 W m K which corresponds to the thermoelectric material Bismuth telluride The electric conductivity o is a second user input for the Thermoelectric Model The default value is set equal to 1 1e5 S m which also corresponds to the thermoelectric material Bismuth telluride The Seebeck coefficient S is a third and final user input for the Thermoelectric Model The default value is set equal to 200e 6 V K which once again corresponds to the thermoelectric material Bismuth telluride 148 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES To make the definition of the weak equa
97. f the periodic condition or pair Operation Performs an operation between several selection components defined under the Building Blocks branch 4 5 The supported operations are the same as for selections in the Model Builder see Selections in the COMSOL Multiphysics Reference Guide Component link The selection refers to a selection component under the Building Blocks branch that defines the selection see Selection Component For all options except Global you can also choose the output entity from the Output entities list This list has the following options Adjacent boundaries The variable selection contains the adjacent boundaries to the selection which typically is a domain selection If the selection is a boundary selection this option returns the boundaries adjacent to the selection Adjacent domains The variables selection contains the adjacent domains to the selection Adjacent edges The variables selection contains the adjacent edges to the selection Adjacent points The variables selection contains the adjacent points to the selection For the option Adjacent boundaries you get yet another option to restrict the output boundaries to certain conditions These restrictions only make sense if the original selection determined by the Selection list is a domain selection In the Restrict to list you can choose among the following options All adjacent boundaries This option just returns all boundaries
98. ficient form equation to an equivalent weak form before solving a model It is possible to disable this conversion by selecting the Use coefficient form element check box The only situation when this is necessary is when you intend to use a special wave form discretization You must then specify an expression different from NaN in the Lax Friedrichs flux parameter edit field This wave form also requires that you use the Nodal discontinuous lagrange element in the shape function definition of the dependent variable that the coefficient form refers to PHYSICS BUILDER TOOLS If you want to use a different base vector system than the parent feature or property you can choose a different system in the Base vector system list See Using Coordinate Systems for more information about choosing coordinate systems Creating Variables a Dependent Variable Definition See Also e Coefficient Form PDE Interface c in the COMSOL Multiphysics User s Guide CREATING EQUATIONS 7l 72 Creating Constraints CHAPTER 3 A feature that puts some sort of constraint on a dependent variable a Dirichlet boundary condition for example needs a Constraint node ree A constraint forces an expression to be zero using the expression together with a constraint force expression In most cases the constraint force can be generated from the constraint expression but the constraint node also provides the possibility to customize the constrai
99. fter each radio button It is also common that you activate the group members depending on the value of the radio button input See Figure 3 6 that PHYSICS BUILDER TOOLS displays an example with two radio buttons one has two allowed values z Description Boundary Selection It needs three user inputs where the first Selection Manual gt Override and Contribution Section Choice1 Choice 1 0 Choice 2 Figure 3 6 A screen shot of a window created with the layout option Radio buttons from first user input others interleaved GROUP MEMBERS DEFINE COLUMNS Use this option when you wish to combine IN A TABLE several user inputs into a table GUI component where each user input represents a column in the table This requires that the user inputs are vectors and have the same dimension In the Table height field you set the height of the table in pixels You can control the behavior of the table through a couple of check boxes listed in the table below CHECK BOX DESCRIPTION Automatically add new rows Rows can be added Rows can be deleted Rows can be moved up and down Table data can be saved to file and loaded Select if you always want an empty row below the entered ones Select to enable adding of rows Select to enable deleting of rows Select to enable row content to be movable Select to add toolbar buttons for saving and loading table content DESIGNING THE GUI LA
100. g for a dependent variable The settings window has the following sections GENERAL In the Dependent variable reference and Physical quantity lists you specify what dependent variable to change the scaling for See Dependent Variable Declaration for more information about the dependent variable reference Use the option Use field name in the Dependent variable reference list to specify a variable defined as a degree of freedom SCALING Set the scaling method in the Method list See Dependent Variables in the COMSOL Multiphysics Reference Guide for more information about scaling CREATING STUDY AND SOLVER DEFAULTS 99 100 CHAPTER 3 Absolute Tolerance Use the Absolute Tolerance node if you want to set the default absolute tolerance for a dependent variable The settings window has the following sections GENERAL In the Dependent variable reference and Physical quantity lists you specify what dependent variable to change the absolute tolerance for See Dependent Variable Declaration for more information about the dependent variable reference Use the option Use field name in the Dependent variable reference list to specify a variable defined as a degree of freedom ABSOLUTE TOLERANCE Set the absolute tolerance method in the Method list See Time Dependent Solver in the COMSOL Multiphysics Reference Guide for more information about setting absolute tolerances Outer Job Parameters If the interface uses pr
101. h is timeDerivative A in time dependent study types but iomega A in frequency domain study types The most important study types are Stationary Time dependent Frequency domain Eigenfrequency and Eigenvalue There are also several other alternatives and some of these are only for very specific interfaces For more information on study types see Study Types in the COMSOL Multiphysics Reference Guide The final condition can depend on user inputs either in the parent feature parent property or some property You enable this condition by selecting the User input check box If the usage condition is under a feature or property which might contain other user inputs you can directly refer to any of those user inputs by choosing By reference in the Specify user input list You then choose the user input from the User input list and the type of condition in the User input condition list The options in this list differ depending on the type of user input you refer to but the condition can either check if the user input is active or if it has a certain value The other option in the Specify user input list is By name which means that you enter the name in the User input field The name is entered in the Input name field of the user input you want to refer to For the By name option you also have the list User input from where you can choose if the user input is under the parent feature This feature option or under a property in the ph
102. h of the tools in the Physics Builder that allow you to create custom physics interfaces for specific application EXAMPLE The Examples of Custom Physics Interfaces chapter provide two examples to show how to create custom physics interfaces The Thermoelectric Effect and The Schr dinger Equation INTRODUCTION Physics Builder Tools This chapter provides an overview and a description of the tools in the Physics Builder that you can use to create custom physics interfaces for specific applications Go to the Overview section to get started 20 Overview CHAPTER 3 In this section Using the Physics Builder The Physics Builder Window In This Chapter Using the Physics Builder STARTING THE PHYSICS BUILDER To access the Physics Builder start COMSOL and select Options gt Preferences In the Preference window click Builder Tools and then select the Enable Physics Builder check box With this preference enabled the File menu gets a New from Physics Builder option that starts the Physics Builder The Physics Builder file contains a Physics Builder window with a tree similar to the Model Tree in the Model Builder From the View menu you can open the Physics Builder Manager that allows you to administers testing of Physics Builder files and deployment of entire Physics Builder packages see The Physics Builder Manager SAVING AND OPENING CUSTOM PHYSICS INTERFACES Saving Physics Builder files works in the
103. has Root as parent area You can also control the position of your physics area in the list of areas it currently belongs to Click the Move Up 4 or Move Down J buttons to move the area in the list PHYSICS AREA SETTINGS In the Name field you define a unique string that identifies the physics area which must be unique among all areas present in the Model Wizard The text you write in the Description field is the text COMSOL Multiphysics displays for the physics area in the Model Wizard You can also specify an icon image in the Icon field either by typing the name or by choosing an icon from the file system The Weight field controls the position of your physics area in the list it currently belongs to The higher the weight a larger number the further down the position in the list The Move Up and Move Down buttons in the Physics Area section provide another way to change the weight CREATING PHYSICS AREAS 9I Q The Model Wizard and Model Builder in the COMSOL Multiphysics 5 Seas User s Guide 92 CHAPTER 3 PHYSICS BUILDER TOOLS Creating Material Property Groups When adding a Material Property node P as an input under a feature or property you can choose a basic property type or among other options a property type defined locally in the current Physics Builder file The latter choice refers to a Material Property Group node 8 under the Definitions Library branch JJ A material property grou
104. hat the Include model input check box in the Feature node s Preference section is selected A model input is by default only shown when a material requests it In the Always visible list add the model inputs that ignore the materials so that they should always appear in the settings window of the feature instance 40 CHAPTER 3 PHYSICS BUILDER TOOLS Creating Properties A Property ED contains user inputs and variables that are important to the entire physics interface A property instance always exist in only one instance for a physics interface Any variables or equations defined by a property typically inherit the selection of the physics interface although it is possible to change this In this section e Property Property Link Property The Property node CD settings window of a feature contains the following sections IDENTIFIER The Type is a unique string that identifies the property which must be unique among all properties supported by a physics interface The text you write in the Description field is only used as the default section description If you create one or several manual sections using the User Input Group the description in the Description field is unused RESTRICTIONS In the Allowed space dimensions list you can define what space dimensions this particular property can be used in The option Same as parent the default option means that the feature supports the same space dimensions as the physics
105. he default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar 156 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES number Type 1 165 typical value for Bismuth telluride in the Default value edit field 10 Leave all other default values Il Right click the User Input node and select Variable Definition a This user input then becomes available as a variable tee sigma in for example the predefined expressions for results evaluation You can also refer to sigma directly in the weak equation I2 Leave all other settings at their default values I3 Right click the Feature 2 ThermoelectricModel node and select Inputs gt User Input P In the settings window locate the Declaration section I4 Type S in the Input name edit field and Seebeck coefficient in the Description edit field Type S in the Symbol LaTeX encoded edit field Select None from the Physical quantity list and enter V K as the SI unit This is needed since the Seebeck coefficient is not a built in material property I5 Keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Type 200e 6 typical value for p type Bismuth telluride in the Default value edit field l6 Leave all other default values I7 Right click th
106. hen handles all migration operations to the current version until you create a new version node This means that the last node in the list of versions performs the migration to the current version All other nodes perform the migration from a older version to the next version node Physics Interface A Physics Interface node x7 contains all migration operations for the interface s settings and for the features that you use in the interface If an interface uses feature links to a feature under the Building Blocks branch there must be a feature link node MIGRATION 131 132 CHAPTER 3 under the physics interface You handle the migration of the linked feature in a feature node under the Version gt Building Blocks branch You handle property links in a very similar manner Feature A Feature node contains all migration operations for the feature s settings and for the subfeatures that you use for the feature Ifa feature uses feature links to a feature under the Building Blocks branch 4 4 there must be a feature link node under the feature You handle the migration of the linked feature in a feature node under the Version gt Building Blocks branch Property A Property node contains all migration operations for the property s settings perty g P property g Change Type Use the Change Type node M to change the type of a physics interface or a feature Changing the type makes all files saved in
107. her device model A device cannot instantiate an abstract device model Select the Abstract model type check box to make a device model abstract DEVICE INPUTS Fill the table in this section with the device inputs that the device model supports Each device input also needs a default value You can also define device inputs with the CREATING DEVICE SYSTEMS 75 76 device input child node Use the Input Modifier of a device to override the default value of a device input Device Feature Device Inputs Device Variables E e Device Equations See Also Port Port Model Input Modifier CHAPTER 3 Device Feature The Device Feature node is a special device that can only exist under a Device Model Feature node see Device Model Feature The device is of the type that the device model feature defines and it is placed at the same level as the device model feature in the device system hierarchy Note that this is what makes it different compared to a normal Device node placed under a Device Model Feature node Such a device is part of the device model defined by the device model feature as a subdevice to it The settings window for a Device Feature node is identical to a Device node Port Model A Port Model declares types of ports that a devices use to communicate with each other To a port model you can only add device variables and device equations where a variable can be declared as a flow v
108. hese coefficients for boundary conditions which differs slightly from the General from PDE interface in the Model builder It is straightforward to convert a Flux Source boundary condition from this interface to an equivalent representation using only the f coefficient instead of the g coefficient DEPENDENT VARIABLE Under this section you choose the dependent variable to use for the coefficient form equation Similar to the dependent variable definition you specify a reference to a dependent variable In the Dependent variable reference list you choose if you can use the physical quantity as the reference choose Use physical quantity which is the default or if you have to append an unique tag choose Use physical quantity tag and enter a tag in the Unique tag field See Dependent Variable Definition for more information about specifying dependent variable references SELECTION The options in the Selection list and Output entities list define the selection where this variable definition is valid See Specifying Selections for more information about using these lists PREFERENCES Clear the Use volume factor in axial symmetry and for non orthonormal systems check box if you want to skip any volume factors in the weak form integration In axial symmetry this means that you do not get the factor 2nr For more information on non orthonormal systems see Using Coordinate Systems ADVANCED By default the program converts your coef
109. hich provide a scalar quantity with the default value 0 10 Right click the Feature 3 WaveFunc node and select Constraint eo In the Constraint settings window locate the Declaration section Il Type par psiO psi in the Expression edit field to make Y on the boundary The par prefix indicates a local parameter scope and is necessary in order to refer to a user input that is not defined as a variable D In the Shape Declaration section select Dimensionless 1 from the Physical quantity list to declare the correct dimension for the constrained variable Y This feature uses an user input that should appear in a section in the settings window The constraint automatically adds an extra section for enabling weak constraints and set the type of constraint so it is necessary to specify a section for the user input I3 Right click the Feature 3 WaveFunc node and select Inputs gt User input group In the User Input Group settings window locate the Declaration section I4 Type WaveFunc section in the Group name edit field and Wave function in the Description edit field I5 Beneath the Group members list click the Add button f and select User input psi0 from the Group members list then click OK 16 In the GUI Options section select Group members define a section in the GUI Layout list The remaining boundary condition Axial Symmetry appears automatically on symmetry boundaries in axisymmetric models ADD
110. i UserInput2 sigma a Variable Definition 1 def1 4 Pi UserInput3 S a Variable Definition 1 def1 ariable Declaration 1 q friable Definition 1 q ariable Declaration 2 J ariable Definition 2 J ariable Declaration 3 P ariable Definition 3 P a Variable Declaration 4 E a Variable Definition 4 E a Variable Declaration 5 Q a Variable Definition 5 Q fou Weak Equation 1 weak Jou Weak Equation 2 weak2 4 Feature 3 Temperature 4 Pj UserInput1 TO a Variable Definition 1 def1 E User Input Group 1 TemperatureSection re Constraint 1 constr1 4 C Feature 4 ElectricPotential 4 Pi UserInput1 VO a Variable Definition 1 def1 User Input Group 1 ElectricPotentialSection ree Constraint 1 constr1 4 Feature 5 HeatFiux 4 Pj UserInput1 gin a Variable Definition 1 def1 User Input Group 1 HeatFluxSection Jeu Weak Equation 1 weak1 O Feature 6 Insulation Result Defaults 1 pdef1 b B Physics Areas I Material Groups Migration Thermoelectric Effect Physics Interface Adding It Step by Step The following steps show how to define the Thermoelectric Effect physics interface using the implementation defined in the previous section THERMOELECTRIC EFFECT IMPLEMENTATION 151 CREATING THE BASICS I 2 Start COMSOL Multiphysics From the Options menu choose Preferences In the Preferences dialog box select Physics Builder in the list and then select the
111. ially if an expression occurs in several places All variables in the Physics Builder are tensors that you first declare and then define You typically do the declaration once in a central place It is possible to do several declarations for the same variable but then it is important that they are consistent An example of two inconsistent declarations is when they have different dimensions and that results in an error message when you try the physics interface in the Model Builder A declaration does not specify anything about the value of a variable This is what you use the variable definition for A variable definition declares the expression or shape function for the variable and where a selection the definition is valid CREATING VARIABLES 53 54 CHAPTER 3 VARIABLES FOR DEGREES OF FREEDOMS There are two methods to create variables to solve for dependent variables usually referred to as the unknowns or degrees of freedom DOF You can either use a dependent variable or a variable with a shape definition The dependent variable can only be declared by an interface using the Dependent Variable Declaration under the physics interface All dependent variables need a shape function definition to add the DOFs that the solver solves for For this you use the Dependent Variable Definition under a feature or property If you are unsure what you need use the default Lagrange shape function The other method to create DOFs is
112. ic equations V kVT P oVV oSVT oVV oSVT VV In other words Joule heating oVV VV J E Thomson heating oSVT VV J SVT THERMOELECTRIC EFFECT IMPLEMENTATION 165 166 Example Model Thermoelectric Leg In this section Introduction to the Thermoelectric Leg Model Results Reference Modeling Instructions Introduction to the Thermoelectric Leg Model A thermoelectric leg is a fundamental component of a thermoelectric cooler or heater The component in this example is 1 by 1 by 6 mm capped by two thin copper electrodes The thermoelectric part is made of Bismuth telluride Fa fo wem Ope mw g D aaa eceev EEG 8 as gt ome kk kl aEdocenvzelW cms The material properties needed are the thermal conductivity the electric conductivity and the Seebeck coefficient of copper and bismuth telluride The material properties of this model is taken from the paper in Ref 1 PROPERTY SYMBOL AND UNIT BISMUTH TELLURIDE COPPER Thermal conductivity k W m K 1 6 350 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES PROPERTY SYMBOL AND UNIT BISMUTH TELLURIDE COPPER Electric conductivity o S m l le5 5 9e8 Seebeck coefficient S V K p 200e 6 6 5e 6 n 200e 6 The bottom electrode surface is held at 0 degrees C and is electrically grounded at 0 V The top electrode is set to 0 05 V and is thermally insulated Applying a constraint for only one degr
113. icable RESTRICTIONS The Allowed space dimensions list specifies the geometry dimensions that the physics interface supports 3D 2D ID Axial symmetry 2D Axial symmetry ID and 0D Choose 0D to create a physics interface with a global scope for example a system of ODEs The default is to support all space dimensions except 0D Delete items from the list in cases where not all space dimensions are applicable In the Allowed study types list add the study types that the physics interface can create equations for The most important alternatives are Stationary Time dependent Frequency domain Eigenfrequency and Eigenvalue There are also several other alternatives and some of these are only for specific interfaces For more information see Study Types in the COMSOL Multiphysics Reference Guide SETTINGS From the Top geometric entity level list choose the top level for the governing equations of the physics interface Global Domain Boundary Edge or Point Domain is the default and the most common which means that the top level is the same as the geometry dimension It is also possible to define shell and wire interfaces that have dependent variables and equations defined on entity levels lower than the geometry dimension For a Shell interface choose Boundary The governing equations are then defined on faces in a 3D geometry or lines edges in a 2D geometry You can also choose how the physics interface behaves together w
114. ick the Physics Interface node and select Feature 2 In the Feature settings window locate the Identifiers section 3 Type WaveFunc in the Type edit field Type wvfcn in the Default identifier and tag edit field Type Wave function value in the Description edit field 4 In the Restrictions section leave the default setting Same as parent for the Allowed space dimensions and Allow study types lists 5 In the Settings section keep the default One level below top level Boundary condition type in the Supported geometric entity levels relative to top geometric entity level list Leave Exterior Interior and Pair in the Allowed domain types list This makes the boundary condition available for all those boundary types 6 Leave the Category for overwriting selections at the default setting Exclusive SCHR DINGER EQUATION IMPLEMENTATION 178 CHAPTER 4 7 Leave the settings in the Input base vector system and Base vector system lists to the default setting Frame system compatible with material type 8 Right click the Feature 3 WaveFunc node and select Inputs gt User Input P In the User Input settings window locate the Declaration section 9 Type psiOin the Input name edit field and Wave function value in the Description edit field Type psi_0 in the Symbol LaTeX encoded edit field for the symbol Y Select Dimensionless 1 from the Physical quantity list Use the default values in the Settings section w
115. ics interface 164 180 probability density function 184 for electron s position 173 182 properties 21 41 property links 42 quantum numbers 183 radio buttons 120 reduced mass 170 reduced Planck constant 170 referencing equations 86 renaming inputs migration branch 132 results defaults 102 scalar multiplication 172 scalar product 148 172 Schr dinger equation 170 scope for variables 108 Seebeck effect 142 selections 83 selections specifying 63 shape functions 54 60 singleton features 34 solver defaults 99 sublayouts 118 technical support COMSOL 13 tensor operations 107 tensor parser 106 testing a physics interface 127 thermoelectric effect 142 Thomson effect 142 transformations between coordinates 113 typographical conventions 13 Unicode standard 106 use conditions 84 user community COMSOL 13 user input 44 user input rename 132 user inputs 43 118 accessing 108 Variable Declarations section 35 Variable Definitions section 35 variables adding 53 entering 108 vs user inputs 43 versions for migration 131 weak constraints 72 weak equations 66 web sites COMSOL 13 widgets 115
116. in the outer regions for low energy eigenvalues Right click the Mesh node and select Size to add an extra Size node for defining the mesh size in the inner circular domain Domain 2 In the Size settings window select Domain from the Geometric entity level list and then add Domain 2 to the Selection list 2 In the Element Size section click the Custom button 3 In the Element Size Parameters section select the Maximum element size check box and type 0 05e 9 in the corresponding edit field to use a mesh size no larger than 0 05 nm in Domain 2 4 Right click the Mesh node and select Free Triangular to add a node that meshes Domain 2 using the specified mesh size 5 Select the top Size node and in its settings window change the value in the Maximum element growth rate edit field to 1 1 to make the mesh size grow more slowly toward the perimeter of the geometry 6 Press F8 or right click the Mesh node and select Build All to create the mesh COMPUTING THE SOLUTION Specify that the eigenvalue solver should solve for 10 eigenvalues searching around a small negative number where the first energy eigenvalues are located Select Study I Step l Eigenvalue and in its settings window locate the top Study Settings section 2 Enter 10 in the Desired number of eigenvalues cdit field and 2e 18 in the Search for eigenvalues around edit field 3 Right click the Study I node and select Compute to start the eigenvalue solver RE
117. inate system A non orthonormal coordinate system has two sets of base vectors the covariant and contravariant base A covariant tensor component use contravariant base vectors and a contravariant tensor component use covariant base vectors For all orthonormal systems these two set of base vectors are identical Now assume that D is given in a different coordinate system that n To compute D properly D first have to be transformed as a contravariant tensor x j U u D J Di _ where x is the i th coordinate for the desired system and uj is the i th coordinate for the original system To separate tensor indices they also include the coordinate name If the tensor was covariant the transformation would become Dj x aD ju These transformation are used whenever there exist several systems in an expression or variable assignment The most common example is when you use an input coordinate system for your user inputs that differs from the base vector system in which the variables are stored A material tensor from the material library for example may undergo a rotation to align its z axis with the y axis in the tensor variable used in the model A coordinate system for rotation is always orthonormal so in this case it does not matter if the tensors are covariant or contravariant ENTERING NAMES AND EXPRESSIONS 114 CHAPTER 3 Another situation when a variable might undergo an automatic conversion is if you try
118. ined from the Physical quantity list the top item in the list and then select the added physical quantity from the Link list Physical Quantity The settings window for a Physical Quantity node 4 contains the following sections PHYSICAL QUANTITY In this section you define the physical quantity using the following properties Type a Name for the physical quantity seebeck coefficient for example Type a Description for the physical quantity Seebeck coefficient for example Type a symbol for the property in the Symbol LaTeX encoded field S for example You can use LaTeX syntax for Greek letters subscripts superscripts and mathematical symbols if desired See Mathematical Symbols and Special Characters in the COMSOL Multiphysics Reference Guide You define the dimension of the physical quantity by typing the corresponding SI unit V K for example The Dimension list determines the dimension of the physical quantity Use the default value Scalar for a scalar quantity or select Vector 3x1 for a vector valued quantity Matrix 3x3 for a tensor quantity or Custom to type a dimension in the NXM format PREFERENCES To specify that the physical quantity also is a material property select the Is material property check box To use the added physical quantity in a Material Property node select Locally defined from the Physical quantity list the top item in the list and then select the added physi
119. ing a weak formulation for all features that contribute to the governing equations The equation contributes to the weak form of representing the system of PDEs you wish to solve for You can enter the equations in three different forms Directly as a weak form equation which is the most general technique to specify an equation Inthe general form similar to the General from PDE interface in the Model builder In the coefficient from similar to the Coefficient PDE interface in the Model builder In this section Weak Form Equation General Form Equation Coefficient Form Equation Weak Form Equation To add the Weak Form Equation node fu go to Building Blocks Components and right click Component Then select Weak Form Equation from the Equations list The settings window for a Weak Form Equation contains the following sections INTEGRAND The content of the Expression field adds up as a weak form contribution to the system of equations that you later solve for in the Model Builder For information about writing expressions see Entering Names and Expressions SELECTION The options in the Selection list and Output entities list define the selection where this variable definition is valid See Specifying Selections for more information about using these lists PREFERENCES Clear the Use volume factor in axial symmetry and for non orthonormal systems check box if you want to skip any volume factors in the
120. ing base vector systems Variable Definition A Variable Definition a specifies the expression or shape of a variable and where the definition is valid A variable definition can exist in several places and has a slightly different user interface depending on where you use it For example it is not necessary to specify a variable name if the definition is a subnode to a variable declaration or user input For a user input it is not even necessary to specify an expression because it is always set to the value entered by the user input see Creating User Inputs for more information To add this node go to Building Blocks gt Components gt and right click Component Then select Variable Definition from the Variables list The settings window for a variable definition contains the following sections DEFINITION For a standalone definition not being a subnode to a declaration for example you type the name of the variable you add the definition for in the Variable name field The variable name follows the rules described in Entering Names and Expressions and must match the name of a variable declaration somewhere in the same physics interface For a subnode definition there is no Variable name field because it always use the same name as the parent In the Type list you specify if this definition is an Expression or a Shape function If you choose Expression you can enter an expression in the Expression field according to the r
121. ions menu choose Preferences A Code monospace font indicates you are to make a keyboard entry in the user interface You might see an instruction such as Enter or type 1 25 in the Current density field The monospace font also is an indication of programming code or a variable name An italic Code monospace font indicates user inputs and parts of names that can vary or be defined by the user An italic font indicates the introduction of important terminology Expect to find an explanation in the same paragraph or in the Glossary The names of other user guides in the COMSOL documentation set also have an italic font THE DIFFERENCE BETWEEN NODES BUTTONS AND ICONS Node node is located in the Model Builder and has an icon image to the left of it Right click a node to open a context menu and to perform actions Button Click a button to perform an action Usually located on a toolbar the main toolbar or the Graphics toolbar for example or in the upper right corner of a settings window Icon An icon is an image that displays on a window for example the Model Wizard or Model Library or displays in a context menu when a node is right clicked Sometimes selecting an item with an icon from a node s context menu adds a node with the same image and name sometimes it simply performs the action indicated for example Delete Enable or Disable 14 CHAPTER 2 INTRODUCTION KEY TO THE GRAPHICS Throughout
122. is sequence represents indices of a tensor element Assume that there is a 3 by 3 tensor A with physics interface scope and that it is used in a 2D axisymmetric model where the coordinate names are r phi and z If you type A 1 2 in a builder expression it becomes Arphi in the 2D axisymmetric model The standard naming convention for components of a vector or matrix is a base name concatenated with the coordinate names You can override this naming convention using the Component Settings node Dependent variables are treated differently Firstly they always have model scope so unscoped names get this scope Secondly the user can change their names so you always specify them by their default name The default name lookup has precedence over other variables so if you want to use a variable with physics scope that has the same name as the default name of a dependent variable you must use the phys prefix USING CUSTOMIZED NAMES AND DESCRIPTIONS In the Component Settings node you can define custom names and descriptions by selecting different options in the Create components by list The first option Appending ENTERING NAMES AND EXPRESSIONS 109 HO CHAPTER 3 coordinates to the name is the default behavior for spatial tensors that concatenate the tensor name with the coordinate name for each tensor component Axy The option Appending indices to the name concatenate the tensor name with the tensor index A12
123. ith mesh deformation using the Default frame list Select Spatial Material the default Geometry frame or Mesh Most interfaces use either Spatial or Material Typically a spatial frame is used for fluid mechanics and other Eulerian based physics whereas the material frame is used for solid mechanics and other Lagrangian based physics It is not recommended to use the Mesh frame Select the Deformed mesh check box to make this interface responsible for splitting frames into a reference frame and a moving frame You choose the moving frame from the Moving frame list For example an interface that computes a displacement of the spatial frame have this check box selected and the Moving frame set to Spatial From the Geometry shape order list select Same as first dependent variable the default or PHYSICS BUILDER TOOLS Custom The Geometry shape order setting controls the order of polynomials used for representing the geometry shape in the moving frame o Curved Mesh Elements in the COMSOL Multiphysics Reference Guide See Also GUI OPTIONS Select the Hide interface in the Model Wizard check box if required This can be useful if you want to define an interface that is only used in another multiphysics interface and does not make sense to use as a standalone interface OVERRIDE RULE This section summarizes the override rules defined by all features of the interface If two features uses different override rules you can fi
124. ition By adding it as a variable you can make it available as a predefined expression in plots and results evaluation Schrodinger Equation Interface Adding It Step by Step The following steps show how to defined the Schrodinger Equation interface using the implementation defined in the previous section CREATING THE BASICS Start COMSOL Multiphysics 2 From the Options menu choose Preferences In the Preferences dialog box select Physics Builder in the list and then select the Enable Physics Builder check box if not selected already 3 From the File menu choose New gt Physics Builder A Physics Builder window then replaces the Model Builder window on the COMSOL Desktop 4 Right click the root node Untitled mphdev and select Physics Interface This adds a Physics Interface node y Move to the settings window for the Physics Interface node 5 In the Identifiers section type SchrodingerEg in the Type edit field scheq in the Default identifier and tag edit field and Schrodinger Equation in the Description edit field If you have a custom icon for the interface you can click the Browse button to locate the icon file The default is to use the physics png icon Si SCHR DINGER EQUATION IMPLEMENTATION 173 174 CHAPTER 4 6 The Schrodinger Equation interface should support all space dimensions except 0D so leave the Allowed space dimensions list with the default contents which includes all spa
125. ks work to other modules model examples and documentation sets CHAPTER 2 THE DOCUMENTATION The COMSOL Multiphysics User s Guide and COMSOL Multiphysics Reference Guide describe all interfaces and functionality included with the basic COMSOL Multiphysics license These guides also have instructions about how to use COMSOL Multiphysics and how to access the documentation electronically through the COMSOL Multiphysics help desk To locate and search all the documentation in COMSOL Multiphysics Press Fl for Dynamic Help Click the buttons on the toolbar or Select Help gt Documentation 7 or Help gt Dynamic Help 1 from the main menu and then either enter a search term or look under a specific module in the documentation tree THE MODEL LIBRARY Each model comes with documentation that includes a theoretical background and step by step instructions to create the model The models are available in COMSOL as MPH files that you can open for further investigation You can use the step by step instructions and the actual models as a template for your own modeling and applications SI units are used to describe the relevant properties parameters and dimensions in most examples but other unit systems are available To open the Model Library select View Model Library III from the main menu and then search by model name or browse under a module folder name Click to highlight any model of interest a
126. l 22 CHAPTER 3 See Creating a Physics Interface for more information about creating physics interfaces DEFINITIONS LIBRARY In the Definitions Library branch Jf custom material properties group can be added using available or additional material properties Also create physical properties in addition to the predefined ones in COMSOL Multiphysics See Creating Material Property Groups and Adding Physical Quantities for more information In This Chapter The rest of this chapter describes these features of the Physics Builder Creating a Physics Interface Creating Features Creating Properties Creating User Inputs Creating Variables Creating Equations Creating Constraints Creating Device Systems Creating Operators and Functions Creating Components Building Blocks External Resources Creating Physics Areas Creating Material Property Groups Adding Physical Quantities Creating Override Rules Creating Study and Solver Defaults Creating Result Defaults Creating Mesh Defaults Entering Names and Expressions Designing the GUI Layout PHYSICS BUILDER TOOLS Creating Elements The Physics Builder Manager Migration Adding Comments and Documentation OVERVIEW 23 Creating a Physics Interface In this section Introduction to Creating a Physics Interface Physics Interface Settings Multiphysics Interface Contained Interface Introduction t
127. l to the tag of the feature instance Feature Attributes A feature can have one Feature Attribute node that contains a collection of various settings for its parent feature that you usually do not need to change In its settings window you find the following sections GUI ATTRIBUTES Enter a valid image file name in the Icon field to use a different icon for the feature If this field is empty the feature uses a default icon which is different depending on the feature s entity level HARMONIC PERTURBATION Select the Perturbation method from the list that has the following options No perturbation support the default Can act as contribution Enables an option so that a user can choose if a feature instance can act either as a stationary contribution or as a harmonic contribution This option only makes sense for contributing features Can add contribution as child Adds a subfeature to this feature that adds the harmonic contribution This is typically used for exclusive features From the CREATING FEATURES 39 Harmonic contribution feature list choose Automatic generation of the subfeature or link to a feature with the From link option The automatically generated subfeature adds harmonic contributions for all variables in the parent feature that are defined under a user input and that have the preference property Interpret as right hand side selected VISIBILITY OF MODEL INPUTS This setting requires t
128. lar values for example a global plot Default Plot Parameters For the Default Plot Parameters 4 fill the columns Name Value and Description in table for the parameters that you need in your new plots Any result node in the Model Builder that has the Parameters table is filled with the values you enter here CREATING RESULT DEFAULTS 103 Creating Mesh Defaults Right click a Physics Interface or Multiphysics Interface node to add a Mesh Suggestion node You can customize the mesh generation if your physics interface is the interface controlling the mesh If you need to vary the mesh generation depending on space dimension or user input value you use the Usage Condition node This section describes the Mesh Size Mesh Size In the Mesh Size node 49 specify how the predefined mesh sizes generate meshes If the physics interface is the controlling interface for the mesh these settings are used when automatically generating the mesh each time it is solved Fill in the table with suitable values for the following settings Maximum element size Minimum element size Resolution of curvature Maximum element growth rate Resolution of narrow regions You have to define these values for each of the predefined mesh sizes Extremely fine Extra fine Finer Fine Normal e Coarse Coarser Extra coarse Extremely coarse 104 CHAPTER 3 PHYSICS BUILDER TOOLS o Meshing in the
129. lation tries to merge the language files by adding new descriptions removing unused descriptions and leave translated descriptions untouched Unused or unreferenced files are kept in the archive Do not open a builder file from the Compiled builder files folder in an archive or add it to the development files These files might contain file A references that only work in an compressed archive jar Caution Furthermore they might also contain encrypted expressions that you cannot read or change CHAPTER 3 THE BUILDER ARCHIVES Under the Builder Archives node Z7 you find your compiled archives You can add and remove archives manually from this list but a compilation always adds the compiled archive This list has several purposes exporting archive as a plug in recompiling archives and open the source files for editing Once you compiled the development files to a new archive you should work with the source builder files in that archive which are copies of the ones that you added to the development files You find them under the Source Builder Files folder under the archive node You can right click any file under the Source Builder Files node and click Open Selected to edit the file Right click the archive node and choose Compile Archive to recompile the entire archive This replaces all builder files under the Compiled Builder Files adds new or replaces existing icons and updates the language files as described
130. ld to a Record node you specify the name of this record in the Name field To add this node go to Building Blocks Right click Components to add both a Component and Element node Then select Record Or add it as a child node to an Array Record or String node String A String node x is used for string data for the element The settings window contains one or two sections depending if it is a child to a record node or not To add this node go to Building Blocks Right click Components to add both a Component and Element node Then select String Or add it as a child node to an Array Record or String node STRING VALUE In the Value type list you choose the type of string data that you enter in the Value field The option Custom string means that the data can be an arbitrary string Use PHYSICS BUILDER TOOLS Variable name to interpret the value as a variable name according to the rules outlined in Entering Names Choose Expression to interpret the value as an expression RECORD NAME If this node is a child to a Record node you specify the name of this record in the Name field Elinv The Elinv node 1 is a special element for inverting square matrices using numerical algorithms which is more efficient than an analytical inversion for large matrices size 3 The declaration is similar to the Variable Declaration node and this node also generates a new matrix variable for the inverse You ente
131. le represent the following logical expression Condition 1 and not Condition 2 or Condition 3 Domain Condition A Domain Condition node defines a single condition of override rules specified through their feature groups and a list of allowed domain types see Override Rule The condition represents a geometry selection given by the selection of the features that THE DEFINITIONS LIBRARY 97 98 CHAPTER 3 belong to the given feature groups The specified domain types define what kind of selection it should be for example exterior boundaries to the features selection Under the Definitions Library node II right click Domain Type Conditions to add the Domain Condition subnode The settings window for a Domain Condition node 4f contains the following section CONDITIONS Fill the Feature group ids list with the feature groups to use for this condition Then add the Allowed domain types Exterior Interior or Pair to the list Plot Menu Categories A Plot Menu Categories node defines the categories that you can group related variables into see Variable Declaration A category shows up as a submenu in the Replace Expression E menu of the result nodes in the Model Builder Specify another category as parent if you need several levels of submenus otherwise leave the parent field blank The category of a variable is specified under the variable declaration node below the Show in plot menu op
132. levels the domain type or the category for overriding selections The contained features determine these settings The entity level and domain type get their values from an intersection like operation and as category you get the most strict one The most strict category is first one in the Category for overriding selections list in the Settings section of the Feature node PREFERENCES Almost identical to the Preferences section of the Feature node except that you cannot change the model input setting A multiphysics feature includes model inputs if any of the contained features does PHYSICS BUILDER TOOLS Contained Feature The Contained Feature node C specifies the features that a multiphysics feature inherits from This is actually a link node almost identical to the Feature Link node The difference is that the settings window only contains the Source Feature section If you use a multiphysics interface that links to a built in interface you EI can choose the features of that built in interface as a contained feature Use such links with care because not all built in features support the Note automatic GUI generation that the Physics Builder uses Device Model Feature A Device Model Feature node is a combination of a Feature node and a Device Model node It behaves identical to a feature node with additional functionality to make it work as a device model The device model gets a type identica
133. lick the Physics Interface node and select Feature 2 In the Feature 4 settings window locate the Identifiers section 3 Type ElectricPotential in the Type edit field Type ep in the Default identifier and tag edit field Type Electric Potential in the Description edit field 4 Change the Category for overwriting selections to Contributing 5 Leave all other default values 6 Right click the Feature 4 ElectricPotential node and select Inputs gt User Input P In the settings window locate the Declaration section 7 Type VO in the Input name edit field and Electric Potential in the Description edit field Type V in the Symbol LaTeX encoded edit field Select Electric Potential V from the Physical quantity list 8 Keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Type 0 in the Default value edit field 9 Leave all other default values I0 Right click the User Input node and select Variable Definition a This user input then becomes available as a variable tee VO in for example the predefined expressions for results evaluation You can also refer to VO directly in the weak equation Il Leave all other settings at their default values Now define a Section in the settings window for the boundary condition D Right click the Feature 4 ElectricPotential node and select Inputs
134. ll in the table with rules between categories in different override rules For more information see Creating Override Rules DEFAULT FEATURES This section has no user input It contains a list of all default features that you declared for the physics interface and what geometric entity level and domain type they exist on When you create a new physics interface in the Model Builder COMSOL always adds the default features in this list to the new physics interface VARIABLE DECLARATIONS This section contains read only information It lists all variables that are declared directly under the physics interface node see Information Sections for more details Multiphysics Interface A Multiphysics Interface isa combination of other physics interfaces behaving like one single interface The multiphysics interface inherits all features and properties that all its contained physics interfaces have which are added through Contained Interface nodes It is possible to remove features that for some reason do not work in a multiphysics context The settings window for the multiphysics interface is very similar to a physics interface but with some settings removed because they are inherited from the contained interfaces CREATING A PHYSICS INTERFACE 27 28 CHAPTER 3 IDENTIFIERS Identical to the Identifiers section of the Physics Interface Settings node RESTRICTIONS Choose Contained interfaces from the Intersect sp
135. llows for more than one instance of the same boundary condition on a given boundary where the model includes the combined effect of these boundary conditions An exclusive boundary condition overrides any other previously defined boundary conditions on the given boundary Ideally the constraint conditions should also be exclusive however this prevents you from having a boundary with simultaneous temperature and voltage constraints If you accidentally set several contributing constraint boundary conditions on the same boundary then the last boundary condition overrides all previously defined The final Physics Builder tree displays as below 150 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Ly Physics Interface Builder Ev Sy tg g O 4 VS ThermoelectricEffect mphdev root E External Resources 4 di Building Blocks Components Properties C Features 4 V Physics Interface 1 ThermoelectricEffect 4 xw Dependent Variable Declaration 1 temperature uxw Initial Values 1 iv1 4 usw Dependent Variable Declaration 2 electricpotential uw Initial Values 1 iv1 4 G Feature 1 HeatTransferModel uxw Dependent Variable Definition 1 temperature a Pi UserInput 1 k a Variable Definition 1 def1 feu Weak Equation 1 weak1 4 G Feature 2 ThermoelectricModel uxw Dependent Variable Definition 1 temperature uxw Dependent Variable Definition 2 electricpotential 4 Pi User Input 1 k a Variable Definition 1 def1 4 P
136. lue definition using this node To add this node go to Building Blocks Components and right click Component Then select Degree of Freedom Initialization from the Variables list CREATING VARIABLES 6l 62 CHAPTER 3 DEFINITION You type the name of the variable you add the initial value for in the Variable name field The variable name follows the rules described in Entering Names and Expressions and must match the name of a variable declaration somewhere in the same physics interface The name should also be the name of a variable that has a shape definition but no errors result if this is not the case Select the Set initial value on time derivatives check box to add the initial values for the first time derivative SELECTION The options in the Selection list and Output entities list define the selection where this variable definition is valid See Specifying Selections for more information about using these lists PREFERENCES The options in this section are identical to the ones in the Preferences section of the Variable Definition PROTECTION The options in this section are identical to the ones in the Protection section of the Variable Definition Component Settings You can override the default names and descriptions for tensor elements with the Component Settings node This node is a valid subnode of user inputs and variable declarations and simply changes the default behavior for the parent node It
137. lus where you want the user to enter a node that port p connects to Then you enter p in the right column and par plus in the right If two features exist where the user entered the same value for the parameter plus the port p of those device gets connected Input Modifier A device model defines a set of device inputs that you define a default value for If you want to change this default value for a certain device you do that by adding an Input Modifier P to a device Fill the table with the name of the input you wish to modify and an expression for the new value CREATING DEVICE SYSTEMS 79 80 Creating Operators and Functions CHAPTER 3 In this section Introduction to Operators and Functions Average Integration Maximum Minimum Function Nodes Introduction to Operators and Functions You can add an operator to a feature property or component Defining an operation is similar to the way it works in the Model Builder but with a few differences The operator names follow the same rules as variables see Entering Names You usually have to use feature scope for any operation defined by a feature otherwise you get a duplicate definition if you have more than one feature of that type Inthe Physics Builder you cannot specify absolute selections as you can in the Model Builder See Specitying Selections for more information about this topic For more information about the other
138. mathematical typesetting See Mathematical Symbols and Special Characters in the COMSOL Multiphysics Reference Guide for all available LaTeX commands Click Preview Selected to display a preview of the text including formatting in the Preview window The Preview Window The Preview window ES opens when you click the Preview Selected E or Preview All button It shows the current documentation in HTML format so that you can test the documentation for a physics interface with the links to move up and down in the document You can use the arrow buttons at the top of the window to move back forward or up to the top of the document ADDING COMMENTS AND DOCUMENTATION 139 140 CHAPTER 3 PHYSICS BUILDER TOOLS Examples of Custom Physics Interfaces The two examples in this chapter show how to create custom physics interfaces for two different applications Joule heating is a well known fundamental multiphysics phenomenon but it is not the only type of electro thermal interaction In addition there is the thermoelectric effect which historically is known under three different names the Seebeck Peltier and Thomson effects The first example in this chapter shows how to use the Physics Builder to create a custom physics interface for solving generic combined Joule heating and thermoelectric effects See The Thermoelectric Effect and the following sections The Schr dinger equation describes the beha
139. me and description for the physics interface The supported space dimension for the physics interface The study types stationary time dependent eigenvalue and so on that the physics interface supports The equations written using a weak formulation to solve and the input variables that they need The boundary conditions that the physics interface needs including the default boundary condition and the inputs that they need Any additional variables that are relevant to define for use in for example results analysis and visualization Asuitable default plot to be displayed when the solver has finished and possibly custom quantities as default plot expressions for new plots Optionally you can also add customized default settings for the mesh generation and the solvers NAME AND DESCRIPTION The name of this interface is Thermoelectric Effect The short name is tee There is also an identifier ThermoelectricEffect which is used by the Java and MATLAB interfaces SUPPORTED SPACE DIMENSIONS The Thermoelectric Effect interface is available in all space dimensions THERMOELECTRIC EFFECT IMPLEMENTATION 147 THE STUDY TYPES The Thermoelectric Effect can be made available as a stationary and time dependent study type and perhaps even other study types for more exotic applications In this example stationary is the only study type THE EQUATIONS The first equation is called a Heat Transfer Model and is repr
140. me as parent for the Allowed space dimensions and Allow study types lists 5 Inthe Settings section keep the default One level below top level Boundary condition type in the Supported geometric entity levels relative to top geometric entity level list Leave Exterior Interior and Pair in the Allowed domain types list This makes the boundary condition available for all those boundary types 6 Leave the Category for overwriting selections at the default setting Exclusive 7 Leave the settings in the Input base vector system and Base vector system lists to the default setting Frame system compatible with material type 8 In the Preferences section select the Add as default feature check box Keep the settings in the Default domain level and Default domain type lists to make this a default boundary condition on exterior boundaries only 9 Right click the Feature 2 ZeroProb node and select Constraint 5 In the Constraint settings window locate the Declaration section 10 Type 0 psi in the Expression edit field to make V 0 on the boundary Il In the Shape Declaration section select Dimensionless 1 from the Physical quantity list to declare the correct dimension for the constrained variable Y Notice that the equation model and the Zero Probability boundary condition now appear in the Default Features list in the Physics Interface settings window Add the Wave Function Value boundary condition V Vg Right cl
141. model file and then reload it after updating the physics interface definitions to see how it behaves after applying some extensions or corrections SCHR DINGER EQUATION IMPLEMENTATION 181 Example Model Hydrogen Atom In this section Introduction to the Hydrogen Atom Model Results Modeling Instructions Introduction to the Hydrogen Atom Model The quantity v corresponds to the probability density function of the electron s position in a hydrogen atom In this example Mm e zm E MIm e where M equals the mass of the nucleus and m represents the mass of an electron 9 1094 10781 kg The hydrogen nucleus consists of a single proton more than 1800 times heavier than the electron so the approximation of is valid with a reasonable accuracy Thus you can treat the problem as a one particle system The system s potential energy is e2 4n amp gr where e equals the electron charge 1 602 10 1 C 9 represents the permittivity of vacuum 8 854 102 F m and r gives the distance from the center of the atom In the model the boundary condition for the perimeter of the computational domain is a zero probability for the electron to be outside the specified domain This means that the probability of finding the electron inside the domain is 1 It is important to have this approximation in mind when solving for higher energy eigenvalues because the solution of the physical problem might fall
142. n materials option from the list by clearing the Allow domain material check box GUI OPTIONS If you want the material list to disappear when it is inactive select the Hide user input in GUI when inactive check box Select the Show no description check box to hide the text label containing the description above the GUI component of the material list Similarly you can hide the symbol from the GUI by selecting the Show no symbol check box As a final option it is possible to add a divider above the GUI component and any description text label The divider is a horizontal line with an optional descriptive text Select the Add divider above the material list check box to add the divider When selected you can enter the divider text in the Text field Q Designing the GUI Layout for more information about GUI options See Also e Materials in the COMSOL Multiphysics Reference Guide CHAPTER 3 Activation Condition Use an Activation Condition node lt gt to specify the conditions to dynamically enable or disable an user input material property feature input and material list The condition can depend on user inputs in the parent feature or property or any other user input in a property within the physics interface Conditions can either be true if the other user input has a specified value or if it is active The settings window of the activation condition contains the following section ACTIVATION CONDITION The activation
143. n section 2 In the Expression edit field type hbar_const 2 2 mu Vpsi test Vpsi V lambda psi test psi This expression implements the Schrodinger equation formulation for this interface See Entering Names and Expressions for the keyboard entries to create the del operator V and the dot product B In the Selection section leave the Selection list setting From parent as is to inherit the selection from the top node Also leave the Output entities list to its default setting Selected entities to use the selected domains as the output Leave the remaining settings at their default values 24 Right click the Feature 1 SchrodingerEqu node and select Variables Dependent Variable Definition x In the settings window locate the Definition section 25 Select Dimensionless 1 from the Physical quantity list Leave the default shape function element type as Lagrange in the Shape function list Lagrange elements are the most widely used and are suitable for this physics interface The default order becomes 2 Add the default boundary condition Right click the Physics Interface node and select Feature C3 EXAMPLES OF CUSTOM PHYSICS INTERFACES 2 In the Feature settings window locate the Identifiers section 3 Type ZeroProb in the Type edit field Type zpb in the Default identifier and tag edit field Type Zero probability in the Description edit field 4 In the Restrictions section leave the default setting Sa
144. nd select Open Model and PDF to open both the model and the documentation explaining how to build the model Alternatively click the Dynamic INTRODUCTION Help button E or select Help gt Documentation in COMSOL to search by name or browse by module The model libraries are updated on a regular basis by COMSOL in order to add new models and to improve existing models Choose View gt Model Library Update m to update your model library to include the latest versions of the model examples Ifyou have any feedback or suggestions for additional models for the library including those developed by you feel free to contact us at info comsol com CONTACTING COMSOL BY EMAIL For general product information contact COMSOL at info comsol com To receive technical support from COMSOL for the COMSOL products please contact your local COMSOL representative or send your questions to support comsol com An automatic notification and case number is sent to you by email COMSOL WEB SITES Main Corporate web site www comsol com Worldwide contact information www comsol com contact Technical Support main page www comsol com support Support Knowledge Base www comsol com support knowledgebase Product updates www comsol com support updates COMSOL User Community www comsol com community Typographical Conventions All COMSOL user guides use a set of consistent typographical conventions that make it easier to follow the discussion
145. nderneath the list Then click the Add button f and select Same as top level Domain condition from the Supported geometric entity levels relative to top geometric entity level list then click OK Leave Active in the Allowed domain types list Leave the Category for overwriting selections at the default setting Exclusive From the Material type list select Selectable by user 0 N Oo Leave the settings in the Input base vector system and Base vector system lists to the default setting Frame system compatible with material type 10 In the Preferences section select the Add as default feature check box to make this the default feature for all domains Il Right click the Feature SchrodingerEqu node and select Inputs gt User Input P In the settings window locate the Declaration section I2 Type mu in the Input name edit field and Reduced mass in the Description edit field Type mu LaTeX syntax for the Greek letter u in the Symbol LaTeX encoded edit field Select Mass kg from the Physical quantity list I3 In the Settings section keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Type me const the electron mass which is a built in physical constant in the Default value edit field I4 Right click the User Input node and select Variable Definition a This use
146. nditions now live on lines edges in 3D and points in 2D For such shell interfaces the governing equations live on faces in 3D and lines edges in 2D The boundary condition to a line for example is a point The choices Edge and Point always refer to the geometric entities edge and point no matter what the top level is Finally if your interface has Global as Top geometric entity level the relative choices Same as top level Domain condition and One level below top level Boundary condition refers to the geometry dimension the global interface belongs to If you add it toa 3D geometry the entity levels becomes domains and faces A global interface can also live on a global model no geometry and in this case it does not make sense to use anything else than the Global option It is therefore recommended that you restrict the space dimensions of features that use any of the other options Allowed Domain Types It is possible to limit the types of entities where a feature can be active For example a boundary condition may be limited to only interior boundaries All other selected boundaries get marked as not applicable For more complex situations you can use conditions on domain types to decide if a specific boundary is applicable or not PHYSICS BUILDER TOOLS Select an Allowed domain types from the list From list the default or From Condition IfFrom list is selected select one or all of the options Exterior Interior
147. nds to the following quantum triplets 2 0 0 2 1 0 and 3 0 0 3 1 0 3 2 0 The computed values are separated due to the approximate numerical solution By refining the mesh and solving again you can achieve more accurate results The states with J 0 correspond to spherically symmetric solutions while states with 1 or 2 correspond to states with one or two radial node surfaces The 0 energy level corresponds to the energy ofa free electron no longer bounded to the nucleus Energy levels closer to 0 correspond to excited states The wave function by itself has no direct physical interpretation Another quantity to plot is v T which is proportional to the probability density unnormalized function for the electron position after integration about the z axis The plot shows the unnormalized probability density function To determine the ground state energy you can use adaptive mesh refinement 184 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Modeling Instructions The following steps show how to build this model using the Schrodinger Equation interface MODEL WIZARD Start COMSOL Multiphysics 2 In the Model Wizard click the 2D axisymmetric button on the Select Space Dimension page Then click the Next button 3 On the Add Physics page select Mathematics Quantum Mechanics gt Schrodinger Equation scheq Click the Next button amp 4 On the Select Study Type page select Preset Studies g
148. ne its value equal to the value of the user input It is possible to add a variable definition to a user input node which represents a variable declaration and a variable definition The declaration takes the information from the user input and the definition gives the declared variable the value of the user input The are also some special versions ofthe user input which add predefined declarations of one or several user inputs with a special relation These special user inputs are summarized below Material Property Defines two user inputs one for selecting the source of the material data and the other for specifying a user defined value CREATING USER INPUTS 43 44 CHAPTER 3 Feature Input Defines two user inputs one for selecting the source of the feature input data and the other for specifying a user defined value Material List Defines a user input that contains a material selection A user input also needs information about its appearance in the user interface It is possible to control how it appears when it appears and where it appears in the settings window of a feature or property You control these settings from the GUI Options section of each user input node and through a special activation condition node see Activation Condition User Input A User Input P fora feature or property becomes a data storage editable by the user for the corresponding instance in the Model Builder see Crea
149. nsor syntax becomes un C Vpsi test Vpsi V psi test psi lambda psi test psi In this expression V is the nabla or del vector differential operator and represents an inner Zot product scalar product represents normal scalar multiplication The variable lambda represents the eigenvalues E in Equation 4 1 The following equation parameters must be defined The reduced Planck constant which is a predefined physical constant hbar const The reduced mass u which for a one particle system like the hydrogen atom can be approximated as Mm 4 2 enm H MIm e where M equals the mass of the nucleus and m represents the mass of an electron 9 1094 10 3 kg The hydrogen nucleus consists of a single proton more than 1800 times heavier than the electron so the approximation of is valid in this case The Schrodinger Equation interface therefore includes a user input for the reduced mass u with a default value equal to the electron mass mg which is a predefined physical constant me const The potential energy V which for a one particle system s potential energy is e 4n gr d where e is the electron charge 1 602 10 1 C o represents the permittivity of vacuum 8 854 101 F m and r gives the distance from the center of the atom The Schrodinger Equation interface includes a user input for the potential energy V with a default value of 0 You can easily enter the expression above where the
150. nt force Constraints can also be formulated as a Weak Form Equation using an extra degree of freedom This technique is called weak constraints which you can read more about in the COMSOL Multiphysics User s Guide Constraint To add a Constraint node ree go to Building Blocks gt Components gt and right click Component Then select Constraint from the Equations list The settings window for a constraint contains the following sections DECLARATION In the Expression field you enter the constraint expression that the solver forces to zero when solving for example the expression T 293 15 K makes T equal to 293 15 K For information about writing expressions see Entering Names and Expressions The options in the Constraint force list let you change how the constraint affects the governing equations The Automatic option means that the user can choose between Bidirectional symmetric and Unidirectional constraints in the Constraint type list of an instance of this feature in the Model Builder see Bidirectional and Unidirectional Constraints If you choose Customized a Force expression field becomes visible Here you can write an expression for controlling the constraint force SELECTION The options in the Selection list and Output entities list define the selection where this variable definition is valid See Specifying Selections for more information about using these lists PHYSICS BUILDER TOOLS SHAPE DECLARATION
151. ntire harmonic cycle in frequency domain simulations It is also used to identify right hand sides for harmonic perturbation features see Harmonic perturbation The Show in plot menu check box Select this check box the default setting if you want the variable to show up when a user clicks the Insert expression dp and Replace expression buttons in any of the Results nodes during a Model Builder session Use the Category and Parent edit fields to group the variable into a submenu The Announce variable to feature inputs check box The variable notifies its existence to all physics interfaces The variable uses the selected physical quantity as an identifier Any feature input parameter with the same physical quantity can pick up an announced variable so that the variable can be used by the physics interface that the feature input belongs to An example of a feature input is any of the model input parameters in the Model Inputs section of a physics feature instance in the Model builder CREATING VARIABLES 55 56 CHAPTER 3 ADVANCED This section contains advanced options that you do not have to change in most cases In the Base vector system list you can override the base vector system specified by the parent for example a feature or property by choosing something other that the option Same as parent See Using Coordinate Systems and Transformation Between Coordinate Systems for more information about select
152. nts the full path to the feature or property The subsequent identifier is an input and the value of that input replaces the entire sequence The subsequent identifier is a material property and the material property value either from the material or the user defined replaces the sequence phys A gt root mod1 es A mod u gt root mod1 u root h gt root h item VO gt root mod1 es gnd1 par sigma gt 12 S m mat rho gt root mod1 mat2 def rho root mod1 T CHAPTER 3 PHYSICS BUILDER TOOLS PREFIX DESCRIPTION EXAMPLE map The subsequent identifier is an map src2dst c1 gt extrusion operator of a pair or a root mod1 src2dst_p1 c1 periodic condition rot The subsequent identifier defines a rot src2dst A gt rotation of a vector or matrix variable in C0S 30 Ax sin 30 Ay sin 30 a periodic condition Ax cos 30 Ay minput The subsequent identifier is a valid minput T gt root mod1 ht T model input variable name and the value of the model input parameter replaces the entire sequence entity The subsequent identifier is a valid get entity tag gt init1 method from the current feature or property dev Replaced by the current device scope dev v gt root mod1 cir R1_v If the prefix is left out it is assumed to be phys for variable names but not for dependent variables operators and functions see below After the identifier there can be a trailing sequence of integers Th
153. o Creating a Physics Interface In the Model Builder you can add physics interfaces and physics interface features in the Model Wizard Depending on your license the Model Wizard may contain different physics interfaces grouped in different physics branches The physics interfaces shipped with COMSOL are referred to as built in physics interfaces With the Physics Builder you can create a new physics interfaces that also show up in the Model Wizard either in an existing physics branch or in a new physics branch THE MAIN STEPS TO CREATE A PHYSICS INTERFACE The steps below outline how to build a new physics interface with the Physics Builder Define the physics by formulating domain equations domain sources boundary conditions and boundary sources which represent the features of the physics interface Depending on the application equations conditions and sources for edges and points can also be added 2 Identify the physical quantity or quantities to solve for the dependent variables using the physics interface 3 List the parameter settings that have to be available for the entire physics interface which are the parameters that do not depend on the selection of geometric entities geometric entities are domains boundaries edges or points Organize similar such parameters in groups representing the properties of the physics interface 4 Adda new physics interface to the tree right click the root node and choose Physics
154. o the frame type and is the coordinate systems to use for spatial vectors and matrices The Base vector system list specify the coordinate system used by the equations and variables declared by this feature If any of these lists has the selection Selected input coordinate system the user gets an option to choose coordinate system in the settings window of the feature instance in the Model Builder See Using Coordinate Systems and Transformation Between Coordinate Systems for more information about using base vector systems The Frame type list specifies if the equations assumes that they live on the material or spatial frame The options are Material the default Spatial and Selectable by user The latter means that the frame type can be controlled when using the feature instance The CREATING FEATURES 33 34 CHAPTER 3 instance then gets a Material type list with the options Solid Non solid or From material The feature uses the material frame for the solids and the spatial frame for non solids typically a fluid such as a liquid or a gas For more information see Using Coordinate Systems When any of the base vector systems choices are Selected input coordinate system you get an option to filter the supported coordinate systems In the Filtering of systems list choose between the options Allow boundary systems No boundary systems and Only boundary systems Note that the filtering only affects features that live on
155. ocumentation node adds a heading and the PHYSICS BUILDER TOOLS topic description used for the context help when clicking the node in the COMSOL Desktop When you have created the documentation contents right click the main Physics Interface node and select Compile Documentation from the various User Documentation nodes into a complete document that appears to compile the documentation under the Documentation node E9 at the bottom of the tree in the Physics Builder window Under Documentation you can add additional documentation components to describe parts of the physics that are not directly connected to the nodes for the interface such as an introduction or a theory section User Documentation The User Documentation node amp contains the end user documentation for a physics interface node feature node or other builder component that needs documentation By default a User Documentation text node appears under the main User Documentation node for Feature nodes documentation for example Right click the main User Documentation node to add other documentation components as required In the Section Heading section you add the following e A Heading which is typically the name of the node that the documentation is for The default headings ref entity doc physics gt for a physics interface and ref entity doc feature for a features are references to the contents of the Description fields in those no
156. oded string in the Symbol LaTeX encoded field to define a symbol mu for example to display the Greek letter u The Dimension list contains the choices Scalar Vector 3x1 Matrix 3x3 and Custom If you choose Custom you can specify a nonstandard dimension for example 3x3x3 PHYSICS BUILDER TOOLS if you need a tensor of rank 3 with indices of dimension 3 Do not use tensors of rank higher than 4 due to the rapid increase in memory usage The Physical quantity list defines the unit of the variable and is identical to how it works for dependent variable declarations see Dependent Variable Declaration In Entering Names and Expressions you can find more detailed information about how you can customize variable names with scopes and parameter values PREFERENCES In the Preferences section you specify different options about the variable These are described briefly below The Operation between multiple definitions list Any variable definition for this variable uses the selected operator to combining multiple variable definitions of the same variable You typically use the option Add when several contributing features add contributions to the same variable heat sources for example The Interpret as right hand side check box Select this check box if you use the variable in any right hand side of an expression Such variables get an extra factor i phase e P that enables plotting and animations of the e
157. oelectric Model in the Description edit field In the Settings section select the default One level below top level Boundary condition geometry level in the Supported geometric entity level relative to top geometric entity level list and click the Delete button 59 underneath the list Then click the Add button fs and select Same as top level Domain condition from the Supported domain levels relative to top domain level list then click OK Leave Active in the Allowed domain types list Leave the Category for overwriting selections at the default setting Exclusive From the Material type list select Solid THERMOELECTRIC EFFECT IMPLEMENTATION 155 9 In the Preferences section select the Add as default feature check box Keep the settings in the Default domain level and Default domain type lists to make this a default physics model in all domains Leave the rest of the settings in the Feature settings window at their default values 10 Right click the Feature 2 ThermoelectricModel node and select Variables gt Dependent Variable Definition P In the settings window locate the Definition section II Select Temperature K from the Physical quantity list D Leave the other settings at their default values I3 Right click the Feature 2 ThermoelectricModel node and select Variables Dependent Variable Definition P In the settings window locate the Definition section I4 Select Electric Poten
158. of how to improve model design and other information that may or may not be useful to the user for example g It can be more accurate and efficient to use several simple models instead of a single complex one Tip See Also The See Also icon Q indicates that other useful information is located in the named section Ifyou are working on line click the hyperlink to go to the information directly When the link is outside of the current document the text indicates this for example Theory for the Single Phase Flow Interfaces E The Laminar Flow Interface in the COMSOL Multiphysics User s See Also Guide Model The Model icon III is used in the documentation as well as in COMSOL Multiphysics from the View gt Model Library menu If you are working online click the link to go to the PDF version of the step by step instructions In some cases a model is only available if you have a license for a specific module These examples occur in the COMSOL Multiphysics User s Guide The Model Library path describes how to find the actual model in COMSOL Multiphysics Acoustics of a Muffler Model Library path COMSOL Multiphysics Acoustics automotive muffler If you have the RF Module see Radar Cross Section Model Library path RF Module Tutorial Models radar cross section Model CHAPTER 2 Space Dimension Icons Another set of icons are also used in the Model Builder the model space dimension is indic
159. ommands Press Ctrl Space to get a list of predefined operations to choose from You can also click the Add Expression cfs or Replace Expression E toolbar buttons for the same list of operations Use the Add Expression toolbar button to concatenate expressions to the entered expression and Replace Expression to overwrite Use the Expression Converter button Au to display the Expression Converter dialog box In this dialog box you can enter an expression and convert it to an equivalent expression using LaTeX commands Click Add or Replace to concatenate or overwrite the existing expression in the Enter equation in LaTeX syntax field You can see a preview of your entered expression below the Equation preview divider Each Equation Display node has an identifier that the user defines by entering text in the Name field This identifier is necessary when creating equation expressions that link to other expressions REFERENCES IN EQUATION EXPRESSIONS Sometimes it is useful to reuse parts of equations or combine multiple equation expressions into one equation This can be achieved by using the syntax symbref eq PHYSICS BUILDER TOOLS in an expression This inserts the equation expression from the equation display node with the name eq This referenced node can be local that is defined in the same feature or property as the referee or it can be defined in the definitions library It is also possible to insert the name of
160. only makes sense to use this node for non scalar tensors like vectors or matrices The Create component names by list contains several options that allows you to create names and description according to different rules The first option Appending coordinates to the name is the default behavior for spatial tensors that concatenate the tensor name with the coordinate name for each tensor component AXy The option Appending indices to the name concatenate the tensor name with the tensor index A12 PHYSICS BUILDER TOOLS This is the default for non spatial tensors Use the option Specifying a template if you have a certain naming convention for the i th component For example assume that you want to have the following component names Xx vel y vel z vel Then you enter the following template str append coor i vel To get the descriptions x velocity y velocity z velocity you type coord i velocity The last option for vector valued variables is Specifying each component separately To get the same names and descriptions as the previous example fill in the following to the table under the Create component names by list COMPONENT NAMES COMPONENT DESCRIPTIONS str append coord 1 vel coord 1 velocity str append coord 2 vel coord 2 velocity str append coord 3 vel coord 3 velocity C Entering Names See Also Specifying Selections Specifying the selection where a certain variable definition i
161. ons in the Physics Builder The Physics Builder requires partial differential equations to be entered in the weak form To transfer to weak form multiply each of the two equations with the test functions corresponding to the unknowns T and V here called vp and vy respectively and integrate over the whole computational domain D V vp Qvr D D V J yy 0 D Partial integration gives THE THERMOELECTRIC EFFECT 143 fa V n avr eve D B D J Vvy n Jwy 0 D B where B is the boundary of D and n is the unit normal of D Assuming that there are known values for the heat and current flux in the direction of the boundary normal as qo and Jo respectively the equations become a Vvp faovr Qvr D B D I Wwy Jovy 0 D B The Physics Builder requires you to enter the domain parts of the weak form equations while the boundary parts are more or less automatically available The integrands of the domain parts are 0 q Vvp Qvp 0 J Vvy g The COMSOL convention collects all terms on the right side Note Using Physics Builder syntax the right side expressions become q test VT Qtest T J test VV and this is what you type into the weak form text fields when creating the thermoelectric physics interface This example also uses the fact that you get the heat equation as a subset of the thermoelectric equation system To handle cases where one or more domains are el
162. ons on exterior boundaries Pair Feature A Pair Feature ii is a special feature that defines conditions on pairs A pair has a source and a destination side and a pair condition typically connects the dependent variables between them using pointwise constraints The most common pair condition is the continuity pair condition which simply makes the dependent variables equal on both sides All physics interfaces gets this pair condition by default so you do not have to add it This feature is useful to define other types of pair conditions The major difference between a pair feature and an ordinary feature lies in subnodes that define selections For pair features there are two extra options in the Selection list of the Selection section Source and Destination With these options you can specify to use the source or destination boundaries in the condition of a pair feature see Specifying Selections for more information The settings window of a pair feature is very similar to the Feature node s settings window Identifiers Restrictions and Information Sections for the Feature node Pairs in the COMSOL Multiphysics Reference Guide a See Also SETTINGS Except for a few removed settings identical to the same section for the Feature node see Settings For a pair feature you do not have to specify the geometric entity level 36 CHAPTER 3 PHYSICS BUILDER TOOLS because it is always boundary level The same is
163. or Pair Use the buttons under the list to organize as required If From condition is selected select a Domain condition source Locally defined the default or Imported from external resource If Locally defined is selected select a Domain condition from the list Click the Go to Source button as required Override Rule Source Some features cannot exist on the same selection for example a boundary and COMSOL uses override rules to decide how the selection of one feature override another feature s selection Select an Override rule source Built in the default Locally defined or Imported from external resource If Locally defined is selected also select a Link from the list Click the Go to Source button 4 as required IfImported from external resource is selected select an Imported file from the list Click the Go to Source button as required Then select a Link from the list Override Type ID The Override type id list specifies if the feature is Exclusive or Contributing to other features In the Model Builder an exclusive feature constraints fixed values replaces all previous feature instances for intersecting selections whereas a contributing feature loads sources adds to other contributing features sharing the same selection COORDINATE SYSTEMS In the Input base vector system list you choose what coordinate system all user inputs and material parameters are given in This is related t
164. out the Physics Builder In this section What Can You Do With the Physics Builder Where Do I Access the Documentation and Model Library Typographical Conventions What Can You Do With the Physics Builder The Physics Builder is a graphical programming environment where application experts can design tailored physics interfaces through an interactive desktop environment and without the need for coding With the Physics Builder you can deploy these tailored physics interfaces to create your own products and applications 10 CHAPTER 2 INTRODUCTION The workflow for creating new physics interfaces is similar to creating a multiphysics model except that the result is a new interface rather than a new model Building the interface Using the interface IT Physics Interface Builder W Untitled xml root Building Blocks 89 Components Component 1 mak1 Pi UserInput1 sigma Pj UserInput 2 mur Component 2 mak2 a Variable1 J a Variable 2 B link a Variable 3 E a Variable 4 Je a Dependent Variable 1 magneticfield Properties Features Feature 1 FaradaysLaw Component 1 mak1 Component 2 mak2 Jeu Weak Equation 1 weak1 Feature 2 PerfectMagneticConductor T Feature 3 Electriclnsulation S t Constraint 1 constr V Physics Interface 1 MagnicFieldFormulation amp Feature FaradaysLaw Feature 2 PerfectMagneticConductor 5 Fe
165. outside the domain and no eigenvalues are found for the discretized problem Ideally the domain is infinite and higher energy eigenvalues correspond to the electron being further away from the nucleus Results The solution provides a number of the lowest eigenvalues 182 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Three quantum numbers n l m characterize the eigenstates of a hydrogen atom nis the principal quantum number listhe angular quantum number mis the magnetic quantum number These quantum numbers are not independent but have the following mutual relationships n 1 2 8 O0 lt l lt n 1 I lt m lt l An analytical expression exists for the energy eigenvalues in terms of the quantum number n h2 uns 81 uagdn where hE dg 2 4 4 ne This expression is called the Bohr radius and has an approximate value of 3 107 m The first three energy eigenvalues according to the above expression with u Me are E4 2 180 10 715 e E5s 5 450 10 1 J E4 2422410 19 J EXAMPLE MODEL HYDROGEN ATOM 183 lambda 1 2 17771e 18 Surface Wave function 1 Ys t t t t A 25 555 x10 3 F 0 f i 1 1 1 v 3463x10 1 3 2 1 0 1 2 3 x107 Figure 4 1 The wave function y for the first energy eigenvalue Comparing these numbers with the computed eigenvalues you can see a 2 fold degeneracy for n 2 and a 3 fold degeneracy for n 3 This degeneracy correspo
166. p contains a set of material properties which can come from the list of basic material properties or be custom material properties When you define a material property group physics interfaces can use its properties through a material property and you can also add values for each property in a material library In this section Material Property Group Material Property Material Property Group A Material Property Group 8 contains a set of Material Property nodes that you can refer to when using material properties in your interfaces The settings window for has the following sections PARENT CATEGORIES FOR GROUPS Each material property group can be categorized under one or several group categories This is only to simplify access in the Material node of the Model Builder You create a new parent for the current property group by clicking on the Create New Parent button Lj below the tree view You can also click the Set As Parent button 2 to choose an existing category as parent For categories that you created you can change their name in the field under Category The category tree view also contains COMSOL s built in property groups and categories 9 You can use a built in category as parent but you cannot change the name of it MATERIAL PROPERTY GROUP In the Name field you define a unique string that identifies the property group which must be unique among all property groups available to ma
167. p contents for the section The GUI layout option under the GUI Options section controls the behavior of a user input group You can choose among the following layouts GROUP MEMBERS BELOW EACH OTHER The GUI components that each group member represents appear below each other The member can be another group so the entire layout of that group gets a spot in this sequence The figure below shows a schematic drawing of this layout Section GUI component s from member GUI component s from member 2 GUI component s from member 3 Figure 3 3 A schematic of the layout of the option Group members below each other If any of the user inputs or user input groups has the option Hide user input in GUI when inactive selected it gets hidden when inactive It is still present and its presence can be noted because it occupies a small empty space in the layout If you only have one hidden member like this you hardly notice it but if there are several such hidden members in a row you get a clearly visible empty space You should then use the option Group members placed in a stack see below GROUP MEMBERS PLACED IN A STACK The GUI components of each member are placed in separate sublayouts called cards Each card can appear and disappear as a unit giving the effect that a part of the layout changes instantly The activation condition on each member controls when its card appears or disappears Each c
168. puts one list with the options From material or User defined and one property value field for user defined values PHYSICS BUILDER TOOLS DECLARATION The type of material property can either be a basic material property or a property that belongs to a predefined material property group In the Property type list you choose the type you want The basic material properties belongs to a predefined set of quantities that are commonly used in material libraries You choose the quantity in the Physical quantity list The quantity identifies the corresponding property in the material libraries A property in the material library has a certain dimension but it is possible to use a smaller dimension for a material property in a feature You set this dimension with the Dimension list which can only contain Scalar and Custom for a scalar material parameter For a basic material property you can also specify the name description and symbol similar to variable declaration see Variable Declaration A parameter from a predefined material property group can be taken from a locally defined group a built in group or a group defined in an external builder file In the Material property group list you select the property group to choose parameter from which you choose in the Material property list In the Default value for user defined field which can be a table you enter the default value for the user defined option OPTIONS In addition to
169. r window to reload all physics interfaces listed in the Development Files branch Z7 See The Physics Builder Manager for more information about organizing development files The Physics Builder Window THE PHYSICS BUILDER TREE The Physics Builder window shows the tree containing all physics interfaces and building blocks within a file To add new functionality right click a node in the tree and choose a functionality from the context menu It is only possible to add new physics interfaces to the root of the tree Each new node represents a new physics interface that can be chosen from the Model Wizard when the interface is complete THE PHYSICS INTERFACES Under each physics interface node any of the following items can be added e A feature or a link to a feature in the Features branch C3 under Building Blocks 4 property or a link to a property in the Properties branch Ep under Building Blocks 4 A dependent variable declaration for the variable used by the physics interface This node does not add a dependent variable to the physics interface it just declares that it exists See Dependent Variable Declaration for more Note information e A variable declaration with variable definitions as child nodes where the definitions are expressions in terms of other declared variables A declared variable can also be made available for plotting and results evaluation see Creating Variables OVERVIEW 2
170. r Equation This section is an Introduction to the Schr dinger Equation Introduction to the Schr dinger Equation The Schr dinger equation from the Austrian physicist Erwin Schr dinger is an equation that describes the behavior of the quantum state of a physical system as it changes in time EY HY how L 2n0t TOY where VY is the quantum mechanical wave function the probability amplitude for different configurations of the system and H is the Hamiltonian h the Planck constant over 27 is often called the reduced Planck constant h bar For describing the standing wave solutions of the time dependent equation which are the states with definite energy the equation can be simplified to a stationary Schr dinger equation The following version of the stationary Schr dinger equation models the atom as a one particle system E A VY EY 4 1 The equation parameters are e h approximately 6 626 10784 Js is the Planck constant pis the reduced mass e Vis the potential energy E is the unknown energy eigenvalue Y is the quantum mechanical wave function The physics interface in this example implements this form of the stationary Schr dinger equation 170 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Schrodinger Equation Implementation In this section Overview Schrodinger Equation Interface Adding It Step by Step Overview To implement a physics interface for solving
171. r feature Select Customized to control the space dimensions manually CREATING FEATURES 3l 32 CHAPTER 3 Special restrictions on study types can also be controlled for this feature If you try to solve a problem for a feature that does not support the current study type it does not add any contributions to the model Choose Customized from the Allowed study types list to control the supported study types manually The option Same as parent the default means that the feature supports the same study types as the parent SETTINGS Supported Geometric Entity Levels The Supported geometric entity levels list specifies the level of the selection that the feature uses when adding all its contributions like variables equations and constraints The choices in this list have a slightly different meaning compared to the top level you choose in the Top geometric entity level list of the physics interface settings see Creating a Physics Interface The choices Same as top level Domain condition and One level below top level Boundary condition are relative to the top level of the interface If the top level of the interface is Domain choosing Boundary means that the feature contains a boundary condition to the governing equations These boundary conditions then live on faces in 3D and lines edges in 2D On the other hand if the top level is Boundary choosing Boundary still means that the feature contain boundary conditions but the co
172. r input then becomes available as a variable schequ mu in for example the predefined expressions for results evaluation You can also refer to mu directly in the weak equation I5 Leave all other settings at their default values SCHR DINGER EQUATION IMPLEMENTATION 175 176 CHAPTER 4 16 Right click the Feature 1 SchrodingerEqu node and select Inputs gt User Input P In the settings window locate the Declaration section I7 Type V in the Input name edit field and Potential energy in the Description edit field Type V in the Symbol LaTeX encoded edit field Select Energy J from the Physical quantity list I8 In the Settings section keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Use the default value 0 in the Default value edit field I9 Right click the User Input node and select Variable Definition a This user input then becomes available as a variable schequ V in for example the predefined expressions for results evaluation You can also refer to V directly in the weak equation 20 Leave all other settings at their default values 21 Right click the Feature SchrodingerEqu node and select Weak Equation fau This adds the Weak Equation node where you specify the equation for the domains in the physics interface In the settings window locate the Declaratio
173. r the expression to be inverted in the Expression field under the Input Matrix Definition section To add this node go to Building Blocks Right click Components to add a Component node Then select Elinv from the Elements menu Elpric The Elpric node ak is a special element for computing the eigenvectors and eigenvalues of square 3 by 3 matrices The declaration is similar to the Variable Declaration node and this node also generates three new vector variables plus three scalar eigenvalues You enter the expression of the input matrix in the Expression field under the Input Matrix Definition section To add this node go to Building Blocks gt Right click Components to add a Component node Then select Elpric from the Elements menu Event The Event node 4 defines a solver event that can trigger the solver to stop reinitialize some dependent variables and then continue For more information about solver events see The Events Interface in the COMSOL Multiphysics User s Guide The reinitialization step can either be defined by the adding a Degree of Freedom Initialization node to the Event node or adding a Degree of Freedom Re Initialization node somewhere else To add this node go to Building Blocks Right click Components to add a Component node Then select Event from the Elements menu CREATING ELEMENTS 125 126 DECLARATION Enter a unique tag in the Event tag field to identify the event to
174. rface node and select Feature C0 2 In the Feature 3 node s settings window locate the Identifiers section 3 Type Temperature in the Type edit field Type tp in the Default identifier and tag edit field Type Temperature in the Description edit field 4 In the Restrictions section leave the default setting Same as parent for the Allowed space dimensions and Allow study types lists 5 In the Settings section keep the default One level below top level Boundary condition type in the Supported domain levels relative to top domain level list Leave Exterior Interior and Pair in the Allowed domain types list This makes the boundary condition available for all those boundary types 6 Change the Category for overwriting selections to Contributing THERMOELECTRIC EFFECT IMPLEMENTATION 159 160 CHAPTER 4 Leave the settings in the Input base vector system and Base vector system lists to the default setting Frame system compatible with material type Right click the Feature 3 Temperature node and select Inputs gt User Input P In the settings window locate the Declaration section Type TO in the Input name edit field and Temperature in the Description edit field Type T in the Symbol LaTeX encoded edit field Select Temperature K from the Physical quantity list Keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to
175. rocess in Designing the GUI Layout A user input group node contains the following sections DECLARATION The Group name field is an identifier of the group which cannot be in conflict with any other user input or user input group In the Description field you can enter a text to display for the group For groups that represent a section this description becomes the title of the section For other groups the description pops up above the location of the group if visible and usually looks strange Clear the Description field to avoid this which is the default behavior In the Group members list you add members to the group Click Add to get a list of all possible members to add GUI OPTIONS In the GUI Layout list you can choose how to organize the group members in the window There are several options here which are described in more detail in the section Designing the GUI Layout If you choose Group members define a section for example the group members are placed sequentially in a section in the window Depending on the choice you made in the GUI Layout list different options appear beneath the list See Designing the GUI Layout for a detailed description of all options Material Property The Material Property node P is a special case of a User Input that also supports linking with material properties from the Materials node in the Model Builder A material property node is actually a collection of two user in
176. s at their default values 21 Right click the Feature 2 ThermoelectricModel node and select Variables Variable Declaration P In the settings window locate the Declaration section 158 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES 2 Type Q in the Variable name edit field and Joule heating in the Description edit field Type Q in the Symbol LaTeX encoded As Size select Scalar Select Heat source Wim from the Physical quantity list B Right click the Feature 2 ThermoelectricModel node and select Variables gt Variable Definition P In the settings window locate the Definition section 24 In the Expression edit field type J E 25 Leave all other settings at their default values ADDING THE WEAK EQUATIONS Right click the Feature 2 ThermoelectricModel node and select Weak Equation fa In the settings window locate the Declaration section 2 In the Expression edit field type q test VT Q test T 3 Right click the Feature 2 ThermoelectricModel node and select Weak Equation faw In the settings window locate the Declaration section 4 In the Expression edit field type J test E Note that here E is used instead of VV Either syntax would work ADDING BOUNDARY CONDITIONS Boundary conditions are defined in a way that is similar to domain features Boundary conditions can have their own user inputs and equations The Temperature Boundary Condition Right click the Physics Inte
177. s that contains an overview of the items that you have declared for the feature The contents of these sections are read only and the sections are initially empty The following information sections are valid for the feature Variable Declarations Lists all variable declarations found in the feature excluding the ones declared through any component link The table also provides information about the description dimension and physical quantity of the variables Variable Definitions Lists all variable definitions found in the feature excluding the ones defined in component links The table also specifies if the definition is an expression parameter or shape definition and also displays the actual definition Necessary Variables Lists the variables found in expressions This list corresponds to all the variables that must exist for this feature to work properly in all cases Some of the variables can be declared by the feature itself but others must be declared elsewhere Dependent Variable Definitions Lists the dependent variables defined by this feature with their identifier and physical quantity All these definitions must have a corresponding declaration under the physics interface Necessary Property User Inputs Lists the user inputs read from properties found in this feature These properties and user inputs must exist in any physics interface that uses this feature User Inputs Lists the added user inpu
178. s valid works in the same way for all types of definitions throughout the Physics Builder You find these settings under the Selection section of all nodes that support a selection Itis not possible to give an absolute selection because you do not know enough about the geometry that the physics interface is used in Instead you set up the selection relative to selections that are known in the Model Builder In the Selection list you specify what selection to start from The list below explains the options in the list CREATING VARIABLEs 63 64 CHAPTER 3 assuming that the selection belongs to a variable but this is also valid for all other types of nodes that support selections From parent The selection becomes identical to the selection of the feature If the variable belongs to a property or a physics interfaces the selection becomes identical to the selection of the physics interface Global The variable gets a global selection This option can disable other settings like shape selection for example A shape selection does not make sense for global selections because the only valid degree of freedom is an ODE variable Source Only available for periodic condition features and pair features The selection is identical to the source selection of the periodic condition or pair Destination Only available for periodic condition features and pair features The selection is identical to the destination selection o
179. se volume factor in axial symmetry and for non orthonormal systems check box if you want to skip any volume factors in the weak form integration In axial symmetry this means that you do not get the factor 2nr For more information on non orthonormal systems see Using Coordinate Systems ADVANCED By default the program converts your general form equation to an equivalent weak form before solving a model It is possible to disable this conversion by selecting the Use coefficient form element check box The only situation when this is necessary is when you intend to use a special wave form discretization You must then specify an expression different from NaN in the Lax Friedrichs flux parameter edit field This wave form also requires that you use the Nodal discontinuous Lagrange clement in the shape function definition of the dependent variable that the general form refers to PHYSICS BUILDER TOOLS If you want to use a different base vector system than the parent feature or property you can choose a different system in the Base vector system list See Using Coordinate Systems for more information about choosing coordinate systems Creating Variables e General Form PDE Interface g in the COMSOL Multiphysics User s See Also Guide Cocfficient Form Equation As an alternative to the weak form you can enter the equation using the Coefficient Form Equation node fau To add this node go to Building Blocks Components
180. ssions for results evaluation You can also refer to k directly in the weak equation I8 Leave all other settings at their default values I9 Right click the Feature 1 HeatTransferModel node and select Weak Equation fu This adds a Weak Equation node where you specify an equation for the domains in the physics interface In the settings window locate the Declaration section EXAMPLES OF CUSTOM PHYSICS INTERFACES 20 In the Expression edit field type bea Settings Log 8 Physics Interface Builder Area k VT test VT This expression implements the heat equation formulation for this interface See Entering Names and Expressions for the keyboard entries to create the del operator V and the dot product Ju Weak Equation v Declaration Expression k V T test V T v Selection Selection From parent Zi Output entities Selected entities M v Preferences V Use volume factor in axial symmetry or for non orthonormal systems v Advanced Base vector system Same as parent 21 Leave all other settings at their default values A DDING THE THERMOELECTRIC MODEL Next add the Thermoelectric Model as a domain feature I 2 Right click the Physics Interface node and select Feature C3 In the Feature 2 settings window locate the Identifiers section Type ThermoelectricModel in the Type edit field Type tem in the Default identifier and tag edit field Type Therm
181. stem ENTERING NAMES AND EXPRESSIONS III 112 lists this is the option Frame system compatible with material type The table below summarizes all possible options for the Base vector system list OPTION DESCRIPTION Frame system compatible with Uses a coordinate system that represents the frame material type compatible with the selected material type for the feature Selected input coordinate system This options activates a coordinate system selection list for a feature where the user can choose between user defined systems and a global system that corresponds to the feature s frame Spatial frame system Uses the coordinate system for the spatial frame no matter what the feature s frame is Material frame system Uses the coordinate system for the material frame Mesh frame system Uses the coordinate system for the rarely used mesh frame The feature determines its frame from the Material type list which has the options Solid Non solid or Selectable by user The Solid option corresponds to the material frame and the Non solid typically fluids option corresponds to the spatial frame For the Selectable by user option the material type depends on user choice or material setting during a Model builder session See Frames in the COMSOL Multiphysics User s Guide to get more information about frames When you select the base vector system for a feature it acts as a default for all variables user inputs weak form
182. t Click the Go to Source button 4 to move to the Physical Quantity node for the selected local physical quantity Select Imported from external resource from the Physical quantity list to use physical quantities from another imported Physics Builder file which you choose from the Imported file list Click the Go to Source button to move to the Import node for the imported Physics Builder file All dependent variables need a shape function declaration to add the unknowns that the solver solves for You choose it from the Shape function list If you are unsure what you need use the default Lagrange shape function SELECTION The options in the Selection list and Output entities list define the selection where this variable definition is valid See Specifying Selections for more information about using these lists PREFERENCES The options in this section are identical to the ones in the Preferences section of the Variable Definition PHYSICS BUILDER TOOLS ADVANCED The options in this section are identical to the ones in the Advanced section of the Variable Definition Initial Value A dependent variable needs an initial value for nonlinear and transient simulations In the Initial Value node uxw you define the initial value for the dependent variable declared in the parent node This node represents a special type of feature in the Model Builder that you get by default when you add a physics interface In th
183. t 106 148 172 double dot product 107 double level inputs 117 E Eclipse Help plug in for documentation 136 Einstein summation notation 13 electron charge 172 electron mass 172 elements creating 123 emailing COMSOL 13 equations referencing 86 equations displaying 86 exclusive boundary condition 150 exclusive feature 33 exclusive features 33 external resources 90 feature input rename 133 feature inputs 48 55 feature links 37 features 88 files importing 90 Frobenius inner product 107 functions 81 GUI layout 115 Hamiltonian 170 HTML format for documentation 136 hydrogen atom example 182 importing files 90 initial values 61 input groups 118 Internet resources Joule heating 142 knowledge base COMSOL 13 LaTeX encoding 54 59 86 low level elements 123 material list rename 133 material parameter rename 132 material properties 49 93 INDEX 189 190 INDEX matrix symmetry options for 116 mesh generation 104 mesh sizes predefined 104 migration 130 model inputs 34 Model Library 12 Model Object API 130 Model Wizard 91 MPH files 12 multiphysics features 38 nabla operator 106 172 one particle system 170 182 operators 80 Peltier effect 142 permittivity of vacuum 172 physical quantities 95 physics areas 91 Physics Builder Manager window 127 Physics Builder window 21 Planck constant 170 plot groups creating 102 preview of documents 136 preview of the phys
184. t Eigenvalue Click the Finish button s GEOMETRY MODELING Adda semicircle centered at the origin 0 0 with a radius of 3 10 m 3 nm Use a sector angle of 180 degrees and a rotation of 90 degrees to create a semicircle in the right half plane 2 Add another semicircle centered at the origin 0 0 with a radius of 0 5 10 m 0 5 nm Use the same sector angle and rotation as for the first semicircle 3 Build the geometry by pressing F8 for example The final geometry consists of two semicircles in the r gt 0 half plane PHYSICS SETTINGS In the Schrodinger Equation Model node the default in the Reduced mass edit field is the electron mass m Type the following expression into the Potential energy edit field e const 2 4 pi epsilonO const sqrt r 2 2 2 where e const and epsilonO const are built in physical constants the electron charge and the permittivity of vacuum respectively sqrt r 2 z 2 is the distance r from the origin This expression is the potential energy in Equation 4 3 2 Verify that the default boundary conditions are correct the Axial Symmetry condition applies to the symmetry boundaries at r 0 and the Zero Probability condition applies to the exterior boundaries of the geometry EXAMPLE MODEL HYDROGEN ATOM 185 MESH GENERATION The reason for the inner circular domain is to use a finer mesh in that part because the solution shows greater variations in the center region than
185. t nodes with the a correct new type COMPATIBILITY Identical to the Compatibility section of the Change Type node Migration Links The following nodes are described Feature link Property link Contained interface Contained feature The migration link nodes contain a link to the actual node under the Building Blocks branch that handles the actual migration You specify the link in the Link list License Settings If you define a feature that is available only if the license includes one or some of the modules in the COMSOL Multiphysics product suite add a License Settings node 13 to any of the feature nodes The settings window contains the following section MIGRATION 133 134 Adding Comments and Documentation CHAPTER 3 Introduction Depending on the use of the created physics interfaces the need for internal documentation comments about implementation and for simplifying extending and maintaining the implementation and external documentation user documentation and context help varies The Physics Builder includes tools for creating documentation for both internal and external documentation There are two main types of nodes that you can add to the physics interface and its features Comment nodes where you can add comments about each feature for internal use Those comments can provide information about the implementations its benefits and limitations any remaining issues or ide
186. t the default nodes appear as expected and that their settings windows contain the user inputs that you specified Proceed by building an example model see the example model below to verify that the Thermoelectric Effect interface solves the correct equation using the correct boundary conditions and that you can plot the various physics quantities Correct any errors or problems that you find and save the physics interface again When you have successfully created a first instance of a physics interface you can consider improvements or additions for future development Typically you can save a model file and then reload it after updating the physics interface definitions to see how it behaves after applying some extensions or corrections The Thermoelectric Effect physics interface has some natural extensions Adding additional boundary conditions for current input and convective cooling Adding a Time Dependent study type which requires user inputs for density and heat capacity Allowing for the thermal and electric conductivities to be anisotropic Making use of Material Groups in order to be able to reuse material properties from one modeling session to another Using Building Blocks to make the physics interface easier to maintain and extend Creating additional variables for the separate heating contributions from Thomson heating and Joule heating These correspond to the right hand terms in the first of the thermoelectr
187. ter completing some steps From the File menu choose Save and create a physics interface file ThermoelectricEffect mphdev in the default location Click Save This concludes the initial steps that set up the fundamentals for the physics interface The next steps adds equations boundary conditions and variables ADDING THE DEPENDENT VARIABLES First declare the dependent variables T and V 2 Right click the Physics Interface node and select Variables gt Dependent Variable Declaration iw In the Dependent Variable Declaration node s settings window locate the Declaration section 152 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Leave the setting in the Dependent variable ID list as Use physical quantity Type T in the Default variable name edit field Type Temperature in the Description edit field Type T in the Symbol LaTeX encoded edit field Leave the Size list s default setting Scalar because T is a scalar field Select Temperature K from the Physical quantity list In the Preferences section leave the default settings that makes the dependent variable available for plotting Plot and for use as an input in other physics interfaces Announce variable to feature inputs Once again right click the Physics Interface node and select Variables gt Dependent Variable Declaration iw In the Dependent Variable Declaration settings window locate the Declaration section Leave the setting in the Depend
188. terials The text you write CREATING MATERIAL PROPERTY GROUPS 93 94 in the Description field is the text COMSOL Multiphysics displays for the property group in the Material properties section of the Material node in the Model builder e Materials in the COMSOL Multiphysics Reference Guide See Also CHAPTER 3 Material Property The Material Property node P is a subnode to a Material Property Group and declares a new property for a node It is similar to the Material Property node used in features or properties but with fewer options The settings window has the following section MATERIAL PROPERTY In the Property type list you choose if the type of material property is a basic material property or a custom material property For the option Basic material property you only need to select a material quantity from the Physical quantity list If you choose Custom material property you must declare name description unit and dimension similar to how you do it for the Variable Declaration node PHYSICS BUILDER TOOLS Adding Physical Quantities In addition to the predefined physical quantities that you can use for variable declarations and definitions of material properties you can add physical quantities to a Physics Builder file To do this right click the Definitions Library node JJ and add a Physical Quantity node To use the added physical quantity in a Variable Declaration node select Locally def
189. that the option Same as parent See Transformation Between Coordinate Systems for more information about selecting base vector systems CREATING VARIABLES 59 60 CHAPTER 3 Dependent Variable Definition The Dependent Variable Definition node uw is used for the definition of a dependent variable means that you specify the shape function to use and where that shape function is to be used To add this node go to Building Blocks gt Components gt and right click Component Then select Dependent Variable Definition from the Variables list In the settings window of the variable you must first specify the identifier of the dependent variable which you can select from the Physical quantity list if you select Use physical quantity the default from the Dependent variable reference list As an option it is also possible to specify an arbitrary unique tag identifier by selecting Use physical quantity tag and entering the tag in the Unique tag field It is important that you have a matching dependent variable setting under the physics interface otherwise you get an error when you try to use the physics interface In addition to the predefined physical quantities you can use locally defined physical quantities or physical quantities imported from an external resource Select Locally defined from the top of the Physical quantity list to use one of the locally defined physical quantities which you choose from the Link lis
190. the documentation additional icons are used to help navigate the information These categories are used to draw your attention to the information based on the level of importance although it is always recommended that you read these text boxes Caution A Caution icon A is used to indicate that the user should proceed carefully and consider the next steps It might mean that an action is required or if the instructions are not followed that there will be problems with the model solution for example a This may limit the type of boundary conditions that you can set on the Euer eliminated species The species selection must be carefully done aution Important An Important icon is used to indicate that the information provided is key to the model building design or solution The information is of higher importance than a note or tip and the user should endeavor to follow the instructions for example 1 Do not select any domains that do not conduct current for example the gas channels in a fuel cell Important Note A Note icon is used to indicate that the information may be of use to the user It is recommended that the user read the text for example 5 Undo is not possible for nodes that are built directly such as geometry objects solutions meshes and plots Note ABOUT THE PHYSICS BUILDER 15 16 Tip A Tip icon 9 is used to provide information reminders short cuts suggestions
191. the options From material and User defined you can add extra items to the list in the feature instance by adding them to the Extra list items table In the Model Builder most material properties get their values from the material assigned to the geometric entities overlapping with the selection of the feature instance You can add a Material List to the feature which enables you to choose among all materials added to a model Use the Couple to material list check box to specify that this property gets linked to the material selected in the list You choose what list to couple against in the Material list cither by entering a name or choosing a particular material list reference GUI OPTIONS If you want the material property to disappear when it is inactive you select the Hide user input in GUI when inactive check box Select the Show no description check box to hide the text label containing the description above the GUI component of the property Similarly you can hide the symbol from the GUI by selecting the Show no symbol check box As a final option it is possible to add a divider above the GUI component and any description text label The divider is a horizontal line with an CREATING USER INPUTS 47 48 optional descriptive text Select the Add divider above the material property check box to add the divider When selected you can enter the divider text in the Text field Designing the GUI Layout for more information
192. tial V from the Physical quantity list I5 Leave the other settings at their default values ADDING USER INPUTS Right click the Feature 2 ThermoelectricModel node and select Inputs gt User Input P In the settings window locate the Declaration section Type k in the Input name edit field and Thermal conductivity in the Description edit field Type k in the Symbol LaTeX encoded edit field Select Thermal conductivity W m K from the Physical quantity list Keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Type 1 6 typical value for Bismuth telluride in the Default value edit field Leave all other default values Right click the User Input node and select Variable Definition a This user input then becomes available as a variable tee k in for example the predefined expressions for results evaluation You can also refer to k directly in the weak equation Leave all other settings at their default values Right click the Feature 2 ThermoelectricModel node and select Inputs gt User Input P In the settings window locate the Declaration section Type sigma in the Input name edit field and Electric conductivity in the Description edit field Type sigma in the Symbol LaTeX encoded edit field Select Electric conductivity S m from the Physical quantity list Keep t
193. ting User Inputs for an overview The settings window of a user input contains the following sections DECLARATION In the Declaration section you specify the name ofthe parameter in the Input name field The description symbol and physical quantity of the user input works identical to variable declaration see Variable Declaration and Dependent Variable Declaration The dimension and default value of the user input is a bit different compared to variables For scalars vectors and matrices you set the desired dimension in the Dimension list Use the Single array type for the Array type list which also is the default When you need user inputs that are vectors of vectors or vector of matrices choose Double in the Array type list You can then choose the outer dimension with the Outer dimension list and the inner dimension with the Inner dimension list The Inner dimension list is identical to the Dimension list but the Outer dimension list has fewer options For all double array user inputs the default value refers to the inner dimension and fills up the outer dimension with identical defaults When the user input is a scalar there is an option to define a set of allowed values In the Allowed values list you can choose Any or From list If you choose From list a table shows up that you can fill the with allowed values The Default value list only contains the values entered in the Allowed values list If you choose Any in the Allowed
194. tings Adding Comments and Documentation Introduction Physics Interface Documentation User Documentation Developer Comments The Documentation Node Documentation Text Components The Preview Window 115 115 118 123 123 123 124 124 124 124 125 125 125 126 127 130 130 131 131 132 132 132 132 133 133 134 134 134 135 135 136 137 139 CONTENTS 7 8 CONTENTS The Thermoelectric Effect Introduction to the Thermoelectric Effect Equations in the Physics Builder Thermoelectric Effect Implementation Overview Thermoelectric Effect Physics Interface Adding It Step by Step Example Model Thermoelectric Leg Introduction to the Thermoelectric Leg Model Results Reference Modeling Instructions The Schr dinger Equation Introduction to the Schr dinger Equation Schr dinger Equation Implementation Overview Schrodinger Equation Interface Adding It Step by Step Example Model Hydrogen Atom Introduction to the Hydrogen Atom Model Results Modeling Instructions Chapter 3 Examples of Custom Physics Interfaces 142 142 143 147 147 151 166 166 167 167 168 170 170 171 171 173 182 182 182 185 Introduction This guide describes the Physics Builder a set of tools for creating custom physics interfaces directly in the COMSOL Desktop In this chapter About the Physics Builder Overview of the User s Guide Ab
195. tion Using plot menu categories you can create a structure where related variables are grouped into separate categories Right click the Definitions Library node JJ to add a Plot Menu Categories node The settings window for a Plot Menu Categories node 4f contains the following section CATEGORIES In the table under each column enter the Name Description and Parent to define a new category PHYSICS BUILDER TOOLS Creating Study and Solver Defaults To define Study Solver Defaults ge for a physics interface create a solver sequence or part of a solver sequence This sequence is used as a solver suggestion when solving a model in the Model Builder that includes the interface There are many alternatives to create a solver default but the most important rule is to try to specify as little as possible You can also vary the solver defaults using the Usage Condition node for example to specify one default for 3D and another for time dependent problems For most of the nodes in the actual solver sequences this works in exactly the same way as in the Model Builder see Solver Features in the COMSOL Multiphysics Reference Guide This section only describes the nodes that differ significantly or do not have a counterpart in the Model Builder In this section Field Absolute Tolerance Outer Job Parameters Eigenvalue Transform Study Sequence Field Use the Field node 3 to set the default scalin
196. tion components are available as references in other selection components or in any other item using selections for example Variable Definition nodes and Weak Form Equation nodes If the component link is in the same builder file use Local in the Link from list of the component link node The components in the Components branch of another builder file are also available if included as an Import node under the External Resources branch pg PHYSICS BUILDER TOOLS Properties In the Properties branch CD you can add several Property nodes The properties in this list are available to all Property Link nodes If the property link is in the same builder file use Local in the Link from list of the property link node The properties in the Properties branch of another builder file are also available if included as an Import node under the External Resources branch Features In the Features branch you can add several Feature nodes for defining physics features such as material models boundary conditions loads and sources The features in this list are available to all Feature Link nodes If the feature link is in the same builder file use Local in the Link from list of the feature link node The features in the Features branch of another builder file are also available if included as an Import node under the External Resources branch Code Editor The Code Editor node provides the possibility to enter
197. tion easier you define a variable for the heat flux q as a 3x1 vector with the following expression P J k VT There is a dot product between the thermal conductivity and the temperature gradient This makes it easy to generalize the physics interface to an anisotropic thermal conductivity at a later time if needed A variable for the current density J is defined as a 3x1 vector with the following expression sigma VV S VT A variable for the Peltier coefficient P is defined as a scalar with the following expression S T A variable for the electric field E is defined as a 3x1 vector with the following expression VV A variable for the Joule heating Q is defined as a scalar with the following expression J E THE BOUNDARY CONDITIONS The Thermoelectric Effect physics interface includes the following boundary conditions A constraint for the temperature TO T where TO is a user input The expression given for a constraint is understood to be set to zero so the above constraint equation expression means T T A constraint for the voltage VO V where VO is a user input A heat flux qin where qin is a user input An insulation boundary condition with no user inputs See the above theory section THERMOELECTRIC EFFECT IMPLEMENTATION 149 The constraint boundary conditions and the flux condition are contributing while the insulation boundary condition is exclusive A contributing boundary condition a
198. tivation Condition Additional Requirement Creating Variables About Creating Variables Variable Declaration Variable Definition Dependent Variable Declaration Dependent Variable Definition Initial Value Degree of Freedom Initialization Component Settings Specifying Selections Frame Shape Creating Equations Weak Form Equation General Form Equation Coefficient Form Equation Creating Constraints Constraint Creating Device Systems About Device Systems Device Model Device Feature 4l 4l 42 43 43 44 46 46 48 49 50 5 53 53 54 56 58 60 6l 6l 62 63 65 66 66 67 69 72 72 74 74 75 76 Port Model Device Variables Device Equations Device Inputs Device Constants Port Device Port Connections Input Modifier Creating Operators and Functions Introduction to Operators and Functions Average Integration Maximum Minimum Function Nodes Creating Components About Creating Components Component Physics Interface Component Selection Component Component Link Usage Condition Equation Display Building Blocks Components Properties Features Code Editor External Resources Import Creating Physics Areas Physics Area 76 77 77 77 77 78 78 78 79 80 80 80 80 8l 8l 8l 82 8 83 83
199. to a physics feature in the Model Builder This disables any possibility to alter the expression and it also makes it harder to read the expression To further complicate reading of the expression you can select the Encrypt expression check box This turns on an encryption of the expression in the saved model file and when accessing the expression in Model Java code It also encrypts the tensor expression when you compile the archive see Compiling an Archive so the expression in a distributed builder file mphdev cannot be read ADVANCED If you have selected Shape function in the Type list the Create a slit for the selected shape check box becomes editable When selected a shape function is not added but instead removed from the selection You typically use this for slit boundary conditions where you want to allow a jump in the shape variable across a boundary For shape function definitions select the Declare shapes for all frames check box to ensure that the spatial derivatives of the shape functions exist for all existing frames The declaration of frame specific time derivatives of the shape functions is disabled when this check box is selected These have to be declared manually for necessary frames The Solver field type list specifies the type of degree of freedom the shape function declares There are very few cases when this setting needs to be something different CREATING VARIABLES 57 58 CHAPTER 3 than
200. to add a shape definition for a variable declared by a Variable Declaration In contrast to the dependent variable this variable does not show up in the Model Wizard or in the settings window of the physics interface instance in the Model Builder This means that the user cannot change the name of this variable Another minor difference is also that it is possible to define the scope of the variable where the default is physics scope model identifier gt lt interface identifier gt lt name gt see Entering Names and Expressions for information about scopes and variable names The dependent variable always has a model scope Variable Declaration A Variable Declaration a specifies various properties of a variable There are two places to add this node Go to Building Blocks Components and right click Component Then select Variable Declaration from the Variables list Right click Physics Interface or Multiphysics Interface and select Variable Declaration from the Variables list The settings window for a variable declaration contains the following sections DECLARATION Declare the variable name description symbol dimension and physical quantity The Variable name field declares the variable s name and the Description field provides a descriptive text for the variable shown in analysis and variable listings It is also possible to declare a symbol that can be used in equation displays and other tools Enter a LaTeX enc
201. to perform a scalar dot product between to tensor of the same type for example two covariant tensors D n g D n The expression parser performs a raise index operation on D before taking the dot product This is essentially a multiplication with the contravariant metric tensor g The metric tensor is the identity matrix for all orthonormal systems REFERENCE 1l G B Arfken H J Weber Mathematical Methods for Physicists Academic press 1995 PHYSICS BUILDER TOOLS Designing the GUI Layout The design of the GUI layout of a feature or a property is an important and sometimes complex task You often have to compromise between a simple layout and flexibility in the functionality Each User Input node often represent a GUI component or widget for example fields combo boxes and tables Based on the declaration of a user input there is often only one possible choice of GUI component In situations where there are several possible choices you have the option to choose You always find such choices under the GUI Options section of a user input node In contrast to user inputs which controls what GUI components you see the User Input Group node controls when and where to display the GUI components As an example the user input group can list the user inputs you want to see under a specific section This is an option in the GUI Options section of a user input group In this section User Inputs and GUI Components
202. ts in this feature with their array type dimension and description excluding any user inputs added by any component links These sections provide useful information about the feature for example how you can use a feature in different physics interfaces Periodic Feature A Periodic Feature is a special boundary condition that couples usually by pointwise constraints dependent variables on a source side to a destination side It has similarities with the Pair Feature The major difference between a periodic feature and an ordinary feature lies in subnodes that define selections For periodic features there are two extra options in the Selection list of the Selection section Source and Destination With these options you can specify to use the source or destination boundaries in the condition of a periodic feature see Specifying Selections for more information CREATING FEATURES 35 The settings window of a periodic feature is very similar to the Feature settings window Q Identifiers Restrictions Preferences GUI Options and Information Sections for the Feature node See Also SETTINGS Except for a few removed settings identical to the same section for the Feature node see Settings For a periodic feature you do not have to specify the geometric entity level because it is always boundary level The same is true for the domain type setting because the only setting that makes sense is periodic conditi
203. ules described in Entering Names and Expressions For the Shape function option you can choose the shape function from the Shape function list See Element Types and Discretization in the COMSOL Multiphysics User s Guide for more information about the shape functions The shape function selection becomes disabled if you use a global selection for this definition In that case the only type of degree of freedom DOF that makes sense is the ODE variable which is the only available global DOF PHYSICS BUILDER TOOLS SELECTION The options in the Selection list and Output entities list defines the selection where this variable definition is valid See Specifying Selections for more information about using these lists PREFERENCES By selecting the Zero out components check box you can enforce a symmetry to spatial vectors and matrices If you choose Zero out of plane the out of plane component is set to zero in the space dimensions 1D 2D 1D axial symmetry and 2D axial symmetry The out of plane component in 2D axial symmetry is the second component the component The option Zero in plane does the opposite This setting has no effect in 3D for scalars or non spatial tensors length other than 3 PROTECTION In this section you can set preferences that enables protection of your entered expression Select the Hide expressions in equation view check box to remove the definition to display in the Equation View node which is a subnode
204. ures gt and add any of these nodes Device Model Feature Feature or Periodic Feature Then right click these nodes to add a Device from the Devices list Or go to Building Blocks gt Components gt and add a Component node Then right click the node to add a Device from the Devices list Port Connections The Port Connections defines how devices connects to each other There are two situations when you can use port connections The first situation is when you add the port connections to a device model You use this to define connections between devices that belongs to the same device model Fill the table with the names of the ports that you wish to connect where the names in the left column connects to the names in the right This is typically ports defined by the device models that a device refers to so the name of the port is appended to the device name For example you type R p to access port p of the device named R PHYSICS BUILDER TOOLS The other situation is when you add port connections to a device Then you typically want to define how the ports of that device connects to another device that belongs to another feature Fill the table with the port name in the left column and a virtual connection in the right column The virtual connections defines a temporary name space that identifies the port names in the right column in any port connections that connects So lets assume that you have a parameter for a feature called p
205. ut Device Systems For certain global interfaces that do not have any distributed dependent variables no spatial dependence the complexity of the system often lies in the large number of dependent variables it needs It is usually rather complicated to define a set of dependent variables to solve for so there is a special frame work for handling such systems You define a hierarchy of device models that defines a set of variables and equations A Device Model specifies a type ofa device The device model also needs ports that define how devices communicate with other devices A port also has a type called a Port Model A port model defines a set of variables that take part in the communication between devices A typical example of this rather abstract description is an electrical circuit All resistors in a circuit belongs to the same device model the resistor model The resistor model defines two ports representing the two pins that a resistor has Each resistor is a device where the two ports to communicate with other resistors and possibly other types of devices like capacitors and inductors The port model for the port needs a voltage and a current The voltage represents the node potential of the connection and is the same for all ports that are PHYSICS BUILDER TOOLS connected The current that flows out of a port must flow into the other ports so the sum of all currents must be zero The port model declares this behavior
206. values list you specify the default in the Default value field User inputs of the type Boolean is just a special case of a scalar with two allowed values internally represented with 0 and 1 The obvious control type for this user input is a PHYSICS BUILDER TOOLS check box that either can be cleared 0 or selected 1 To make the check box selected by default select the Default selected check box When you want vectors where each element must be in a set of allowed values or is a Boolean you use a double array user input Set the outer dimension as desired and choose Scalar or Boolean from the Inner dimension list If you choose Sealar you can set the allowed values as described above RESTRICTIONS In the Allowed space dimensions list you can define what space dimensions this particular user input can be used in The option Same as parent the default option means that the user input supports the same space dimensions as the parent feature or property If you want to control the space dimensions manually choose Customized from the list You can then select the allowed space dimensions from a list of all space dimensions If the user input does not support a space dimension it becomes E completely removed from the feature or property not just hidden from the user interface If you then try to access it in a variable definition for Note example an error message appears ADVANCED This section contains advanced
207. vior of a quantum state in quantum mechanics The second example in this chapter shows how to use the Physics Builder to create a custom physics interface for solving a version of the Schr dinger equation See The Schr dinger Equation and the following sections Both the Physics Builder files MPHDEV files and model examples MPH files for these two custom physics interfaces are included in the COMSOL Multiphysics installation You find the files in the demo builder directory under your COMSOL Multiphysics installation directory 141 The Thermoelectric Effect In this section Introduction to the Thermoelectric Effect Equations in the Physics Builder Introduction to the Thermoelectric Effect The thermoelectric effect is the direct conversion of temperature differences to electric voltage or the other way around It is the mechanism behind devices such as thermoelectric coolers for electronic cooling or portable refrigerators While Joule heating resistive heating is an irreversible phenomena the thermoelectric effect is in principle reversible Historically the thermoelectric effect is known under three different names reflecting its discovery in experiments by Seebeck Peltier and Thomson The Seebeck effect is the conversion of temperature differences into electricity the Peltier effect is the conversion of electricity to temperature differences while the Thomson effect is heat produced by the product of current d
208. wing table lists the operator symbols and operations that the tensor parser supports OPERATION PRECEDENCE EXAMPLE Cross product Same as multiply a x b orcross a b Inner dot product Same as multiply a b or dot a b Double dot product Same as multiply a b Gradient Function Va or gradient a Tangential gradient Function gradientT a Divergence Function V a or divergence a Curl Function V xa orcurl a Tangential curl Function curlT a Inverse of a matrix Function inverse a Transpose of a matrix Function aT or transpose a Normalize a vector Function normalize a Norm of a vector Function norm a Sum over last index Function sum a The double dot product is a summation over two indices 5 Aa ij a b ajjb Unfortunately there are two definitions of the double dot product and the above is referred to the Frobenius inner product or the colon product The other definition has flipped order for the indices in the second factor boo a b ajjb The former definition is used by the tensor parser ENTERING NAMES AND EXPRESSIONS 107 108 Entering Names All variable names that you write in an expression are first assumed to be a variable defined by the physics interface which means that it has a physics interface scope If no variable is found with that scope it checks the model scope and finally the root scope If you want to access a variable in the root scope but you are unsure if it exists in any other scope
209. wledgebase Part No CM020009 Contents Chapter Introduction About the Physics Builder 10 What Can You Do With the Physics Builder 10 Where Do Access the Documentation and Model Library H Typographical Conventions a a a a l c s s v 1B Overview of the User s Guide 18 Chapter 2 Physics Builder Tools Overview 20 Using the Physics Builder l l 20 The Physics Builder Window c 2l In This Chapter rrr 22 Creating a Physics Interface 24 Introduction to Creating a Physics Interface 24 Physics Interface Settings llc 25 Multiphysics Interface lc 27 Contained Interface u a a l l c 28 Physics Interface Component Link a 29 Creating Features 3l Feature 242 4 mocheibqe amp eo d dat xl uec eno foro hes 31 Periodic Features srs eM Ies nudes d o rus de Pair Eeat re 1 op ted epo X 4 DO sue Se qp pO os cq 30 Feature inks 42 02 ROSA gem agate a a wee Rau t uua Multiphysics Feature 2 2 a a ww 38 Contained Feature 2 2 1 2 8D Device Model Feature 2 2 ll l c 39 Feature Attributes 8 CONTENTS 3 4 CONTENTS Creating Properties Property Property Link Creating User Inputs Introduction to Creating User Inputs User Input User Input Group Material Property Feature Input Material List Ac
210. x in the Description edit field Type q in in the Symbol LaTeX encoded edit field Select Inward heat flux W m 2 from the Physical quantity list Keep the default settings in the Levels Single and Size Scalar lists for a basic scalar quantity Also leave the Allowed values setting to Any for an entry of a general scalar number Type 0 in the Default value edit field Leave all other default values Right click the User Input node and select Variable Definition a This user input then becomes available as a variable tee qin in for example the predefined expressions for results evaluation You can also refer to gin directly in the weak equation Leave all other settings at their default values Now define a Section in the settings window for the boundary condition Right click the Feature 5 HeatFlux node and select Inputs gt User Input Group P In the settings window locate the Declaration section Type HeatFluxSection in the Group name edit field Type Heat Flux in the Description edit field Add User Input qin to the Group members list Use the button to get a selection list of available user inputs 162 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES 10 Locate the GUI Options section Change the GUI layout to Group members define a section Now define the weak equation Il Right click the Feature 5 HeatFlux node and select Weak Equation P In the settings window locate the Declaration s
211. xt Select the Add divider above the feature input check box to add the divider When selected you can enter the divider text in the Text field Designing the GUI Layout for more information about GUI options Materials in the COMSOL Multiphysics Reference Guide ol See Also Material List In the Model Builder most material properties get their values from the material assigned to the geometric entities overlapping with the selection of the feature instance As an option it is possible to add a Material List node P Any material property coupled to a material list makes it possible to choose among all materials added to a model See Material Property for information how to couple a property to a list For a feature instance in the Model Builder a list displays with the first option Domain material followed by all materials The Domain material option is identical to CREATING USER INPUTS 49 50 the original behavior without a list By choosing a specific material all material properties coupled to this list get the property values stored in that material independently of any selection MATERIAL LIST Specify the name of the material list in the Name field and the description in the Description field Similar to the Material Property and Feature Input nodes you can add extra list items apart from the automatically added ones Domain materials and list of materials in this case You can also remove the Domai
212. y you can clearly see which boundaries are insulated The last boundary condition sets the value of the heat flux in the direction of the boundary normal The heat flux boundary condition is implemented with a weak equation aovr B which is one of the terms in the complete weak form equation for the heat transfer part of the thermoelectric equations as seen earlier THE THERMOELECTRIC EFFECT 145 The following table summarizes all quantities relevant for the thermoelectric physics interface NAME DESCRIPTION SI UNIT SIZE GEOMETRY USER LEVEL INPUT k Thermal conductivity W m K Scalar Domain Yes sigma Electric conductivity S m Scalar Domain Yes S Seebeck coefficient VIK Scalar Domain Yes TO Temperature K Scalar Boundary Yes vo Electric potential Vv Scalar Boundary Yes qin Heat flux W m Scalar Boundary Yes T Temperature K Scalar Domain No V Electric potential V Scalar Domain No q Heat flux W m 3 by vector Domain No J Current density Alm 3 by vector Domain No P Peltier coefficient Vv Scalar Domain No E Electric field V m 3 by vector Domain No Q Joule heating Wim Scalar Domain No 146 CHAPTER 4 EXAMPLES OF CUSTOM PHYSICS INTERFACES Thermoelectric Effect Implementation In this section Overview Thermoelectric Effect Physics Interface Adding It Step by Step Overview To implement a physics interface for the thermoelectric effect you need to specify the following items The na
213. yntax This procedure is referred to as compatibility for the Model Object API Generally API migration is more complex to handle and there is situations when you cannot avoid breaking old Model Java files There are settings that you can change without any need for migration There are also settings that you cannot handle with migration at all for example if you change the PHYSICS BUILDER TOOLS list of supported space dimensions The table below summarizes some common changes and if you should consider migration for the change CHANGE OPERATION OPEN MODEL MIGRATION API MIGRATION Change type Yes Yes Rename input Yes Yes Remove feature No Not possible Remove input No Not possible Remove input group No No Change description No No Change expression No No Change icon No No Change symbol No No Remove supported space dimension Not possible Not possible Add supported space dimension No No Remove supported study types Not possible Not possible Add supported study types No No For the most common operations that do require migration you automatically get the proper migration operation included under the last version This only works if there is a version when you did the change Version Right click the Migration node to add a Version branch which contains migration operations from an older version to a newer version The old version is the current version at the time when the version node was created It t
214. you can collect nodes that define something specific that you need in several places or to group nodes together to avoid long lists of nodes under a physics interface The settings window does not contain any user settings only read only information sections These sections are identical to these sections for physics interfaces see Information Sections Selection Component With the Selection Component node 9g you create selections that you can use in defining other selections You can either link to a selection component directly or as part in a operation between selection such as a union intersection or difference Selection components can be referenced from other selection components or from any item that has a selection section For more information about specifying a selection see Specifying Selections Component Link Use a Component Link 4 to include all items defined within a component under the Building Blocks Components branch as if they were part of the feature containing the link see Creating Components The settings window of the component link contains the following additional section CREATING COMPONENTS 83 84 CHAPTER 3 SOURCE COMPONENT In the Links from list you choose where to look for a certain property Possible options are Building blocks Lets you choose among the components listed under the Components branch in the Building Blocks branch You choose the component from the
215. ysics interface Property option With the Property option you must also enter the type of the property that contains the user input in the Property field CREATING COMPONENTS 85 86 CHAPTER 3 For usage conditions under study solver defaults result defaults and mesh suggestion the By name option is the only way to refer to a user input so these nodes do have that choice Furthermore they can only refer to user input under a property so there is no such choice either Instead there is an option to choose the type of condition in the Condition on list The option User input in property enables the usage condition on a user input under a property With the option Feature is active the usage condition is true if there exists an active feature of a certain type You specify the type in the Feature type field As a final option you can select the Invert condition check box to invert the entire condition Equation Display With the Equation Display i node you can enter pretty print equations in LaTeX that shows up in the Equations section of a physics interface or feature in the Model builder Enter the La TeX encoded expressions in the Enter equation in LaTeX syntax field see Mathematical Symbols and Special Characters in the COMSOL Multiphysics Reference Guide for information about all available LaTeX symbols and commands There are a couple of tools that you can use to get assistance with entering specific LaTeX c

The COMSOL Multiphysics Physics Builder User's Guide

Contents

Download Pdf Manuals

Related Search

Related Contents