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Visualization Tools For 2D and 3D FEM

1. The strings Draw1 and Draw2 are the same as used in the Draw submenu 2 2 1 of the graphical user interface Each pair Drawx iDoFx selects a draw mode and a number of the degree of freedom to be displayed in this mode The logical argument decides if the color bar 2 2 6 is to be shown The mode Draw2 will overlay the first drawing Thus it should be something like grid or isolines or none if there is no overlaying draw e g call GrafSetQuiet Isol F 3 Isolin 1 FALSE Or call GrafSetQuiet Filled 1 none 0 TRUE The next call to one of the subroutines from Section 2 1 1 will execute that pre defined drawing without any interaction unless the user unlocks this quiet mode by pressing any key inside the graphics window in due time With both Draw1 and Draw2 set to none any previous quiet mode is finished and the next call uses interactive mode 2 2 User s Interface for 2D Visualization The visualization appears in an extra window together with the simple menu for interaction Fig 1 The initial display may be determined by the programmer iDoF Table 1 but the user may now select any options parts of the solution and display mode Furthermore it is possible to produce a postscript file for high quality printing We will now give a summary of the various menu options At the top of the window there is a menu bar with 6 entries from left to right these are pull down menu to sele
2. Npol Mnod Tldof i n k kn J Tj yj Zj description of response data identification string and description number of processors of the parallel machine where PFEM runs type information as in 3 3 3 number of polygons nodes and degrees of freedom per node polygons defined by node numbers for i 1 M a1 restricted to n 3 or n 4 coordinates of node 7 lor J Elia Ned Req ID 2 response data PFEMread 1 2 filename levels tt nproc type Nyol Tlnod Tldof jCOEDQ A H J Tj yj Zj 8 Ah EOF Ndof string l s String Ndof for 1 lt n lt naof PFEMread 1 3 k Urn for n 0 PFEMread 1 3 ae ani Uknaof for n lt 0 or n gt ndof PFEMread 1 3 Appendix description of response data identification string and description number of processors of the parallel machine where PFEM runs type information 3 for tetrahedrons 4 for hexahedrons number of volumes nodes and degrees of freedom per node volumes defined by node numbers for t 1 Nvo where type 3 im plies n 4 and type 4 implies n 8 coordinates of node 7 Oel acknoledgement for closing connection no response modification will affect next data transmission for request 0 1 or 2 number of components per node in the solution menu name for the first component max 6 characters each n argument of the request string identification string for PFEMdata n th component
3. 7 0 100000E 02 0 100000E 02 0 100000E 02 8 0 000000E 00 0 100000E 02 0 100000E 02 1 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 2 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 3 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 4 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 5 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 6 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 T 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 8 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 The data columns of the last section are the components of the computational solution u Ou Ou Ox Oy Oz For a tetrahedral mesh of the same cube we obtain similar files which differ only in the header and the first data section since vertices are the same e g Type 3 tetrahedra here u grad ul FFRead 1 0 3 6 8 5 32 3 3 User s Interface for 3D Visualization 11234 22154 31654 47134 57164 68674 1 0 100000E 02 0 000000E 00 0 000000E 00 2 0 100000E 02 0 100000E 02 20 000000E 00 3 0 000000E 00 0 100000E 02 0 000000E 00 4 0 000000E 00 0 100000E 02 0 100000E 02 5 0 100000E 02 0 100000E 02 0 100000E 02 6 0 100000E 02 0 000000E 00 0 100000E 02 7 0 000000E 00 0 000000E 00 0 000000E 0OO 8 0 000000E 00 0 000000E 00 0 100000E 02 1 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 2 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E
4. of L line 35 switches on the lighting effects of the program yielding a more realistic 3D impression of the pictures written to postscript files not on the screen display 3 3 3 Third User Interface for 3D File or Socket Refering to an example demonstrating the visualization of FEM data by means of the IRIS Explorer 17 on Silicon Graphics workstations we implemented an appropriate simple external file data structure as an interface to any external visualization program A header defines the type of data 2 faces 3 tetrahedra 4 hexahedra and the three counters number of elements number of nodes number of data values per node The data structures are either e volume structure a list of elements tetrahedra or hexahedra by node numbers or e face structure a list of all faces triangles or quadrangles as 3D polygons by node numbers or e surface a reduced list of faces only the surface polygons of the 3D domain each followed by a list of nodes k xz yz 2 and a list of data values for each node k fik Se Tby Loris Renggli Swiss Federal Institute of Technology Lausanne Switzerland 1993 23 3 Visualization of 3D Domains CONOOFRWNE PPRP RPP PPP BPWBWWWWWWWWWNONYNNNNNNNNNRPRP PRP RP RP RP RY RE o OoN DODOPWNHRF DOO NDAIPWNHRFODOODADAONODOOPWNHFODOOAOAN DA PWNHRrF Oo CO WwW Table 6 Example 2 of a user s dialog enter components of the view vector directed from
5. which requires a simple global sum of local results only We denote this as our classic FE data structure I Each finite element is defined by a list of references indices to the nodes belonging to it The list of elements is stored in an array parameter Vol in 3 2 1 Corresponding to the assembled matrix K or local matrices K we have a set of vectors for the degrees of freedom per node The nodes belonging to edges or faces of subdomain boundaries or more general of the coarse grid are placed within the list of all nodes as continuous chains defined by Ket1D Ket2D This placement requires a little bit more effort in mesh refinement but yields much less effort in communication 1 19 3 Visualization of 3D Domains 3 1 2 Element by Element Computation For adaptive mesh refinement in parallel computation it is very hard to rebalance the com putational effort by redistribution of the mesh If the matrices are assembled as described above it is almost impossible to rebalance without loss of information and restarting the assembly process for the whole mesh The better alternative is to keep element data together including the element matrix Ke as well as the element s right hand side In order to enable a quiet simple implementation of the redistribution of elements or clusters of elements among the processors it is convenient as well to keep nodes and corresponding degrees of freedom together However numerica
6. 1 0 dark Shsq 1 true def use a quadratic scale hhhhhhhhhh END OF PARAMETER SECTION Yhkkhhhkhh This section is what you can modify without being an expert in postscript writing The numerical and Boolean values in braces may be changed other text should stay unmodified In detail this means in the following lines Border Change true to false if you want no border line around the picture The border line has just the size of the bounding box Capt Change true to false if no text is to be displayed within the picture CaptText The caption text which is displayed at the bottom of the picture only if Capt true By default this is the name of the data file the user s coarse grid file the number of refinement steps levels and the number of processors that were used for computation You may change only the text inside the brackets CaptSize The text height which is specified in points pt Note however that this may be a relative value if the figure is scaled by includegraphics width or includegraphicsl height wGrd wBnd wIso Line width specified in points pt for the different kinds of lines in a picture grid lines boundary lines isolines The line width is also scaled by Nincludegraphics i cBnD cBnN cpat Define some special colors for boundary lines with Dirichlet bound ary conditions green by default or with Neumann boundary conditions red by defa
7. 333333343 16 2d x axis O 0r108 68 0 707106769 Q 17 2d y axis 0 235702261 0 235702261 0 942809045 19 grafische Darstellung jl n 21 Select new view point ENTER n or cut p lane p 22 Select component x y z d PIS 3D Box molvlie ENTER 24 distance from origin 0 25 normal vector screen gt eye 20 Us Us di 2 2d X axis L Os Us 28 2d y axis 0 1 30 grafische Darstellung jl n Any change of parameters is displayed in the auxiliary graphics window showing the bounding box as a cuboid in the current view coordinate system In the example we did not change anything Finally pressing the RETURN key causes the program to compute a 2D FEM data structure representing the projected 3D surface and calls gebgraf In line 19 we have to confirm that the result may be displayed in the graphics window Now we have the same interaction as described for 2D problems in Section 2 2 Finishing this 2D visualization clicking on goon returns to our simple 3D dialog having the alter natives shown in line 21 Typing p for plane or e for Ebene switches to the cutting plane mode The auxiliary window shows the bounding box from a default view point and the current position of the cutting plane upper left picture in Figure 7 The next line 22 is similar to linell described above Here we may specify the normal vector of the cutting plane and its distance from the origin Note that the normal vec
8. The program will refuse to overwrite an existing file You may press the Return key without typing a name to return to the graphics menu without opening a postscript file 4 Everything you draw to the screen from now on will also be written to the postscript file iie as vector graphic and with a higher resolution for the coordinates about 30000 x 30000 dots instead of a few hundred pixels on the screen Writing to the file takes a little bit more time than only drawing to the screen Preparing the output however may take much more time because of a slow optimization to reduce the size of the output file and speed up later loading times for the postscript file cf notes on OptFil p 14 5 Select Draw PSclos This is implicitly done if you select goon from the top menu How to use the postscript file The postscript file is written as in EPS format Thus it is easy to embed into BIFX e g usepackage graphicx begintcenter includegraphics width 0 6 linewidth mysolution end center An important row within the postscript file is that defining the bounding box It looks somewhat like this 37 4 Special Features 4BoundingBox 30 150 500 660 The includegraphics or epsfig command needs this bounding box to check the space to be reserved for the figure All the other data of the postscript file is only used by dvips Thus you can substantially improve the performance of the BIEX compile step if
9. below field of material indicators integer numbers for each volume elementk Scratch array length of scratch array counted in integer words error indicator a nonzero return value indicates an error no X server found to display 2 not enough memory on scratch array H 3 probably wrong parameter values 29 3 Visualization of 3D Domains 3 2 4 Subroutine out3dexpl call out3dexpl nDoF nVol mVol VolN nNode mNode nDoF nVol mVol VolN nNode mNode Node 1Umode Ket1D Ket2D H maxH Node U iUmode Keti Ket2 H maxH number of components of the solution degrees of freedom per node number of volume elements number of nodes per volume element 4 10 8 20 or 27 volume elements listed by node numbers Integer VolN mVol nVol total number of nodes leading dimension of the array Node coordinates of the nodes Real Node mNode nNode components of the solution double precision real stored as an array of vectors either nDoF vectors of length nNode one per component of the solution Or nNode vectors of length nDoF one per node indicates the storage scheme of the field of solutions iord 1 means U nDoF nNode and iord nNode means U nNode nDoF boundary edges boundary faces see notes on page 21 Scratch array length of scratch array counted in integer words The purpose of this program is to write one of three different data s
10. contents of the window specified by GrabInit and wait for a response by xxgrab that allows to use that window for output again The filename sequence number is increased by 1 Known bugs Overlapping the graphics window by another window will result in bad contents of the grabbed image Although the program automatically raises the window to the top just before grabbing it could happen that you were faster with the mouse If the graphics window is not completely on your screen i e partially outside the screen borders or iconified then xxgrab may crash without any possibility to restart and reconnect to the same running program on computer call grabimagenr nr This is an alternate call similar to grabimage but you can specify your own sequence number nr as an integer value e g the number of the time step or any other indication of the real simulation time call grabdone Close the connection to xxgrab if no more grabimage is to be done The program xxgrab is terminated by this signal What do you have to do to generate a video sequence A 4 Special Features On compute server A you must run your program which contains something like this include include Grafics inc C initialize the graphics window connect to your X server call ginitx 0 IER if IER NE 0 goto no X server found DO lt for all time steps gt C C compute your solution C P call firegraf and display it if
11. first loop gt then call grabinit han IER han comes from Grafics inc endif if IER EQ 0 call grabimage ENDDO On computer B you should change to an empty directory where you want to place all the grabbed images and from here you start the program xxgrab On your desktop C you may control everything After you have selected all parameters in your graphics window that is displayed by the call of firegraf you should select Option Quiet and sit and enjoy what happens for the next hours or days When you have finished because you lost your patience or your compute server crashed or you are pleased with the result stop the quiet mode by pressing any key in the focused graphics window or at any time in between you can use xanim gif amp to view the animation of the stored sequence of images You may also use animate from the ImageMagick package 16 Finally you may learn how to use mpeg encode 13 or other tools to generate MPEG or Quicktime movies Suitable tools for producing animated GIF files are e g gifmerge 15 or gifsicle 4 3 More Realistic 3D View 27 6 999 There are at least two effects to improve the reality of a 3D plot by giving an impression of space depth e foreshortening for a realistic perspective view e light and shadow to give more feeling for angles and directions in 3D Both of them are implemented in our graphics interface 42 4 3 More Realistic 3D Vie
12. for postscript output The file name has to be entered in the console window where the program was started from After opening this file you have to redraw everything you want to see in your postscript picture Note that one postscript file will contain only one image written as EPS encapsulated postscript If you need multiple pictures you will have to close the first file and open a new one Once a file has been opened the menu entry will be changed to PSclos The postscript file will be closed explicitly by selecting PSclos or automatically by selecting to leave the graphics window interaction More details on writing and using postscript files are given in section 4 1 2 2 2 The Submenu The first entries of this submenu are taken from the parameters supplied by the user defined subroutine getdofs p 2 As mentioned above the menu list given by getdofs will be terminated by an entry interpreting the first two components as vector T wo more entries may be added by the graphics subroutine itself Display the 2D element in colors corresponding to their element size This may be useful for adaptive mesh refinement only Display materials in different colors This menu item appears if the program gebmgraf was called with an additional vector of material indices Display subdomains from different processors in different colors This menu item exists if the program is running on a parallel machine 2 2 User s Interface for 2D Vi
13. screen plane to viewer specify a positive distance for a perspective view current state nx 1 000 x 0 00 3 00 ny 1 000 y 0 00 3 00 nz 0 500 zZ 0 00 3 00 d 0 000 Select x y z d M C L R P S 3D Box H elp N o Q uit c Define clipping planes planes so far 0 n new plane n normal vector lt x y z gt pointing into the half space to be cut off lt 0 0 0 gt and distance from origin x y z d 1 0 0 1 5 Define clipping planes planes so far 1 remove this plane No normal vector distance 1 1 0000 0 0000 0 0000 1 500 n new plane or index of plane to be modified n normal vector lt x y z gt pointing into the half space to be cut off lt 0 0 0 gt remove this plane and distance from origin x y z d 0 1 O 1 5 Define clipping planes planes so far 2 No normal vector distance 1 1 0000 0 0000 0 0000 1 500 2 0 0000 1 0000 0 0000 1 500 n new plane or index of plane to be modified Each plane defines a half space You may choose to cut off the intersection or the union of those half spaces I U i Select x y z d M C L R P S 3D Box H elp N o Q uit L lighting effects switched on enter components of the view vector directed from screen plane to viewer specify a positive distance for a perspective view current state nx 1 000 x 0 00 3 00 ny 1 000 Vie 0 00 3 00 nz 0 500 2 0 00 3 00 d 0 000 Sel
14. support In 10 we discussed two models for graphical output from a parallel computer where either the parallel computer or a graphical workstation executes the major part of postpro cessing This manual considers mainly the first kind i e preparing all data in parallel and then transmitting pixel data to the user s workstation We assume that at least standard X library calls are available to the parallel program An approach to use the second model with a 3D visualization tool based on GRAPE 12 was implemented and is described in 7 As another external viewer we can use the IRIS Explorer 17 in the same way A first version of the X11 based approach for 2D visualization can be found in 9 Mean while this graphic tool has been updated and is also used as a kernel for an X11 based 3D visualization Therefore it is appropriate to give a new survey of the current state Note that by default this paper is old For more recent updates refer to http www user tu chemnitz de pester graf2d updates html l There will be always differences between low cost and high performance computers but on another level after some years 2 Visualization of 2D Domains 2 Visualization of 2D Domains lhis part of the visualization package is intended to supply a simple graphical interface for 2 dimensional finite element data structures Furthermore it is used as the low level interface for certain 3D graphics see Chapter 3 This graphic
15. the elements in sequence instead of ordering the polygons by colors This depth sort method should be used for non convex solids to obtain a better representation of hidden surfaces Figures 17 and 16 For convex solids this method is unnecessary However for parallel computations there was not implemented any global comparison between subdomains to decide which faces are visible Each processor operates on its local subdomain only Thus an absolutely correct handling of visibility may be expected either for a convex solid or if the program runs on a single processor Smoothening of the Surface by Light Effects The previously described method to show light effects is related to faces i e each face has a constant brightness 5o one may identify each patch of a curved surface by its own color Figure 18 But the user may define a special degree of freedom Then this value is related to nodes and may be interpolated across the faces yielding a very smooth view of the surface Shadows On a Colored Surface As shown above the light effect of our graphics programs give a nice view on the screen for a grayscale Moreover those shadows may overlay the colors that represent any numerical solution on the surface Figure 20 But this is implemented only for postscript output the screen colors are always fixed and have no overlaying shadows 45 References References H A6 T Apel G Haase A Meyer
16. will be clipped It is intentionally not scaled to window size in order to have a real comparison with the undeformed mesh Draw a 3 dimensional view of the grid with the solution selected from the DoF submenu giving the height of the grid points If this drawing mode is selected there appears a little coordinate system in the upper left corner of the window Clicking this coordinate system will allow to change the viewpoint by rotating via x y or z axis press the corresponding key and shift key for backwards Other keys are available for manipulating the viewpoint u v w p 0 1 2 3 h try it ESC will 2 Visualization of 2D Domains reset to the previous view RETURN will accept You must redraw your current solution explicitly to apply the new viewpoint Draw isolines of the current component of the solution The background is not changed so you can draw different things in the same picture Before drawing the number of isolines can be changed in the Param submenu 2 2 4 LinLvl The color of isolines is blue by default and may be changed in the Param submenu 2 2 4 LinCol Draw contours of the domain filled with standard color white or black and isolines as in the previous menu point Option Isolin p 14 Filled Fill the domain with colors of the current palette corresponding to the current component of the solution Coloring is done by linear interpolation between the grid points Open a new file
17. 00 0 10000E 00 3 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 4 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 5 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 6 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 7 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 8 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 Such data files may be postprocessed by any separate tool possibly after reformatting the file structure or adapting an input module As an example we used the IRIS Explorer 17 which includes a lot of postprocessing modules to be placed connected and controlled on a graphical desktop Figure 9 shows an example where the module placed in the upper left corner of the map editor is used to read a data stream similar to the contents of the data file directly from the FEM program via internet socket The subroutine out3dexpl will use the socket data stream if the user specifies the single character as filename for data output In this case the program will function as server i e waiting for requests from any client to get data The subroutine out3dexpl returns to normal computation mode after the client s request to continue In the follow ing PFEM denotes the parallel FEM server functionality which is realized by the subroutine out3dexpl as described in Section 3 2 4 The user interface for the Explorer visualization is determined by various modules Ther
18. 1 0 4 1 12345673 000000E 00 100000E 02 100000E 02 000000E 00 000000E 00 100000E 02 100000E 02 1 1 2 3 4 5 6 T 8 000000E 00 1 2 3 095 O 0 O 0 0 09009 oOo OOOO ooo 8 5 000000E 00 0 000000E 00 000000E 00 0 000000E 00 100000E 02 0 000000E 00 100000E 02 0 000000E 00 000000E 00 0 100000E 02 000000E 00 0 100000E 02 100000E 02 0 100000E 02 100000E 02 0 100000E 02 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 ol 3 Visualization of 3D Domains 4 0 00000E 00 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 5 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 6 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 7 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 8 0 10000E 01 0 00000E 00 0 00000E 00 0 10000E 00 0 10000E 00 The header is followed by a single line describing the only hexahedron by its node num bers 8 lines with node coordinates and further 8 lines with data values for each node Type 2 3D polygons FERead 1 0 2 6 8 5 141234 24567 8 341265 442376 543487 644153 1 0 000000E 00 0 000000E 00 0 000000E 00 2 0 100000E 02 0 000000E 00 0 000000E 00 3 0 100000E 02 0 100000E 02 0 000000E 00 4 0 000000E 00 0 100000E 02 0 000000E 00 5 0 000000E 00 0 000000E 00 0 100000E 02 6 0 100000E 02 0 000000E 00 0 100000E 02
19. 16 ey RE aco identification string for PFEMdata all components node by node lor oes eos T only acknoledgement no data 49 Index Index A animate 40 42 B BOUNd sus essen 0 7 14 C color bar 15 Color menu 6 10 COlOTS s 9o T 11 15 D deformation o i DoF menu 6 8 Draw menu 6 14 draw3d 21 20 E Elast 129 294 2339 13 element size 8 epstopdf auesee domo a 39 F Filled 8 14 firegraf 2 19 42 G GCPowerPlus 2 gebgraf 144524509 es 2 15 getdofs 2 4 0 28 gifmerge 42 EIFSICHE unse dese s 42 GrafSetQuiet 5 I Infos 2 oducaoeeroae os 14 IDLELTUPE so v2 99 39 ace 16 IRIS Explorer 28 LSOI F 13222433 933093 8 90 ISOIiN 22225433253 8 14 isolines 8 11 L BIPX oceanus cessos 39 lighting 11 27 28 45 LinGGl 4242 22 99 11 EAI i e oe oe 93 33 13 a 2 02 2199 as 200 R3 11 M material gegen 4 os 8 N NO DD ss una gua ee ar 7 11 NO UD 23222 5 299 ue u l NStH oe eos eoe vitres d 4 O o3dgraph 23 28 OpenGL 1 OptFil 14 15 37 Option menu 6 13 out3dexpl sie 24 30 P palette B I0 11 15 Param menu 6 11 Palch 66 b606 0 662 15 45 POP susanne 39 perspective 45 postscript 6 8 10 14 15 37 processors lr 8 DEOGS 235 3
20. Any action of xxgrab is invoked by a signal from the program on the compute server A T herefore a small package of subroutines is available to be used in your parallel program If the program is running as a real parallel application only one processor has to call those subroutines call grabinit iwin ierr Open a socket connection from computer to computer B where the program xxgrab must already run at this time xxgrab acts as server to which grabinit may connect lhe parameter iwin is the handle of the graphics window managed by your X server see 5 If B and C are different computers you will be prompted for the hostname or internet address of computer B at this point written by Michael Seibt AQ 4 2 Video Sequences A compute server B single computer socket firegraf xxgrab DISPLAY DISPLAY C user s desktop console X server Figure 15 Configuration scheme for saving image sequences call grabname call grabsetname string grabname is automatically invoked by grabinit but may be called explicitly at any time to change the filename A call to grabname will ask the user to type in the base of a filename and grabsetname defines the character argument to be this name The name is send to xxgrab The program xxgrab will extend this filename by a 4 digit sequence number and a file extension gif call grabimage lell xxgrab to grab the current
21. Appendix Socket Interface for IRIS Explorer This is a short description of the internal protocol used for socket communication between out3dexpl and the interface modules PFEMread and PFEMdata Section 3 3 3 Messages are sent as packages of varying size either as ASCII strings or in binary mode One package is organized in this way oa dde ooo The data part may consist of multiple logical partitions separated by a delimiter After establishing the connection by a client the server accepts any request message Requests may have the following data format request ID arguments description of the request OLB send surface polygons 1 B send all face polygons 2 B send volume elements 3 go on finish server mode 4 S e set shrink and explode parameters 0 lt s lt 1 1 e lt 2 for subdomains 6 send names for each component of the solution to be placed in the pull down menu of the module PFEMdata 9 B n send data vector for the n th component of the solution where n 0 means all components The optional extension B in the request code indicates to open an extra binary socket for data response which is much faster than ASCII conversion and transfer 48 The server responds to those requests sending the following data the character is used for ASCII streams as a delimiter between certain blocks of information Req ID 0 1 response data PFEMread 1 2 filename levels tt nproc it 2 t
22. B 393 TU Chemnitz SFB 393 TU Chemnitz default mode patch mode SFB 393 TU Chemnitz SFB 393 TU Chemnitz Figure 5 Two examples for drawing in default or patch mode Net 3D for a 2D domain and Net 2D for a 3D surface SFB 393 TU Chemnitz SFB 393 TU Chemnitz S AIN krei2 Level 3 4 proc krei2 Level 3 4 proc Figure 6 Difference of OptFil 1 left and OptFil 2 right where erroneously inner areas are filled if their bound ary is completely inside one processor 17 2 Visualization of 2D Domains J i N N a j N M A p Sy i w f N H w qd IN f Ar L cce A cp zu e ERN S BE Lr d me Em E ey SS n cec ie SQ EE N LL URS cud ja Bek Figure 7 Projection of 3D vectors left displacement vectors in a cut plane right surface plot with scaled 2D projection u u of displacement uz Uy Uz added to the projection of node coordinates above auxiliary display of cut plane and bounding box 1 23E 04 SFB 393 TU Chemnitz 3D Clip Plane DO X I I I I Z E 1 23E 04 z20dr Level 3 ux Figure 8 Cut off the intersection of two half spaces 18 3 Visualization of 3D Domai
23. EHE TECHNISCHE UNIVERSITAT CHEMNITZ Sonderforschungsbereich 393 Parallele Numerische Simulation f r Physik und Kontinuumsmechanik Matthias Pester Visualization Tools for 2D and 3D Finite Element Programs User s Manual Preprint SFB393 02 02 Update Version October 4 2005 More options for displaying tensors 2 1 3 2 2 4 Pre define some default values 2 1 4 Non interactive switch to quiet mode 2 1 5 Completed description of x3dgraph 3 2 2 Fixed errors in example for grabimage 4 2 Lost example reinserted Table 4 Preprintreihe des Chemnitzer SFB 393 ISSN 1619 7178 Print ISSN 1619 7186 Internet SFB393 02 02 January 2002 Contents 1 Introduction 2 Visualization of 2D Domains zt 2 2 Programmer s Interface for 2D Visualization 2 1 1 Invoking Graphics Display 2 1 2 Specify Menu Names for the Degrees of Freedom 2 1 3 Options for Displaying Tensors 2 1 4 Define Parameter Defaults Jo Non interactive Drawing s oe soa ew eee xo eom xo m ox s er s Interface for 2D Visualization d Su bmemi Draw lt adasa eed niad RHE 8 3e RO RR ER 2 P bMEn DoF x 2 u rasana sa D rai eee i pene MS E eee eS A SubmenuParam nn rennen UMC Option 232964599 o9 9 amp X OHH HS b Spesa Elegis ux 09x99 a RO OR ana ike a DDDDDMNA 3 Visualization of 3D Domains 3 1 Notes on Finite E
24. February 2002 W Dahmen H Harbrecht R Schneider Compression Techniques for Boundary Integral Equations Optimal Complexity Estimates April 2002 S Grosman Robust local problem error estimation for a singularly perturbed reaction diffusion problem on anisotropic finite element meshes May 2002 M Springmann M Kuna Identifikation schadigungsmechanischer Materialparameter mit Hilfe nichtlinearer Optimierungsverfahren am Beispiel des Rousselier Modells Mai 2002 S Beuchler R Schneider C Schwab Multiresolution weighted norm equivalences and applications July 2002 Ph Cain R A Romer M E Raikh Renormalization group approach to energy level statistics at the integer quantum Hall transition July 2002 A Eilmes R A Romer M Schreiber Localization properties of two interacting particles in a quasiperiodic potential with a metal insulator transition July 2002 M L Ndawana R A Romer M Schreiber Scaling of the Level Compressibility at the Anderson Metal Insulator Transition September 2002 Ph Cain R A Romer M E Raikh Real space renormalization group approach to the quantum Hall transition September 2002 A Jellal E H Saidi H B Geyer R A Romer A Matrix Model for vi i Ehe Fractional Quantum Hall States September 2002 M Randrianarivony G Brunnett Parallel implementation of curve reconstruction from noisy samples August 2002 M Randrianarivony G Brunnett Parallel implementat
25. U Chemnitz crank pure colors for u crank shaded colors for u Figure 20 Pure colors for a solution left and overlaying shadows right 44 4 3 More Realistic 3D View Perspective View The user interfaces described in Sections 3 3 1 and 3 3 2 have an option to select both the direction x y z and the distance d of the viewer s position The default distance d Q0 is used for parallel projection of the 3D object to the screen plane A positive value of d indicates a perspective projection in Figure 19 d 8 for an object of size 1 The distance should be selected large enough to place the viewer outside the object to be viewed The prompt for the selection of d includes a suggestion for a minimum value A very large value for d will approach the parallel projection again Light Shadow and Visibility In the Sections about the user s interface for 3D we shortly mentioned the option L for lightening the object This effect may be switched on and off by entering this option successively If switched on the behavior of this option is the following e For each 2D polygon projected face of the 3D object there is stored a ma terial value for brightness which can be displayed as described in Section 2 2 2 DoF Mater The best impression will be obtained chosing Gray from the color menu 2 2 3 e The 2D elements are sorted by space depth Hence the option Patch 2 2 5 may be selected to draw
26. U N nDoFs then the i th eigenvector of node j is U j kj UGj k 4 D UCj ki 22 For idim 2 the value of k3 may be considered as dummy argument ii i2 i3 color indices corresponding to the 3 vectors to be displayed in that colors The following color indices may be recommended 0 grid line color white or black 1 background color black or white just for fun 2 red 3 green 4 blue gt 105 color corresponds to the magnitude can be modified using the interactive user interface The following subroutines may be used alternatively call setu2xabs scale call setu2xrel scale where scale is a REAL argument defining the absolute or relative scaling factor respectively The initial default is setu2xrel 5 0 This factor is used for displaying a deformed mesh Net U The meaning of scale is explained with the Param submenu entry Elast More such routines will be available on demand 2 1 5 Non interactive Drawing Usually a call to gebgraf gebgrafm or firegraf will switch to the graphical user inter face and wait for user s action However the user interface includes an option Quiet to continue drawing without interaction in subsequent calls The following subroutine allows the programmer to initiate this Quiet Mode without any previous interaction Subroutine GrafSetQuiet Draw1 iDoF1 Draw2 iDoF2 ShowBar Character 6 Drawi Draw2 Integer iDoF1 iDoF2 Logical ShowBar 2 Visualization of 2D Domains
27. al solution DoFs 4 u if act 3d2d then DoFs 1 u_xE I vectors transformed to screen coordinates DoFs 2 u_yE DoFs 3 u_zE 10 4 nDoFs nDoFs 3 endif DoFs 1 i0 u_x vectors in original coordinates DoFs 2 i0 2 u y DoFs 3 i0 2 u_z if not act 3d2d or act o3d 1051 DoFs 4 i0 sig_11 stress tensor values if computed DoFs 5 i0 sig_22 DoFs 6 10 sig_33 DoFs 7 i0 2 sig 12 DoFs 8 i0 sig 23 DoFs 9 i0 sig 13 DoFs 10 i0 sigl nDoFs 10 10 endif if NDF GE 3 AND act 3d2d OR act o3d then nDoFs nDoFs if act_o3d then DoFs nDoFs entry is useless for 3D else DoFs nDoFs vector first 2 components as 2D Vektor endif endif END 26 3 3 User s Interface for 3D Visualization the screen Figure 7 Thus in the 3D case the 2D operation Net U makes sense only for such a vector mapping Finally we have a short schematic view on the calling hierarchy of the programs 3D FEM program 3D FEM program EN data structure data structure II out3dexpl socket ac aa gebmgraf ac aa graphics library Amm e l 3 3 User s Interface for 3D Visualization 3 3 1 First User Interface for 3D Surface or Intersection This was our first implementation of a 3D visualization frame around the 2D visualization program based on the classic FEM data structure I page 19 If the pro
28. and M Pester Parallel solution of finite element equation systems efficient inter processor communication Preprint SPC 95 5 TU Chemnitz Zwickau Februar 1995 file ftp tu chemnitz de pub Local mathematik SPC spc95 5 ps Z 19 21 T Apel and U Reichel SPC PM Po 3D V 3 3 User s Manual Preprint SFB393 99 06 TU Chemnitz February 1999 http www tu chemnitz de sfb393 Files PS ssfb99 06 ps gz Thomas Apel Frank Milde and Uwe Reichel SPC PM Po 3D v 4 0 Programmers manual II Preprint SFB393 99 37 TU Chemnitz December 1999 http www tu chemnitz de sfb393 Files PS ssfb99 37 ps gz 19 21 U Groh Lokale Realisierung von Vektoroperationen auf Parallelrechnern Preprint SPC 94 2 TU Chemnitz Zwickau M rz 1994 file ftp tu chemnitz de pub Local mathematik SPC spc94 2 ps gz 19 M Pester Bibliotheken zur Entwicklung paralleler Algorithmen Basisroutinen f r Kommunikation und Grafik Preprint SFB 02 01 TU Chemnitz Januar 2002 updated from SPC 95 20 http www tu chemnitz de sfb393 Files PDF sfb02 01 pdf 40 M Meisel and A Meyer Kommunikationstechnologien beim parallelen vorkondition ierten Schur Komplement CG Verfahren Preprint SPC 95 19 TU Chemnitz Zwickau Juni 1995 file ftp tu chemnitz de pub Local mathematik SPC spc95 19 ps gz 19 M Meyer Grafik Ausgabe vom Parallelrechner f r 3D Gebiete Preprint SPC 95 4 TU Chemnitz Zwickau Januar 1995 file ftp tu chemnitz de pub Local mathematik SPC spc95_4
29. at different time the same color means the same value lhis menu entry yields a textual interaction in the console window The user may change parameters for the Net U display deformed grid You may choose to set a relative or an absolute scaling factor for deformation display A relative factor r means that the maximum displacement of all nodes is scaled to ber of the maximum expansion of the domain with the exception that r 100 means original deformation as supplied by the computational solution An absolute factor a means that the deformation is displayed a times the real value i e a 1 0 is the true deformation In this menu you may also select any two of the components of the solution DoFs to be interpreted as horizontal and vertical components of a displacement vector components 1 and 2 are used by default This interaction allows to change some parameters for the appearance of tensors to be displayed refer to Section 2 1 3 The user may select between line or arrow display choose different colors or set a new length scaling factor for Zoom into the picture Left click on a first point in the window The mouse pointer will change its shape and show a rectangle Move the mouse to a second point and left click again to select the rectangle for zooming in Right clicking will terminate the interactive zoom selection and switch to the textual mode where you can enter the world coordinates of a center point x y and a radi
30. ct the display mode 2 2 1 The selected mode is performed immediately pull down menu to select the component of the solution which is to be displayed by the next draw command 2 2 2 pull down menu to select one of various predefined color palettes 2 2 3 pull down menu to set various parameters for drawing modules 2 2 4 pull down menu to set or switch some additional options 2 2 5 leave the interaction and return to the program 2 2 1 The Submenu Select a display mode Clear the graphics window and repeat the previous drawing with possibly changed other options e g line color colormap scaling selected component 2 2 User s Interface for 2D Visualization Draw only the boundary of the subdomains There is an option 2 2 5 to switch between drawing all boundaries of the coarse grid or only the boundaries of the current distribution of subdomains to the processors The color of the lines is green in the case of Dirichlet boundary conditions and red for Neumann boundary conditions Note We assume the information on boundary conditions to be stored in the node field Nod as a bit mask indicator in the third entry behind the coordinates r and y If this information is not stored this display mode has no output Draw the current mesh In general the grid lines are drawn in a standard color white or black However if is selected from the DoF submenu the grid lines are colored according to the processor number an
31. d for the grid line colors correspond to the material numbers Draw small vectors in each grid point This menu entry replaces the previous one as long as the vector solution is selected from the DoF submenu the last entry which is supplied by the subroutine getdofs p 4 in the case of more than 2 components This menu entry appears alternately with the next one as selected from the Option submenu p 14 Draw small orthogonal crosses in each grid point corresponding to the eigenvector directions of a tensor solution if one of the 2 eigenvectors is specified as a vector solution It is also possible to specify all eigenvectors i e 2 or 3 for 2D or 3D graphics with different lengths to show some kind of ellipticity For details refer to Section 2 1 3 This menu entry replaces the Net 2D one as long as the vector solution is selected from the DoF submenu the last entry which is supplied by the subroutine getdofs p 4 in the case of more than 2 components This menu entry appears alternately with the previous one as selected from the Option submenu p 14 Show the deformation of a mesh by adding the displacement vectors to the node coordinates and displaying the grid The line color is the same as for isolines see below and may be selected from the Param submenu entry LinCol The scaling for the deformation may be changed by the Param submenu entry Elast p 13 Note that a large scaled deformation may exceed window bounds and
32. e are two separate modules written for the IRIS Explorer to work as client with the PFEM server PFEMread Establish a connection to PFEM host address of the server is input for this module There are several buttons Fig 10 where the user may select one of three modes to request the 3D FEM mesh polygons of the surface only polygons of all faces or volume data of tetrahedrons or hexahedrons or go on to close the server connection and finish the server mode of out3dexpl The shrink and explode options are related to the subdomains to visualize the domain decomposition on the parallel computer For shrinking of single elements there is a standard module available from the Explorer module library 33 3 Visualization of 3D Domains Figure 9 The Map Editor of the IRIS Explorer PFEMdata This module presumes the module PFEMread to have already received the mesh data as well as the number and names of the data components available on PFEM In the map editor the corresponding output and input links of PFEMread and PFEMdata must be connected The user may choose to receive one particular component of the solution or all components at once Another module may be connected for data arising from elasticity problems PFEMelast Suitable for a solution where the first three components are x y and z components of a displacement to be added to the coordinates of the grid points The user may vary a scaling factor to visualize the dis
33. e a little sub routine that is called by the graphic program This little subroutine getdofs is intended to define the number of components in the solution vector field U and the names of each component to appear in the DOF menu 2 2 2 of the graphics window The program has to return two parameters call getdofs nDoF Dofs nDoF number of components that can be displayed see notes below DoFs the names of all the components in an array character 6 DoFs nDoF i e 6 characters for each name for C programmers we are using Fortran strings i e by default the strings are not NO terminate 2 1 Programmer s Interface for 2D Visualization Table 1 Parameters of the 2D graphics subroutines gebgraf iDoF nEL ne EL nNod Nod U W gebmgraf iDoF nEL ne EL nNod Nod U Mat W firegraf iDoF nEL ne EL nNod Nod U Xi W iDoF preselect one component of the solution vector to be displayed by default iDoF 0 means that the field U contains no data and the program will only allow to draw the grid nEL number of elements of the local finite element mesh ne number of nodes per element the program supports 3 and 6 node tri angles and 4 8 or 9 node quadrilaterals EL integer array in Fortran EL ne nEL of the node numbers for each element nNod number of local nodes of the grid Nod single precision real array in Fortran Nod idim nNod containing x y coordinates and possibly mor
34. e information for each node of the mesh generally the field dimension idim is 3 but might be changed globally by a common variable U components of the solution double precision real stored as an array of vectors one vector of length nNod for each component degree of freedom of the problem solved i e in Fortran this field is U nNod nDoF where the number nDoF and the names of the various components are obtained from a user supplied subroutine named getdofs see below Mat integer array of length nEL containing one number index of material for each element Xi double precision vector of length nNod containing the values of the stream function used by a program for flow simulation W scratch field of sufficient size this is used to store all the computed pixel data which may be essentially more than the list of nodes Single precision is sufficient for visualization but with respect to adaptive mesh refinement this may be changed to double precision in future versions This is buggy since nobody knows before what is sufficient A new version of the program should use an additional parameter indicating the available size on W to avoid crashing by memory lack 2 Visualization of 2D Domains lable 2 For firegraf some components have to be arranged in a special order 1 nDoF 3 arbitrary components with velocity x y as fields 1 and 2 nDoF 2 pressure the last field of the array U however wi
35. ect x y z d M C L R P S 3D Box H elp N 0 Q uit 1888 boundary faces visible grafische Darstellung jl n 3 3 User s Interface for 3D Visualization Table 7 Contents of a data file for external postprocessing line s contents 1 identification string PFEMread 1 0 2 type information an integer value 1 2 3 or 4 where 1 2D polygons 2 3D polygons faces surface plot 3 tetrahedra 4 vertices each 4 hexahedra 8 vertices each 3 np nv nd 3 integers where np number of polygons or polyhedra nv number of vertices nd number of data values per vertex 4 np 3 first data block containing polygons or polyhedra 1 per line polygons i n v Vn n 3 or 4 tetrahedra i v4 v4 tetrahedra i v4 Vg where i index of polygon polyhedron v indices of vertices np 4 second data block containing vertices 1 per line nptnv 3 ix y z index and 3D coordinates for type 1 only i x y nptnv 4 third data block containing data values related to vertices np 2 nvt3 i fi x Zug The general format of the file is given in Table 7 As an example consider simply a cube consisting of only one hexahedral element The program out3dexpl will offer to select which type of data file should be written the complete hexahedra tetrahedra mesh otherwise all faces as 3D polygons or only the polygons of the surface 5o we may obtain one of the following data files Type 4 hexahedra FERead
36. erial Face mFace nFace iBound mBound Edge mEdge nEdge Node mNode nNode H maxH IER nDoF number of components of the solution per node mFaceInVol number of faces per volume element 4 or 6 nNodeInVol number of nodes per volume element 4 10 8 20 or 27 VolF volume elements listed by face numbers Integer VolF mVol nVol VolN volume elements listed by node numbers Integer VolN mVol nVol mVol leading dimension of the arrays VolF VolF nVol number of volume elements iMaterial index of the material indicator such that VolF iMaterial k isa number refering to the material description of volume element k Face faces listed by their bounding edges obviously the number of edges per face is 3 for tetrahedra nFaceInVol 4 or 4 for hexahedra nFaceInVol 6 Integer Face mFace nFace mFace leading dimension of the array Face nFace total number of faces iBound mBound index and bitmask for a flag word such that IAND Face iBound k mBound is mBound if face k belongs to the boundary of the domain and zero for inner faces Edge edges listed by node numbers this program expects to find starting and ending point of an edge as the first two entries further entries e g a middle point are ignored Integer Edge mEdge nEdge mEdge leading dimension of the array Edge nEdge total number of edges Node coordinates of the nodes Real Node mNode nNode containing for each node z y z u1 Undof mNode
37. gh performance 3D graphics program 3 3 3 The user interfaces will be discussed in Section 3 3 First consider the interfaces at the pro grammer s side The following subroutines are available for the appropriate applications data user parameter subroutine structrue interface description draw3d 1 1 3 2 1 x3dgraph II 2 GN o3dgraph T 2 3 2 3 out3dexpl LII 3 3 2 For parallel programs the parameters of those subroutines refer to the local subdomain on each processor 20 3 2 Programmer s Interface for 3D Visualization 3 2 1 Subroutine draw3d call draw3d nDoF nVol nNode Node Vol U NodesInVol W LngW KetiD Ket2D Mat nDoF number of components of the solution in each node including ad ditional values such as derivatives tensors nDoF 0 means that the field U contains no data and the program will only allow to draw the grid nVol number of elements of the local finite element mesh nNode number of local nodes of the grid Node single precision real array in Fortran Nod idim nNode con taining z y z coordinates and possibly more information for each node of the mesh generally the field dimension idim is 3 but might be changed globally by a common variable Vol list of finite elements each defined by nVol node numbers i e the array is Integer Vol NodesInVol nVol U components of the solution double precision real stored as an ar ray of vectors one vecto
38. grammer decided to call the subroutine draw3d 3 2 1 the user will be prompted to select among some options for mapping the 3D data to the 2D screen Consider the following example Table B In line 1 we select s to get a surface plot Next in line 11 we could select to invoke one of the actions x y z change the specified component of the normal vector X Y Z rotate around the specified axis angle is requested d for d gt 0 you will get a perspective projection M rotate the view coordinate system by mouse dragging L switch on off some lighting effects for a more natural view S specify a scaling factor for adding computed elastic deformations P write a postscript file from the auxiliary window coordinate system v F create a sequence of views either rotating or scaling ENTER finish input call the 2D graphics program gebgraf 2f 3 Visualization of 3D Domains Table 5 Example 1 of a user s dialog 1 surface cutting plane quit sl p q s 2 Specify a normal vector from the plane towards the viewer 3 and a positive distance for perspective view 4 5 current view 3D bounding box 6 nx 1 000 x 40 00 165 00 7 ny 1 000 y 20 0 uu 29 97 8 nz 0 500 gu 50 00 50 00 9 d 0 000 10 11 Select component x y z d M L PIS 3D Box molvlie ENTER 13 distance from origin 0 parallel projection 14 normal vector screen gt eye 15 0 666666687 0 666666687 0
39. ion of surface reconstruction from noisy samples September 2002 M Morgenstern J Klijn Chr Meyer R A R mer R Wiesendanger Comparing measured and calculated local density of states in a disordered two dimensional electron system September 2002 J Hippold G R nger Task Pool Teams for Implementing Irregular Algorithms on Clusters of SMPs October 2002 H Harbrecht R Schneider Wavelets for the fast solution of boundary integral equations October 2002 H Harbrecht R Schneider Adaptive Wavelet Galerkin BEM October 2002 H Harbrecht R Schneider Wavelet Galerkin Schemes for Boundary Integral Equations Imple mentation and Quadrature October 2002 E Creus G Kunert 5 Nicaise A posteriory error estimation for the Stokes problem Anisotropic and isotropic discretizations January 2003 S I Solov ev Existence of the guided modes of an optical fiber January 2003 5 Beuchler Wavelet preconditioners for the p version of the FEM February 2003 5 Beuchler Fast solvers for degenerated problems February 2003 03 05 03 06 03 07 03 08 03 09 03 10 03 11 03 12 03 13 03 14 03 15 A Meyer Stable calculation of the Jacobians for curved triangles February 2003 S I Solov ev Eigenvibrations of a plate with elastically attached load February 2003 H Harbrecht R Schneider Wavelet based fast solution of boundary integral equations February 2003 S I Solov ev Precondit
40. ioned iterative methods for monotone nonlinear eigenvalue problems March 2003 Th Apel N D velmeyer Transformation of hexahedral finite element meshes into tetrahedral meshes according to quality criteria May 2003 H Harbrecht R Schneider Biorthogonal wavelet bases for the boundary element method April 2003 T Zhanlav Some choices of moments of refinable function and applications June 2003 S Beuchler A Dirichlet Dirichlet DD pre conditioner for p FEM June 2003 Th Apel C Pester Cl ment type interpolation on spherical domains interpolation error estimates and application to a posteriori error estimation July 2003 5 Beuchler Multi level solver for degenerated problems with applications to p version of the fem Dissertation July 2003 Th Apel S Nicaise The inf sup condition for the Bernardi Fortin Raugel element on anisotropic meshes September 2003 The complete list of current and former preprints is available via http www tu chemnitz de sfb393 preprints html
41. l operations have to be executed using the small matrices K which is more expensive but may have advantages with respect to cache utilization The most important advantage is to assemble new matrices only for new elements after an adaptive refinement step Denoting this as data structure II we may take advantage of some additional infor mation for our purpose of visualization Elements are defined by both lists of nodes and lists of faces Faces are given as lists of edges and edges by nodes Additional informa tion may be included in the lists e g a material indicator for each element or a flag for boundary faces 3 2 Programmer s Interface for 3D Visualization Since our quick and dirty visualization for 3D meshes is based on or reduced to the previously described user interface for 2D we have an additional interaction before calling the 2D graphics module This interaction may select a view point and or a clipping plane or other parameters At the moment there exist three different programming interfaces for the visualization of 3D FEM data They correspond to the two kinds of data structures of the previous section and three different user interfaces 1 The user may choose between surface and intersection cf 3 3 1 2 Only the surface is displayed but the user may clip away whole elements of a half space and display the surface of the remaining part of the domain cf 3 3 2 3 Data transfer to an external hi
42. leading dimension of the array Node nNode total number of nodes H scratch array maxH length of scratch array counted in integer words IER error indicator a nonzero return value indicates an error no X server found to display 2 not enough memory on scratch array H 3 probably wrong parameter values 6 VolF and VolN may be different entries of a contiguous field Vol mVol nVol where mVol gt nFaceInVol nNodeInVol 22 3 2 Programmer s Interface for 3D Visualization 3 2 3 Subroutine o3dgraph call o3dgraph nDoF VolN nNodeInVol mVol nVol nDoF VolN nNodeInVol mVol nVol Node mNode nNode U Mat maxH IER Node mNode nNode U Mat H maxH IER number of components of the solution degrees of freedom per node volume elements listed by node numbers Integer VolN mVol nVol number of nodes per volume element 4 10 8 20 or 27 leading dimension of the arrays VolF VolF number of volume elements coordinates of the nodes Real Node mNode nNode leading dimension of the array Node total number of nodes components of the solution double precision real stored as an array of vectors one vector of length nNode for each component of the solution degree of freedom of the problem solved i e in Fortran this field is U nNode nDoF where the number nDoF and the names of the various components are obtained from a user supplied subroutine named getdofs see
43. lement Data Structures 3 1 1 Assembled Matrices lll 3 1 2 Element by Element Computation 3 2 Programmer s Interface for 3D Visualization O l S bro tine OP soos ox ooo ow B RR HES oy isad 0 2 4 DUPONT XOdEPRDE ovo oum van UR nomo ROMS n Dod S Su broutine gJdgraph sss x s s asd ne bake wd an 3 24 Subroutine out3dexpl oss DIA 5 Subroutine getdofs for 3D problems 3 3 User s Interface for 3D Visualization 3 3 1 First User Interface for 3D Surface or Intersection 3 3 2 Second User Interface for 3D Surface and Clipping Planes 3 9 9 Third User Interface for 3D File or Socket 3 4 Additonal Tools Java Applets 4 Special Features Al Postsorptb LIB eoo ee x X wow Rok o dob a nn 4 2 Video Sequences uoce ob op eee ese hee me Be ee eg ben 4 3 More Realistic 3D View 2 0 0 ee ee References Appendix Index Author Matthias Pester Fakultat fur Mathematik TU Chemnitz D 09107 Chemnitz mailto pester mathematik tu chemnitz de 1 Introduction Visualization of numerical results is a very convenient method to understand and evaluate a solution which has been calculated as a set of millions of numerical values One of the central research fields of the Chemnitz Sonderforschungsbereich SFB 393 Numerical Sim ulation on Massively Parallel Computers is the analysis of parallel nume
44. lutions This will change the corresponding menu entry in the Draw submenu 2 2 1 OptFil Select an optimized way to draw the coloring of the domain 2 2 1 Filled 14 By default for each small triangle or quadrilateral a set of polygons one for each color is generated If all those very small polygons have to be drawn this may take a while There are implemented different optimization algorithms one worse than the other These algorithms are to reduce the number of polygons by connecting them to larger ones This may considerably reduce the pixel data which has to be transferred by 30 90 percent However this will need a lot of computational time but at least this can be done completely parallel on each processor It is sure that the drawing to the window will be faster if the polygons are optimized before But it is generally not clear if the total time can be reduced This depends on the number of nodes in the subdomains the number of colors and the current data values The different modes are 1 a simple and slow sorting algorithm that produces correct output 2 a quick and dirty algorithm that works well in most cases however incorrect if the solution in one subdomain contains a ring of one color with another color inside it may happen that the inner field is overwritten by the color of an outer field Figure 6 3 the same as 2 using XOR mode drawing to the screen this repairs the erro
45. mponents e scalar solution U grad U dU dx dU dy dU dz and grad U i e nDoF 5 for subroutines x3dgraph o3dgraph or out3dexpl or e vectorial solution u Ur Uy Uz stresses o 011 022 033 012 023 013 and es o i e nDoF 10 for those subroutines ij The other components are added by the 3D graphics subroutine automatically depending on the interface being used The component names with a trailing letter E refer to trans formed rotated vector coordinates with respect to the current view point e g ug Uyg is the displacement in the screen plane or the projection of the 3D vector uz Uy uz to 29 3 Visualization of 3D Domains Table 4 Subroutine getdofs default example SUBROUTINE GETDOFS nDoFs DoFs integer nDoFs character 6 DoFs include include net3ddat inc include include Graf3D inc nDoFs NDF NDF is input from COMMON net3ddat inc 1020 if NDF EQ 1 then scalar solution if act 3d2d then I act 3d2d and act o3d are set in Graf3D inc DoFs 1 dU dxE I vectors transformed to screen coordinates DoFs 2 dU dyE DoFs 3 dU dzE 1023 endif DoFs 1 i0 U DoFs 2 10 dU dx gradient was computed additionally DoFs 3 i0 dU dy DoFs 4 i0 dU dz DoFs 5 i0 _ dU if act_3d2d then DoFs 6 i0 dU E projection of vectors to screen plane else DoFs 6 i0 entry is useless for 3D endif nDoFs 6 10 else I vectori
46. ne There is a way to interrupt the output without killing the program press the ESC key while the graphics window is focused or keep the middle mouse button pressed until the cursor changes its shape a ring of two arrows CD This interrupt is recognized after the output of the current processor has finished Thereafter the output of the remaining processors is ignored saving a little bit of time Hotkeys There are some hotkeys for selecting certain menu items by a single key of the keyboard It is unlikely that they will resist in future versions so they are generally undocumented Useful keys may be to enter a Zoom area using real world coordinates 1 44 to select one of the previously established virtual windows p 11 Other secret hotkeys are e g draw the 3D profile of the current solution Net3D draw the current solution as colored area Filled draw the first component as Net3D draw the first component as Filled draw the second component as Net3D draw the second component as Filled specify an interval for isolines LinInt draw isolines for the current solution Isol F O zero draw the boundary of the domain Bound n switch to batch graphics mode Quiet and some more for special components used in firegraf 0 F P R S V 5 Therefore there is no way to interrupt the optimization that is caused by OptFil 16 2 2 User s Interface for 2D Visualization SF
47. ns 3 1 Notes on Finite Element Data Structures 3 1 1 Assembled Matrices Generally the Finite Element Method leads to a system matrix K IR which is assembled from the element matrices Ke IR numel K 2 H K H where N is the number of nodes in the mesh consisting of numel finite elements r is the number of nodes per element e g 4 or 10 for tetrahedra and H IR is a Boolean matrix which rules the mapping of local indices in the element to global indices in the mesh while H extracts the components for element e from a global vector For parallel computation using domain decomposition the assembly procedure may be done locally on each of the P processors for the corresponding subdomain s 0 P 1 getting P local matrices K and again a global mapping P 1 P 1 numels K HKU H gt u H s 0 s 0 e 1 However K is never computed explicitly All computation is performed in parallel using the local matrices AK with only a minimum of communication between the processors for the nodes which are shared on subdomain boundaries 4 6 3 For example consider the matrix vector multiplication y Kr On each processor we have the local part x of the global vector x i e zs H x Then Us Kals may be computed without communication and ys is the contribution of subdomain s to the global vector y X H y Consequently the dot product y x can be computed as Ug Us Y
48. olines should be drawn The default value is 25 11 2 Visualization of 2D Domains 1 proc kifren Level 3 EIER ET Cray Param A H Igi BT EA Merk 1 hu Figure 3 The screenshot shows the graphics window split into two virtual windows with different views of the same 3D object SFB 393 TU Chemnitz qu16 Level 3 grad u SFB 393 TU Chemnitz SFB 393 TU Chemnitz SFB 393 TU Chemnitz LinInt 0 0 1 0 LinInt 0 0 0 5 LinInt 0 0 0 005 wW I Figure 4 Different selection of LinInt for the isolines of a solution u or grad u in this case with a local peak intervals are 0 1 0 0 5 and 0 0 005 12 2 2 User s Interface for 2D Visualization This will ask for an interval The default interval from 0 to 1 corresponds to the minimum and maximum of the current component of the solution Selecting a subinterval will concentrate all the isolines to that part of the component s values This may be useful if there is a small peak in the solution which would attract most of the isolines Figure 4 Define a minimum and maximum value for the currently selected component of the solution You may enter 0 0 for minimum and maximum to return to the default behavior i e automatic scaling from the current data values This facility is important for the visualization of time dependent solutions as a series of pictures It ensures that
49. phics mode You may decide if the visualization should be executed or not in future calls to the graphics subroutines The program repeats up to two different draws e g Filled for one component and IsoLin for another one each time When multiple virtual windows 2 2 4 Window p 11 are active each of them repeats its current view The batch mode can be finished by pressing RETURN or any other key while the graphics window has the focus move the mouse into the window or click on the top bar of the window Then the next call to gebgraf or firegraf enables the interaction menu again This mode is useful if the program runs in a loop where you want to see the differ ences in subsequent steps time dependency or adaptive meshes Together with the xxgrab utility p 40 you may create a series of image files in GIF format in order to produce animations 2 2 6 Special Effects Color Bar There is a small rectangle in the upper right corner of the display area which is used to switch on or off a color bar at the right margin This bar shows all colors of the current palette and the lower and upper bounds of the numerical value of the currently displayed component of the solution 15 2 Visualization of 2D Domains Note that you may fix the lower and upper bounds with Param Scale p 13 Soft Interrupt If parallel program runs on many processors the output of the subdo mains from each processors is displayed one by o
50. placement This module does not connect to PFEM The internal protocol for this client server dialog is not necessary to be described here A short description is given as Appendix An unsolved problem is the handling of large FEM data structures Explorer modules run out of memory very soon Thus the performance of our machine SGI O is sufficient for 50 000 100 000 grid points only Another example for postprocessing from the file data is a small tool fem og1 11 This program reads data of such a file and displays grid and solution in different ways based on OpenGL Figure 12 In 7 10 we discussed another method for interactively connecting a FEM program and an external visualization program based on the Graphical Programming Environment GRAPE 12 Summarizing we have to state that up to now several external viewers are well suited for a nearly perfect 3D rendering but for small problem sizes only Their difficulty is the missing support of parallelism Our hand coded X11 based visualization interface is still 34 3 3 User s Interface for 3D Visualization Figure 11 PFEM modules connected in the map editor of Explorer Solution 1 EX 2 Drawing b Figure 12 A small tool for OpenGL based visualization 30 3 Visualization of 3D Domains the only way to show results of a massively parallel computation within a reasonable time still large enough in relation to the computational time for the nume
51. ps gz 1 34 A Nye Xlib programming manual for version X11 Technical report O Reilly amp Associates Inc 1990 2 M Pester Grafik Ausgabe vom Parallelrechner fur 2D Gebiete Preprint SPC 94_24 TU Chemnitz Zwickau November 1994 file ftp tu chemnitz de pub Local mathematik SPC spc94_24 ps gz 1 M Pester On line visualization in parallel computations In W Borchers G Domick D Kroner R Rautmann and D Saupe editors Visualization Methods in High Per formance Computing and Flow Simulation Proceedings of the International Workshop on Visualization Paderborn 18 21 January 1994 pages 91 98 VSP Utrecht and TEV Vilnius 1996 1 34 References 11 R Ruhmer 3D Finite Elemente Rechnungen und ihre Visualisierung mit Hilfe von OpenGL Diplomarbeit TU Chemnitz 2000 34 12 Andreas Wierse and Martin Rumpf GRAPE Eine objektorientierte Visualisierungs und Numerikplattform Informatik Forsch Entw 7 145 151 1992 1 34 113 Berkeley Multimedia Research Center MPEG Tools http www vis 1lbl gov multimedia mpeg 42 14 E Kohler Gifsicle Animated GIFs for UNIX http www lcdf org ediietwo gifsicle 15 The Labs GIFMerge Merge GIFs to a GIF animation http www the labs com GIFMerge 42 16 ImageMagick Convert Edit and Compose Images http www imagemagick org 42 17 NAG IRIS Explorer Documentation http www nag co uk visual IE iecbb DOC Index html 1 29 53 AT Appendix
52. r of length nNode for each component de gree of freedom of the problem solved i e in Fortran this field is U nNode nDoFs where the number nDoFs gt nDoF and the names of the various components are obtained from a user supplied sub routine named getdofs see below NodesInVol number of nodes per element the program supports 4 and 10 node tetrahedra and 8 20 or 27 node hexahedra W scratch field of LngW double words this is used to store temporary arrays and finally all the computed pixel data LngW length of the scratch array in double words Ket 1D data structure that defines all nodes belonging to boundary edges Ket 2D data structure similar to Ket1D but for inner nodes of boundary faces For the structure of the Ket1D and Ket2D field see 1 and 3 Mat integer array of length nEL containing one integer number material indicator per element The structure of Ket1D and Ket2D is defined in the source code using include include net3ddat inc include include com_prob inc by the following declaration Integer Keti1D K1DDIM NanzK1D Ket2D K2DDIM NanzK2D and KetiD pkzeig k Ket2D pkzeig j are pointers to the first node of a boundary chain and KetiD pkleng k Ket2D pkleng j define the lengths of those chains k 1 NanzK1D j 1 NanzK2D 21 3 Visualization of 3D Domains 3 2 2 Subroutine x3dgraph call x3dgraph nDoF nFaceInVol nNodeInVol VolF VolN mVol nVol iMat
53. re 4 or 9 additional degrees of freedom to be added to the field U Those 2 or 3 vectors are understood as local coordinate system for each grid point To do so the user should call the following subroutine before invoking graphics display call setTensorParam idim itype scale k1 k2 k3 i1 i2 i3 This initializes the options for displaying tensors Table 3 Those values may be changed interactively by calling without arguments the subroutine ChangeTensorParam also invoked by the menu button Param p 13 2 1 4 Define Parameter Defaults There are some routines which may be called to pre define special parameters for the graph ics display in order to overwrite any other default values Subsequently those parameters 2 1 Programmer s Interface for 2D Visualization Table 3 Parameters of setTensorParam idim the dimension of the problem 2 or 3 idim 1 indicates that only one eigenvector is stored in the array U as 2D vector which may be displayed as vector or orthogonal cross itype specifies the kind of symbols for displaying the 2 or 3 eigenvectors 0 straight lines 1 arrows 2 crosses scale a scaling factor for the maximum length of lines or arrows relative to the window size with respect to the global extent of the domain a good choice may be 0 02 0 05 k1 k2 k3 k is the number of the first component of the 2 th vector in the array U ie if the solution array u is declared as
54. rical algorithms for large systems of linear equations arising from differential equations e g in solid and fluid mechanics Special emphasis is paid to the investigation of preconditioners for finite element systems based on domain decomposition and multilevel techniques on massively parallel computers Solving large problems on massively parallel computers more than 100 processors makes it more and more impossible to store numerical data from the distributed memory of the parallel computer to the disk for later postprocessing However the developer of algorithms is interested in an on line response of his algorithms Both visual and numerical response of the running program may be evaluated by the user for a decision how to switch or adjust interactively certain parameters that may influence the solution process Thus it is necessary to have an utility for a quick and rather dirty than slow and perfect interactive visualization directly from the parallel machine to the user s desktop workstation A high quality postprocessing especially in 3D requires a high performance graphic workstation Since at least up to now many users have only low cost machines on their desk we prefer a quick visualization which is only based on X11 for compatibility with a wide field of workstation models Another programming interface such as OpenGL should be better especially for implementing 3D graphics but it would require higher performance or hardware
55. rical solution and without saving masses of data before knowing the worthiness of saving them 3 4 Additonal Tools Java Applets There are two Java applets available They can be used to visualize the objects described by the original 2D or 3D mesh files e http www usercgi tu chemnitz de pester meshes shownets cgi for 2D mesh files Fig 13 shows nodes edges faces and source text of data files worksy workel workcfd und jetzt auch 3D FEM Meshes You have Java V 1 1 5 from Netscape Commmications Corporation on Linux V 2 2 10 i686 Figure 13 Snapshot of the 2D mesh viewer Java applet e http www usercgi tu chemnitz de pester meshes showstd cgi for 3D mesh files Fig 14 with many features including cut planes to view inside Demo s c20 std e Source Directory Fil Figure 14 Snapshot of the 3D mesh viewer Java applet 96 4 Special Features 4 1 Postscript Output If you need a better quality than obtained by a screen snapshot you should produce a postscript file This is supported by the graphics program with the menu item PSopen 2 2 1 p 8 The procedure is very simple but may take a long time for a high level of mesh refinement How to write a postscript file 1 If necessary select optimization level 1 or 0 the default is 2 cf OptFil p 14 2 Select Draw PSopen 3 Enter a name for the output file ps is appended if not typed in Be sure to have write permission
56. rs mentioned above But it is useless for postscript output 2 2 User s Interface for 2D Visualization 4 the default is a very quick and rather reliable method to reduce the number of polygons 0 this selects explicitly no optimization and no re ordering of polygons normally they are sorted by colors This is equivalent to the next menu item Patch Clicking OptFil the first time will ask for the optimization mode clicking the second time switches off the optimization The default case no optimization would lead to very large and hence slowly load able postscript files if PSopen is active Therefore postscript output is always optimized using the last mode selected with OptFil or mode 2 if none was selected before Thus to avoid time consuming optimization and accept large postscript files instead you must select OptFil mode 0 before Switch on or off a so called patch mode In patch mode all elements are drawn one by one otherwise all colors are drawn one by one lhis patch mode is helpful to draw 3D surfaces with elements sorted from back to front the simplest hidden surface method for convex bodies For this purpose there is also a difference in drawing grids Net 2D or Net 3D from the Draw menu in patch mode the polygons are filled with the background color on screen or with a light gray in postscript output see Figure 5 Leave the interactive graphics mode immediately and switch to a batch gra
57. s package uses the interface of the X11 library as documented in 8 no further extensions Hence it has been portable to any unix like machine including special parallel computers as GCPowerPlus No third party libraries are required The look and feel of the user interface was designed to support most of the daily requirements in testing parallel algorithms Figure 1 shows a set of typical views for one example and most of the menu items that are available in the graphics window First we will describe the programmer s interface 2 1 Programmer s Interface for 2D Visualization 2 1 1 Invoking Graphics Display From the programmer s point of view the complete visualization including interaction acts as a black box that is to be initiated by one of the following calls Note that this call has to be executed locally on each of the processors in a parallel program call gebgraf iDoF nEL ne EL nNod Nod U W call gebmgraf iDoF nEL ne EL nNod Nod U Mat W call firegraf iDoF nEL ne EL nNod Nod U Xi W The meaning of the parameters is given in Table 1 lhe program gebgraf is used in the case of layer or elasticity simulation in domains with homogeneous material whereas in the case of multiple materials gebmgraf may be used The firegraf call adds some features for the case of flow simulation 2 1 2 Specify Menu Names for the Degrees of Freedom The use of one of those graphic programs requires the programmer to writ
58. sualization IST Y Colors Mater Colors Option 4 amp proc Staudamm Level 3 ER P 4proc Staudamm Level 3 E X Draw acs 4 Q0E 00 Quiet e C eo ER rn mn fee x SS GER Een quen smt ier dr a rn om ex ADI wg Pan EEE RE EEE Sun 1 00E 00 Figure 1 User interface on an X terminal menus and various views deformation stresses coarse grid isolines subdomains materials of an example 2 Visualization of 2D Domains xg Figure 2 An example displayed using different colormaps 2 2 3 The Submenu Select one of the predefined palettes and switch background or the window s colormap Switch between default and private colormap On pseudo color screens there may be a maximum of 256 entries to the default colormap which is shared by all applications Then the program might be unable to allocate enough colors if the colormap entries are occupied by other applications Clicking this switch will use a private colormap for the graphics window In this case the colors outside this window will change until the mouse pointer leaves the window then the colors inside the window will be wrong On true color screens this switch may have no effect Switch the colors black and white By default the background is black and grid lines are white This switch does not affect the postscript output Selec
59. t a default palette which is the same as 16 Col for pseudo color screens or 70 Col for true color screens An EGA like palette of 14 colors black and white are not used for coloring data areas Useful to show more contrasts Fig 2 top left 70 Col Rainbow palette blue green yellow red Useful for a more continuous coloring Fig 2 top right 99 Col Extended rainbow palette magenta blue green yellow red white 10 2 2 User s Interface for 2D Visualization Black and white coloring i e alternating black and white areas Fig 2 bottom left Grayscale with upto 100 levels The user is prompted for the number of gray levels between black and white Grayscale is intended to use for printing on non color printers since the representation of colors e g of the rainbow palette might depend on printer drivers Fig 2 bottom right This palette is best suited for lighting effects if this program is used for 3D surfaces Fig 3 or Fig 7 For lighting over a coloured solution refer to Section 4 3 2 2 4 The Submenu Select and modify some parameters This will prompt for new width and height of the graphics window in pixels Of course the window may be resized in the usual way using the features of the window manager on your desktop However sometimes you might want to define an exact size e g to make a series of snapshots or mpeg_encode needs a multiple of 8 or 16 pixels Start a text
60. th data values only for the corners of each element undefined and unused entries for inner points of edges or faces nDoF 1 stream function which is not on U but on Xi nDoF a placeholder to be set in getdofs e g as U or vector This menu entry does not match any single component of the solution but causes a vectorial or magnitude display of the velocity field that is stored in the first two fields of the array U For convenience the graphics subroutines make some assumptions on the output of getdofs Thus if the solution consists of k gt 1 components per node then getdofs should return nDoF k 1 Why that If there is vector solution available such as velocity in flow simulation displacement in elasticity simulation or a gradient of a scalar solution its components x and y value are stored as the first two fields in the array U and the last number nDoF is reserved to display the vector solution arrows or the mag nitude of the x y vector Thus U has only nDoF 1 fields of components If firegraf is used there are some more assumptions as defined in Table 2 2 1 3 Options for Displaying Tensors Usually tensors are displayed as tripods of eigenvectors with a length scaled by the mag nitudes of eigenvalues This feature is supported in our graphics subroutines both for 2D and 3D visualization The eigenvectors have to be stored in the same way as other degrees of freedom i e for 2D or 3D problems there a
61. the bounding box definition is placed at the beginning of the file However the program may calculate the bounding box only at the end of all output so you will if you want have to change the file manually i e replace the line hBoundingBox atend at the top of the file by the correct line from the bottom of the file Simple modifications in the postscript file It might happen that you want to make little changes in the postscript file such as chang ing a comment removing the frame border changing line thickness or colors Therefore let s have a short excurse to the user interface within the postscript file At the top of the file you will find a section like this hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh Switch visibility of bounding box Border true def Switch visibility of caption text Capt true def Text and text height pt for caption CaptText qul6 Level 3 4 proc def CaptSize 16 def Width for grid lines wGrd 0 1 SC div w def Width and colors for boundary lines wBnd 0 5 SC div w def cBnD O 1 O sc def Dirichlet cBnN 100 sc def Neumann Width for isolines wIso 1 2 SC div w def patch background color cpat 0 96 sg def enable clipping for Net U or Zoom Clip i true def lighting effects shadows For this purpose I wrote a small shell script BBtop 38 4 1 Postscript Output Shfact 1 0 def range 0 0 bright
62. tor is signed and points to the viewer In the auxiliary display the front side of the plane will appear red and the back side is blue So one may verify the local coordinates within the cutting plane 28 3 3 User s Interface for 3D Visualization 3 3 2 Second User Interface for 3D Surface and Clipping Planes This implementation is based on the extended finite element data structure II page 20 It appears if the programmer decided to call either x3dgraph 3 2 2 or o3dgraph 3 2 3 The prompting is similar to that previously described but not exactly the same Therefore consider one more example Table 6 First at Line 10 we may select among several options to modify the 3D view x y z change the specified component of the normal vector view vector X Y Z rotate around the specified axis angle is requested d for d gt 0 you will get a perspective projection M rotate the view coordinate system by mouse dragging L switch on off some lighting effects for a more natural view C define or modify clipping planes R reset to the default view P write a postscript file from the auxiliary window coordinate system display a short help message ENTER finish input call the 2D graphics program gebgraf In the example we define two clipping planes lines 16 and 24 and choose to cut off the intersection of the two half spaces above those two planes line 33 Figure 8 The input
63. tructures to a file or send this data via TCP IP socket to a remote program The ASCII file format is very simple The details of the file structure is given in Section 3 3 9 Note the special case lhis program written for the first kind of our data structures may handle the second kind with the following modifications in the meaning of parameters mVol iUmode mNode Node is the leading dimension of the Vo1N field different from the special numbers mentioned above is the number of nodes per Volume is larger than 3 since contains Y Z U1 UnpDoF for each node U KetiD Ket2D are dummy arguments The initial indicator for the alternate data structure is the condition mNode gt 3 In this case however the surface mode described below is momentary not supported 24 3 2 Programmer s Interface for 3D Visualization 3 2 5 Subroutine getdofs for 3D problems As in the case of the 2D program we have a user defined subroutine getdofs which returns the names for the different components of the solution This subroutine has to satisfy all the different interfaces and appears slightly more complicated Consider an example of this routine in Table 4 which may be used as a default With this default routine and the calling sequence the DoFs submenu may appear in one of the following forms scalar solution vectorial solution Procs Here we assume that the user s main program has computed the co
64. tures of the solution for all time steps Since this may be a few hundred or thousand single pictures it must be able to run automatically for a while i e without manual interaction Our graphics tools are supporting this purpose with the help of a little external tool xxgrab The general situation is that you may use three computers in the following way Of course any two or all three may be physically the same machine but you might find it better to distribute the work to remote computers Computer A This may be the front end of a high performance parallel computer or the interacting processor 0 of your parallel virtual machine or whatever you use for computation Computer B This may be any compute server where you can run the program xxgrab This program will only in certain intervals need a little bit of CPU time when it grabs a new image from your screen to save it to disk Grabbing takes less than one second but saving may take a few seconds more But while saving an image the grabbed window may be already used to display the next image That s why it can be efficient to use different computers for displaying and saving the image Computer C Your desktop computer running the X server Here you have telnet sessions to any other computers and you can view the graphical output of the parallel program running on computer A Both A and B must have access to your X server on host C environment variable DISPLAY
65. ual dialog to manage virtual windows within the original graphics window You may split the window into 2 4 virtual windows of equal size or delete them if no longer needed The dialog allows either horizontal or vertical arranging of those virtual windows Each of them can be used for a different display Figure 3 is a screen shot of a horizontal placement of two virtual windows Selecting any mode from the Draw menu will always use the active virtual window highlighted by a frame Quickly switching between virtual windows is enabled by hotkeys i e pressing the corresponding key et 4 Select a color from the current palette to be used for drawing isolines The default color is blue A new window appears showing an array of all available colors Click on a color field to select it The last field shows the complete palette once more If this is selected the isoline color will be different corresponding to the value represented by this isoline Note The selected color also affects the appearance of Net 2D 2 2 1 if the mesh has 6 point triangles or 8 or 9 point quadrilaterals i e midpoints of edges for quadratic element functions Then the inner lines connecting such midpoints are drawn in the same color that is selected for isolines If the multi color field was selected the inner lines of the grid elements are not drawn This will ask in the console window for a number that indicates how many levels i e how many is
66. ult or the background color for the patch mode p 15 The color definition is either in RGB mode e g O 1 0 sc means green and 0 54 0 27 0 08 sc means saddle brown or in gray scale where 0 is black and 1 is white e g 0 96 sg is a light gray as in Figure 5 Clip false will disable clipping of Net U display at domain bounds Shfact Shsq You may modify those numbers to find the best view of a 3D picture with light and shadow Some remarks on PDF The includegraphics command as specified above will search for mysolution eps or mysolution ps if it is invoked by the command latex it will search for mysolution pdf or bmp png tif jpg mps if you compile the IATEX file by pdflatex The postscript files written by our graphics program can be converted to PDF Portable Document Format easily using the command epstopdf mysolution ps 39 4 Special Features 4 2 Video Sequences Although computer performance is growing to infinity fluid dynamics simulation cannot be done in real time On current high performance parallel computers a few seconds have to be spent to calculate one time step of 107t 107 s However a single picture of any solution at a certain time step or a few such pictures at different time steps on a sheet of paper are worth nothing compared with an animated video sequence that shows the time dependent behavior of the simulated process Thus one should be able to save pic
67. unas 14 25 programmer s interface 2 20 pseudo color PSopen PSclos 8 15 37 quiet mode R Redraw 6 TESIZE leen 11 S Deal EA 13 shadow 5 aao een 45 shape 2s wes wen aa eax 14 smooth surface 45 socket 32 48 T Tensor a i 13 14 true color 10 V Vector i22393 5 69 5 hs 5 414 video sequence 20 al viewpoint T virtual windows 11 16 visibility wis den ers 45 W Window IOSIZG 244 54 2333 d r 11 split 11 16 WINSIZ asian co aka 11 X El vun oe 4 Gomes poe 2 x3dgraph 22 28 XO 2352 9 3 a REC US 42 xxgrab zusehen 15 40 42 Z ZOOM sax 3s 13 16 return to default 13 Other titles in the SFB393 series 02 01 02 02 02 03 02 04 02 05 02 06 02 07 02 08 02 09 02 10 02 11 02 12 02 13 02 14 02 15 02 16 02 17 02 18 02 19 02 20 02 21 03 01 03 02 03 03 03 04 M Pester Bibliotheken zur Entwicklung paralleler Algorithmen Basisroutinen f r Kommunikation und Grafik Januar 2002 M Pester Visualization Tools for 2D and 3D Finite Element Programs User s Manual January 2002 H Harbrecht M Konik R Schneider Fully Discrete Wavelet Galerkin Schemes January 2002 G Kunert A posteriori error estimation for convection dominated problems on anisotropic meshes March 2002 H Harbrecht R Schneider Wavelet Galerkin Schemes for 3D BEM
68. us r for the zoom area You can enter y y r 0 to leave the zoomed view and return to the default Note The coordinate input mode is available by a hotkey press z on the keyboard while the graphics window is focused 2 2 5 The Submenu Select additional options for special purposes Sometimes this rectangle may be badly visible because of low contrast 13 2 Visualization of 2D Domains You may enter a range of processors between 0 and nProc 1 The next draw will only show the data of those processors Display a few internal statistics e g the total amount of pixel data that had to be transferred Switch between two modes of displaying boundaries 2 2 1 The default is to draw only the boundaries shapes of subdomains 1 processor 1 subdomain The alternate is to draw all initial bounds i e the coarse grid cf note on page 7 Switch between two modes of displaying isolines affecting Isol F in the Draw submenu 2 2 1 The major difference is how to draw the domain s background shape before drawing the isolines The default is a quick mode where the program tries to draw and fill each subdo main as a single polygon Since this may be incorrect if a subdomain had a hole inside it would be filled as the background of the domain cf Fig 6 you may switch to a slow mode where each small element of the domain is filled one by one owitch to the specified drawing mode for vector so
69. w SFB 393 TU Chemnitz SFB 393 TU Chemnitz crank surface mesh crank light and shadow Figure 16 Light and shadow using a grayscaled view SFB 393 TU Chemnitz SFB 393 TU Chemnitz TE 1 a NN Ly m un _ i H jes SIT db PAL e T ai ret eat Ds MALLA LENEF Po bxc N IT Fl aE rt EIS poe ae hollow cylinder some hidden lines are visible hollow cylinder correct view Figure 17 Patch mode for a non convex solid SFB 393 TU Chemnitz SFB 393 TU Chemnitz Hantel Level 3 face related light model Hantel Level 3 node related light model Figure 18 Face related light left or interpolation of node related light right 43 4 Special Features SFB 393 TU Chemnitz SFB 393 TU Chemnitz fichera corner Level 3 parallel projection fichera corner Level 3 perspective projection Figure 19 Parallel and perspective projection of a 3D object SFB 393 TU Chemnitz SFB 393 T

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