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USERS` MANUAL for MONT3D - Code Version 2.4 by Charles N

1. amp TITLE 48 CHARACTERS MAX 3 D BOX TEST PROBLEM amp NDIM NSURF NBANDS NREF S NLOST INSEED amp NUMNP NUMMAT NPHTON NWARNS NEBLOCK 3 8 6 2 1 100 100 100 10 2 0 IGEOM NUMCAT NDIVX NSHADE NWPROC IPAROPT NDTCV amp IPRNT IDATA NDIVY ITRACES NPLOOPS NMACV 110000 0 0 10 10 1 0 0 1000000 1 0 amp XSCALE XSHIFT YSCALE YSHIFT ZSCALE ZSHIFT DELT SPLITOL 1 0 0 0 1 0 0 0 10 0 0 0 01 0 0001 amp GRID NUMBERS READ IF NSHADE lt 0 NGX NGY NGZ amp 5 5 5 amp ERRDEF if NPLOOPS lt gt 0 2 0e 3 amp NODES N INC X Y Z 1 0 0 0 0 0 0 0 2 0 20 0 0 0 0 0 3 0 20 0 30 0 0 0 4 0 0 0 30 0 0 0 5 0 0 0 0 0 10 0 6 0 20 0 0 0 10 0 7 0 20 0 30 0 1030 8 0 0 0 30 0 10 0 amp ELEMENTS amp N N1 N2 N3 N4 NMISS INC MN NPHT INCP ERRMAX 1 1 2 3 4 0 0 2 0 0 0 00 2 5 8 7 6 0 0 2 0 0 0 00 3 1 5 6 2 0 0 0 0 0 00 4 3 7 8 4 0 0 0 0 0 00 5 1 4 8 5 0 0 0 0 0 00 6 2 6 7 3 0 0 0 0 0 00 amp WAVELENGTH BAND BREAKPOINTS READ IF NBANDS gt 1 amp BP1 BP2 BP3 BP4 BP5 BP6 BP7 BP8 amp 5 0 amp MATERIALS NEW MODEL NUMMAT lt 0 amp MN MATNAME 1 Sample Material 1 amp IB IEIP EBX EBY EBZ RRHOD RRHOSS RTAUD RTAUSS 0 0 0 0 QO 0 0 0 0 amp RHOD RHOS RHOSS TAUD TAUS TAUSS DTHRSS DTHTSS 0 2 i 0 0 0 QO O H MN MATNAME
2. 42 2 Sample Material 2 amp IB IETP EBX EBY EBZ RRHOD RRHOSS RTAUD RTAUSS 0 0 D 0 D W I 0 0 H amp RHOD RHOS RHOSS TAUD TAUS TAUSS DTHRSS DTHTSS 1 0 1 O O O 0 O O MATERIAL PROPERTY CURVES NUMMAT lt 0 NMACV gt 0 amp NCP NP 1 6 amp ANGLE VALUE 0 0 0 40 30 0 0 38 50 0 0 35 70 0 0 20 80 0 0 20 90 0 0 80 amp SEMI SPECULAR DEL THETA CURVES IF NDICV gt 0 amp USER DEFINED GRID READ IF NGX lt 0 amp User X grid Read if NGX lt 0 amp XG1 XG2 XG3 XG4 XG5 XG6 XG7 XG8 amp 0 01 0 01 1 5 9 10 01 amp User Y grid Read if NGY lt 0 amp YG1 YG2 YG3 YG4 CH YG6 YG7 YG8 amp 0 01 0 01 1 3 9 20 01 amp User Z grid Read if NGZ lt 0 ZG1 ZG2 ZG3 ZG4 ZG5 ZG6 ZC ZG8 amp 0 01 0 01 1 01 7 30 01 1 e Sit oe 0 0 15 30 75 90 45 60 Incident Angle degrees Figure 4 2 Material Property Curve for File box m 43 4 2 Execution of File box in The following details the execution of the 3 D code using the file box in The output shown below in Section 4 3 is output to the screen The Unix prompt is czeeb n where n is the command number All input from the user is shown bold and italicized The executable file here is mont3d note that Unix is case se
3. A 8 3 Specular Reflectance Condition s MTYPE 3 or 4 omit otherwise 73 CARD 1 Cols Format Entry Note s 1 16 2A8 Name of curve e g specular reflectance CN1 CN2 17 21 I5 Material number MN 1 22 26 I5 Wavelength band number IB 1 27 31 IS Curve number NJ 1 2 32 36 IN Number of points to be input for this material NP CARDS 2 TO NP 1 Cols Format Entry Note 1 10 E10 0 Cone angle 6 3 11 20 E10 0 Specular reflectance p 0 Notes 1 These values are used to check that the data are input properly by material number band num ber and curve number 2 For specular reflectance curve number 2 for MTYPE 2 to 1 and curve number 3 for MTYPE 2 3 NP number of cards must be input for the curve A 8 4 Diffuse Reflectance Condition s MTYPE 3 or 4 omit otherwise CARD 1 Cols Format Entry Note s 1 16 2A8 Name of curve e g diffuse reflectance CN 1 CN2 17 21 I5 Material number MN 1 22 26 I5 Wavelength band number IB 1 27 31 I5 Curve number NJ 1 2 32 36 I5 Number of points to be input for this material NP CARDS 2 TO NP 1 Cols Format Entry Note 1 10 E10 0 Cone angle O 3 11 20 E10 0 Diffuse reflectance Ga 74 Notes These values are used to check that the data are input properly by material number band num ber and curve number For diffuse reflectance curve number 3 for MTYPE 2 to 1 and curve number 4 for MTYPE 2 NP number of cards mu
4. Daylighting Design via Monte Carlo with a Corresponding Scientific Visualization Supercomputing 93 Proceedings IEEE Computer Society Press Los Alamitos CA pp 250 259 Shapiro A B 1983 FACET A Radiation View Factor Computer Code for Axisymmetric Two Dimensional Planer and Three Dimensional Geometries with Shading Lawrence Livermore National Laboratory UCID 19887 67 Shapiro A B 1985 TOPAZ3D A Three Dimensional Finite Element Heat Transfer Code Lawrence Livermore National Laboratory UCID 20484 Statton E S 1983 MONTE A Two Dimensional Monte Carlo Radiative Heat Transfer Code M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Torrance K and Sparrow E M 1966 Off specular Peaks in the Directional Distribution of Reflected Thermal Radiation J Heat Transfer Vol 88 pp 223 230 Zeeb C N 1996 Two dimensional Heat Transfer in Combustion Gases Via Monte Carlo M S Thesis at Colorado State University Department of Mechanical Engineering Fort Collins CO 80523 Zeeb C N 1997 Application of Ray Tracing Techniques to Radiative Heat Transfer Via Monte Carlo Available as a WWW document URL http www colostate edu pburns monte docu ments html Zeeb C N and Burns P J 1997 Random Number Generator Recommendation Report pre pared for Sandia National Laboratories Albuquerque NM Available as a WW
5. 10 Photon Emission Vector d Figure 2 5 Local Material Coordinate System Material properties are presented below in terms of material property curves outgoing direc tional distributions and emission Information about the input format for the new material model 1s given in Sections 3 8 3 10 The old material model is covered in detail in Appendix A 2 5 1 Material Property Curves Material properties describe the interaction of a particle with a material Material properties are independent of incoming azimuthal angle q but may be dependent upon incoming cone angle 6 The properties are defined as constant gray within a particular radiative band k so that Kirchoff s law applies within each band Explicitly 0 a 0 1 p4 pe 8 Ps 8 74 8 t6 07 140 2 1 where k 0 emittance in wavelength band k at outgoing cone angle 6 over absorptance in wavelength band k at incident cone angle O vg diffuse reflectance in wavelength band k at incident cone angle k oe Ps 8 specular reflectance in wavelength band k at incident cone angle 0 k na P 8 semi specular reflectance in wavelength band k at incident cone angle 9 ug diffuse transmittance in wavelength band k at incident cone angle 6 11 k l CR Te 0 specular transmittance in wavelength band k at incident cone angle 9 k ans Es 0 semi specular transmittance in wavelength band k at incident cone angl
6. 2 2 Surfaces Three dimensional radiating surfaces consist of planar quadrilaterals or triangles and are defined by specifying four nodal points If four distinct points are specified then the surface is a general ized quadrilateral as shown in Figure 2 2 a If it is desired to use triangular surfaces then the last two node numbers must be identical as shown in Figure 2 2 b The outward normal for both types of surfaces is defined consistent with the right hand rule i e if the fingers of the right hand are N 1 N 1 a 3 D Quadrilateral b 3 D Triangle Figure 2 2 Radiating Surface Geometries curled in the direction of increasing nodal point number N N then the thumb of the right hand indicates the direction of the outward normal This results in a counterclockwise convention for nodal point numbering when viewing the radiating side of the surface from above Photons are only emitted from the front of the surface 1 e in the direction in which the surface normal points the back side of the surface is transparent as far as the code is concerned When speci fying the surfaces they must be convex for more discussion of convexity see Section 2 3 For quadrilaterals the four nodes should be coplanar to within a small tolerance but the code is able to handle non planar quadrilaterals see Section 2 3 for more details Additional information on the surface input format is given in Section 3 6 Each ra
7. 26 CHAPTER 3 INPUT DECK The following pages contain the instructions necessary to enable the user to construct the input file data deck required by MONT3D Input lines generally referred to as cards are limited to 80 columns in width Cards with the character 2 in column 1 can be placed anywhere in the data deck for use as comment cards or as spaces all such cards are ignored A sample input file is shown in Section 4 1 Some care may be required when entering variables in the input deck How the code handles blanks spaces in the input file depends on the compiler used Some compilers may make the code read blanks as zeroes When blanks are read as zeroes blanks to the right side of the variable become significant For example if 6 is entered with one space after it it may be interpreted as 60 When blanks are read as zeroes variables should be entered right justified For most compilers blanks in the input file are ignored and each variable may be entered anywhere within the columns specified for it in the description below If all the columns are empty the variable is read in as zero It should be noted that for maximum compatibility input files should be right justified The exam ple input file in Section 4 1 is right justified The Format column in the card description below gives the FORTRAN format used to read the variable The only information in that column that may be beneficial to the casual user is that
8. Margolies D 1986 Personal communication LLNL Marsaglia G 1985 A Current View of Random Number Generators Computing Science and Statistics Proceedings of the XVIth Symposium on the Interface L Billard ed Elsevier Sci ence Publishers B V North Holland pp 3 10 Mascagni M Cuccaro S Pryor D and Robinson M 1995 A Fast High Quality and Repro ducible Parallel Lagged Fibonacci Pseudorandom Number Generator Journal of Computa tional Physics Vol 119 pp 211 219 Nagesh S and Burns P J 1994 User s Manual for the Program MPLOT Version 3 3 Depart ment of Mechanical Engineering Colorado State University Fort Collins CO 80523 Pryor D V and Burns P J July 21 25 1986 A Parallel Monte Carlo Model for Radiative Heat Transfer presented at the 1986 SIAM Meeting Boston MA Pryor D V Cuccaro S A Mascagni M and Robinson M L 1994 Implementation of a Por table and Reproducible Parallel Pseudorandom Number Generator Supercomputing 94 Pro ceedings IEEE Computer Society Press Los Alamitos CA pp 311 319 Pryor D V 1997 Personal communication Center for Computer Sciences 17100 Science Drive Bowie MD 20715 Schorn P and Fisher F 1994 Testing the Convexity of a Polygon In Graphic Gems IV Heck bert P S editor AP Professional San Diego CA pp 7 15 Schweitzer R McHugh J Burns P J and Zeeb C N 1993
9. 14 normal termed over cosine while values less than one bias the distribution toward the grazing angle termed under cosine For specular reflection the photon s directional component normal to the surface is reversed and the component parallel to the surface remains unchanged No specular offset angle is modelled in this distribution The semi specular reflectance distribution takes this specular distribution and 1 adds an offset cone angle A 8 to yield the preferred outgoing direction and 2 spreads the distribution in space including a weighting coefficient by revolving the distribution about the preferred outgo ing direction The preferred outgoing cone angle is determined as the specular angle plus the semi specular offset angle 9 6 A9 0 2 4 The same type of distributions shown in Figure 2 8 for the diffuse outgoing distributions are used for the semi specular outgoing distribution except 1 the distribution is scaled in 6 to disallow penetration into the surface i e the distribution is forced to zero at the grazing angle and 2 sym metry about the preferred outgoing direction rather than about the surface normal is applied Here the weighting coefficient r controls the tendency of the distribution to go toward the preferred outgoing direction Figure 2 9 depicts cross sectional views of normalized outgoing distributions about preferred outgoing directions of 30
10. B 8 Temporary Exchange Matrix File Suffix tni Unit 13 The temporary exchange matrix file is used to hold the exchange matrix results when converting back and forth between the regular exchange matrix file and the block exchange matrix files This file only exists for a short time during the input and clean up stages of a MONT3D run This file is binary direct access file with record length 4 NSURE since all results written to disk are 4 byte integers All the code for the reading and writing of this file can be found in the subroutine nijfile in the file m30s f B 8 1 Photon Number Matrix NBAND Sets of NSURF Records Each of Length NSURF Format Entry Note s Integer Numbers of absorbed photons emitted by surface i absorbed 85 by all surfaces j for band k 1 Notes 1 Each record contains the number of photons absorbed by each surface j ranging from 1 to NSURF for each surface i in the band k It should be noted that the file contains results for all surfaces even those that do not emit which therefore have all zeroes for results A new record line is started for each surface The records for all surfaces in order from 1 to NSURF in band k specify an exchange matrix for band k The exchange matrices for the 1 to NBANDS bands are written in order to the file B 9 Block File Suffix blk Unit 14 The block file contains the additional information MONT3D requires to restart from a crashed run The file is generated at the start
11. P 2774 5 7 x 10 2 5 3 x 10182 Even using the more restrictive 21 1 constraint instead of the full period all but the LFG 17 5 31 have random series much longer than a LCG s maximum period about 231 2 1 x 10 The most severe drawback of an LFG is the fact that words of memory are required to be kept current and this is not significant in our application It is necessary to fill the initial state to start the sequence For the LFG an initial state of words is needed When implementing the code in parallel it is important that each worker process have a sequence or cycle of random numbers that is independent of all the other processes Initializing separate cycles is addressed by Mascagni et al 1995 where they describe a canonical form for initializing Fibonacci generators This canonical form is determined solely by and k and is inde pendent of M In general the canonical form for initializing Fibonacci generators requires the pe word be set to all zero bits and the least significant bits of all words in the register set to zero with the exception of one or two characteristic bits that depend on and k Each combination of the remaining 1 m 1 bits called equivalence classes EC s specifies a different cycle of random numbers No two EC s share the same cycle Cuccaro 1996 has extensively tested initializing the EC s bits with a binary shift register generator i e an LFG with M 1 and found e
12. 3 D BOX TEST PROBLEM v 2 4f1 04 15 99 77 in nodin3 in surfin3 in wavin in matinnew reading material property curves in curveset in cumdis in fileset in gridin Memory Allocation and Usage Category Allocated Used 1 Nodes inod 15000 words 8 words 2 Surfaces isrf 5000 words 6 words 3 Materials imat 30 words 2 words 4 Wavelength bands ibnd 5 words 1 words 5 Restart surface block size iblk 200 words 2 words 6 Restart blocks itblk 1000 words 3 words 7 Index digits for filename iimag 4 words 1 words 8 Grid divisions per axis incg 60 words 1 words 9 Surfaces including split surfaces isrfs 7000 words 6 words 10 Surface segments in grid cells iseg 100000 words 6 words in order 47 ee CO CH E AS AS LA E CH E Wu dp N E E EH E E E EDESA in graf in bplane2d input phase band surf converged converged restart file written converged converged restart file written converged converged restart file written 1 2 complete iter 2 2 npht 120000 120000 120000 120000 120000 120000 error tol 0 1984E 02 2000E 02 0 1984E 02 2000E 02 0 1940E 02 2000E 02 0 1938E 02 2000E 02 0 1949E 02 2000E 02 0 1949E 02 2000E 02 Now writing exchange numbers from each block nij file bni to a t
13. 93 100 ASME New York Burns P J and Pryor D V 1995 Random Numbers Available as a WWW document URL http csep1 phy ornl gov CSEP RN RN html Burns P J and Pryor D V 1999 Surface Radiative Transport at Large Scale via Monte Carlo Vol 9 of Annual Review of Heat Transfer Begell House New York NY in press Cuccaro S A 1996 Personal communication Center for Computer Sciences 17100 Science Drive Bowie MD 20715 Crockett D V Maltby J D and Burns P J 1990 User s Manual for MONT3E A Three Dimensional Electron Tracing Code with Non Uniform Magnetic Field Release 5 0 Depart ment of Mechanical Engineering Colorado State University Fort Collins CO 80523 Dolaghan J S 1991 A Monte Carlo Simulation of Molecular Redistribution in an Enclosure due to Sputtering M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Dolaghan J S Loehrke R I and Burns P J 1992 User s Manual for SMOOTH Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Dolaghan J S 1996 A Monte Carlo Simulation in Rarefied Gas Dynamics with Application to Physical Vapor Deposition Ph D Dissertation Department of Mechanical Engineering Colo rado State University Fort Collins CO 80523 Geist A Beguelin A Dongarra J Jiang W Mancheck R and Sunderam V 1994 PVM Par allel
14. 0 and NGZ lt 0 otherwise omit card s Cols Format Entry Note s 1 80 8E10 0 Z grid coordinates ZG N 1 Notes 1 For N 1 to NGZ 1 No more than eight values should be input per card 10 columns per value More than one card may be required 40 CHAPTER 4 PROGRAM EXECUTION This chapter illustrates how MONT3D is executed in a Unix environment The first section details the sample input files used in the examples below The second section explains the com mands and results obtained from a normal execution and a restart execution of the code for this input file The next two sections show the screen output for the normal and restart executions described in the previous section The final section addresses the machine independence of MONT3D results and its implications during restart runs 4 1 Input File box in Figure 4 1 shows a 3 D geometry for analysis by MONT3D Comparison of the picture with the input file box in shown below illustrates the right hand rule for 3 D surfaces The inner surfaces are modeled by two different types of materials which are mixed specular and diffuse reflecting and whose properties vary with incident angle This file demonstrates the new material model The first material which is used for the sides of the box has the diffuse reflectance entered as a constant value 0 2 while the specular reflectance is entered as the curve shown in Figure 4 2 The second material which is used for
15. 1x Format Entry Note s Integer Numbers of absorbed photons emitted by surface i absorbed by all surfaces j for band k 1 2 82 Notes 1 Each record contains the number of photons absorbed by each surface j ranging from 1 to NSURF for each surface i in the band k It should be noted that the file contains results for all surfaces even those that do not emit which therefore have all zeroes for results A new record line is started for each surface The records for all surfaces in order from 1 to NSURF in band k specify an exchange matrix for band k The exchange matrices for the 1 to NBANDS bands are written in order to the file 2 This file contains the full exchange matrices The program SMOOTH Dolaghan et al 1992 may be used to process these files into an upper triangle including the diagonal of numbers of photons which have been smoothed to obey reciprocity B 5 Trajectory File Suffix trc Unit 9 The trajectory file contains the trajectory photon ray end point information for each photon and can be used with MPLOT Nagesh and Burns 1994 to display the trajectories see Section 2 8 for more details All the code for the writing of this file can be found in the subroutine surfloop in the file m32s f The following series of records are repeat for each photon trajectory Records are written in chro nological order B 5 1 Header Card 1 Record of Length 5 FORTRAN Format Specification 5 1x i5 Format Entry Note
16. 21 and 59 607 273 1 105 Pryor 1997 To change the LFG the user need change only these constants and recompile the code zee is the constant z defined in Section 2 7 For 95 confidence in the results z is 1 96 the default value Other values of z as a function of D the percent confidence are given in the normal distribution tables see Kreyszig 1993 5 6 Parallel Version 5 6 1 Running the Parallel Version Much information about setting up PVM and running PVM programs is given by Geist et al 1994 The discussion below gives several tips on how to run the PVM version of MONT3D but for more complete information see Geist For an overview of the master worker model used by MONT3D see Section 2 10 It should be noted that several shell environment variables including the path PVM_ROOT and PVM_ARCH must be set correctly for the PVM code to run There are two ways to create the PVM virtual machine The first way is to type the command pvm and then use the add command at the prompt pvm gt A second way is to create a hostfile If the hostfile is given as an argument to the pvm command then a PVM virtual machine will be created using the commands and options in the hostfile A hostfile allows the user to specify a virtual machine much more easily than manually using the PVM command add A hostfile also has other benefits as will be shown below More detail about hostfiles is given by Geist 1994 The parallel virtual
17. 5 8 Precision MONT3D is coded to compile and run using 64 bit floating point precision For MONT3D it is desirable to use 64 bit precision as the specification of coplanar surfaces is particularly susceptible to precision errors Also 3 D photon tracing generally requires 64 bits to perform intersection cal culations with the requisite accuracy 65 REFERENCES Anderson S L 1990 Random Number Generators on Vector Supercomputers and Other Advanced Architectures SIAM Review 32 pp 221 251 Branner K 1999 An Enhanced Material Model for Radiative Heat Transfer via Monte Carlo M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 In progress Brent R P 1992 Uniform Random Number Generators for Supercomputers Proceedings Fifth Australian Supercomputing Conference SASC Organizing Committee 1992 pp 95 104 Unpublished Burns P J and Pryor D V 1989 Vector and Parallel Monte Carlo Radiative Heat Transfer Numerical Heat Transfer Part B Fundamentals 16 pp 20 42 Burns P J Maltby J D and Christon M A 1990 Large Scale Surface to Surface Transport for Photons and Electrons via Monte Carlo Computing Systems in Engineering Vol 1 No 1 pp 75 99 Burns P J Loehrke R I Dolaghan J S and Maltby J D 1992 Photon Tracing in Axisym metric Enclosures Developments in Radiative Heat Transfer HTD Vol 203 pp
18. 6 15 NMACV and NDTCV are only used by the new material model NUMMAT lt 0 They specify how many material property and specular offset angle del theta curves are to be read See Sec tions 2 5 3 2 1 and 3 8 3 10 for more details 3 2 3 Card 3 Cols Format Entry Note s 1 10 El0 0 Scale for X XSCALE 1 DEFAULT XSCALE 1 0 1120 El0 0 Shift for X XSHIFT 1 21 30 E10 0 Scale for Y YSCALE 1 DEFAULT YSCALE 1 0 31 40 El0 0 Shift for Y YSHIFT 1 31 41 50 El0 0 Scale for Z ZSCALE 1 DEFAULT ZSCALE 1 0 51 60 El0 0 Shift for Z ZSHIFT 1 61 70 E10 0 Increment of cone angle in degrees for integration DELT 2 DEFAULT DELT 0 01 degrees 71 80 E10 0 Tolerance for splitting non planar surfaces SPLITOL 3 4 DEFAULT SPLITOL 0 0001 degree Notes 1 These factors can be used when one needs to scale from one unit to another 1 e meters to cen timeters or when one wishes to shift the coordinate system Since there is no inherent length scale scaling all axes equally has no effect nor does shifting of any axis es The results of scaling and shifting are X X XSCALE XSHIFT Y Y YSCALE YSHIFT and Z Z ZSCALE ZSHIFT DELT A6 the increment used in numerically integrating the cumulative distribution function for emission versus cone angle used to determine the cone angle distribution of emitted pho tons The range is 1E 7 lt DELT lt 0 1 If a value outside this range is entered
19. 60 110 Initial seed for the random number generator INSEED 8 INSEED lt 0 The internal constant value for the initial seed is used INSEED 0 The initial seed is obtained from the time INSEED gt 0 The value INSEED is used for the initial seed Notes NDIM should be equal to 3 for MONT3D Any other value causes the code to issue a warning and continue If NUMMAT is negative the new material model is used Otherwise the old material model is used See Sections 2 5 and 3 8 3 10 and Appendix A for more details Radiative properties are defined in wavelength bands and are constant within a given wave length band The number of photons emitted per surface in each band is equal to NPHTN NDIVX NDIVY where NPHTN is the number of photons emitted from each emission point NPHTON is the default value of NPHTN for all surfaces which may be overridden for any particular sur face s during the surface input See Sections 2 2 2 7 3 2 2 and 3 6 for more detail The maximum number of reflections allowed before a run is aborted is NREFS NWARNS For the parallel version of the code each worker process aborts when it reaches this number If a worker process aborts due to this error the other processes continue to work and the aborting process s block is done by another worker later in the run See Sections 2 10 and 5 6 for more detail Occasionally due to precision problems a photon is lost 1 e no receiving
20. A 8 The old material model has material types defined for each band Seven different material types are available to provide flexibility to the material model These material types allow different com binations of photon material interactions to be defined Table A 1 summarizes the material types and indicates which material property curves must be entered Note that while the old material model supports specular and weighted diffuse reflection p and pg and transmission T and Ta semi specular interactions are only supported by the new material model Table A 1 Material Property Summary Type Emission Interactions Input Curves 2 Function 7 6 p 8 p 8 ol 1 3 T 8 P 8 Pg 9 1 Beam T 0 P 8 p4 9 0 8 1 3 T 8 P 8 Ga 0 e 0 T 0 p 0 p4 0 a 0 1 3 T8 Ps 0 Pa 9 1 S Tq 8 P 8 p4 8 0 8 1 3 Tq 8 P 8 Daf 2 g T O T4a O P O P4a O A 0 1 4 T0 TA O DAHL PaO 3 None Perfect specular reflection None 4 None Perfect diffuse reflection None In addition to photon material interactions the material type also determines the type if any of emission that will take place Just as in the new material model three possible emission modes are modeled emission according to user input function beam emission and normal emission More detail is given below It is possible to specify materials for which the reciprocity relations do not hold more d
21. MONT3D as input To be compatible with TOPAZ3D this file may need to be processed with the program SMOOTH Dolaghan et al 1992 which smooths the full matrix of exchange numbers into an upper triangle of numbers which obey reciprocity All the code for the reading and writing of this file can be found in the subroutines nij file and nijheader in the file m30s f B 4 1 Header Card 1 Record of Length 5 FORTRAN Format Specification 7 i10 1x Format Entry Note s Integer Geometry code NDIM 1 81 Integer Number of surfaces NSURF Integer Factor code IFACT 2 Integer Number of wavelength bands NBANDS Integer Number of materials NUMMAT Notes 1 NDIM is 3 2 IFACT is set to 2 and indicates that the file contains exchange numbers as opposed to view fac tors B 4 2 Surface Areas 1 Record of Length NSURF FORTRAN Format Specification 6 e12 5 1x Format Entry Note s Real Surface areas from 1 to NSURF B 4 3 Surface Emittances NBAND Records Each of Length NSURF FORTRAN Format Specification 6 e12 5 1x Format Entry Note s Real Hemispherical surface emittances A from 1 to NSURF for band k 1 2 Notes 1 The surface emittances are averaged over the hemisphere i e 0 2 The surface emittances are written in order from 1 to NSURE for each band 1 to NBAND A new record line is started for each band B 4 4 Photon Number Matrix NBAND Sets of NSURF Records Each of Length NSURF FORTRAN Format Specification 7 i10
22. Parameter Statements and Memory Allocation oooconnncccnnncccnonccononcnononnnononccnnnnccnnnnccnnnnnss 58 5 5 1 Parameters Specifying E 58 5 3 2 Other it A a eat a E E a ey 59 5 0 Parallel EE 60 5 6 1 Running the Parallel NEIE eegend Age ENEE 60 5 6 2 Worker ProC SSeSi nissa eissii isoin essa e EEE Ea See 61 A ah ects de lle Sa hp Bac le we Gi alt le Mec cd eA Ai de 61 JOA EMOS oa n a a a A A A a a A a 62 5 6 5 ene en 63 5 7 Unix Batch Execution Using SEP A 64 SO PICCISION AE ee 65 REFERENCES viniste 66 APPENDIX A OLD MATERIAL MODE Lt dere 69 IO io AS ate O A O a aN a 69 A 2 Outgoing Angles for Diffuse and Specular Interactions cece eeeeeeseeceeceseeeeeeeeneees 70 A 3 Material Type 2 Emission According to a User Supplied Funcnon 70 A 4 Material Type 1 Beam Emission E 70 A 5 Material Types 0 Thorough 2 Normal Emiseion cons 71 A 6 Material Types 3 and 4 Perfect MATOS ia 71 E T Material Type Dala ars la hous eteee 71 AS Material Property Curves COTOS arrendatario carnada 72 EECHER 12 A 8 2 Diff se Transmittance A E Ah EE RA AAE 73 A 8S 3 Specular Reflectan s score iaa aid 73 A9 4 Dittuse EE 74 111 APPENDIX B FILEFORMAT S nino a ja R AE 76 B 1 Restart File Suffix rer Unt2n ono nnnnncononnano nacos 76 BAT IPAREE EE 76 B 1 2 Photon Eeer eege eebe ie ee araisa 76 B 1 3 Random Number Generator Intformapon conocio no ncnnnccnnnno 77 B14 Block Mettet A ES See Oe Go 77 B 2 Plot File Suffix plt Ud usina
23. S number of photons emitted in wavelength band k from surface i and absorbed by sur face j N total number of photons emitted in wavelength band k from surface i 8 2 4 o Stefan Boltzman constant 5 669x10 Wem ek T absolute temperature of surface i K k e F fraction of the blackbody energy of surface i in wavelength band k A area of surface i m3 i The ordinary definitions of the exchange factor E S and the exchange fraction F S are as follows k No Ge EF E 1 2 Nj II M kk y Ej amp 1 3 or k Ar e 1 4 Equations 1 3 and 1 4 express conservation of energy photons since all photons must be absorbed by a surface Given that there must be zero net heat flow between isothermal surfaces the second law of thermodynamics entropy principle follows from Equation 1 1 as E A EA 1 5 or EFKA dra 1 6 1 1 1 J Jl J The net radiative exchange in wavelength band k from surface i to surface j is then k k k4 k4 Ou Foie ST dag 1 7 or E k_k k4 k4 Oj e Foie ST San 1 8 Either of the relations expressed as Equations 1 5 or 1 6 may be used to test the exchange fac tors or the exchange fractions for consistency convergence Indeed either of these relations may be used to manipulate the values in the matrix if either of Equations 1 3 or 1 4 is used as a con straint 1 3 View Factors The code may be used to compute view factors valid for diffuse
24. Side 4 is between nodes 4 and 1 B 7 Block Exchange Matrix File Suffix bni Unit 12 The block exchange matrix files are used to hold the exchange factor results during a run There is one of these indexed files for each block of surfaces for which results have been calculated on this or any previous run The block exchange matrix files are combined into a regular exchange matrix file at the end of a MONT3D run Since load balancing has not been implemented yet blocks are determined as follows A list is kept of all surfaces ordered by band and by surface num ber within band This list is broken sequentially into blocks of size INEBLOCKI see Sections 2 9 and 3 2 1 for more information All the code for the reading and writing of this file can be found in the subroutine nijfile in the file m30s f B 7 1 Exchange Information for the Block INEBLOCKI Records of Length NSURF FORTRAN Format Specification 7 i10 1x Format Entry Note s Integer Numbers of absorbed photons emitted by surface i absorbed by all surfaces j for band k 1 Notes 1 Each record contains the number of photons absorbed by each surface j ranging from 1 to NSURF for the surface 7 in the band k The i and k values for a block are determined using the formula mentioned above It should be noted that the file contains results for all surfaces even those that do not emit which therefore have all zeroes for results A new record line is started for each emitting surface
25. T11 LE 77 B2 2 Control Wit Orman ees A ea BO A E dia BAe catia 78 B 2 3 Limiting Dimensions for the Geometrie 78 B24 Surface Informatio eer 78 B 2 3 Material Information EE 79 B 2 6 Number of Records in the Binary Exchange Matrix File oooococnoconnoccccnoncccnonnnos 80 B 3 Lost Photon File Suffix Ist UnrtAn 80 BIS IAH Card WEE 80 B 3 2 Photon Rays Starting Poio 81 B 3 3 Photon Ray s Ending PO me ccconcec cect vancaescauasapa Egeter Eege 81 BA Exchange Matrix File Suffix nij Unit Bsc lt 2 siess i 81 B 4 1 Header Cat EE 81 te E 82 BAS Surlace ue ici 82 B 4 4 Photon Number Matronas 82 Boo Trajectory Bile SUE UA ta 83 Be Header Car A OS 83 B 5 2 Photon Ray s Starting PO nissan iris 84 BO Photon Rayos End Pointo aoei is 84 B 6 Leaks File Suffix lks Unit Ui 84 BO L E ak toro rita 84 B 7 Block Exchange Matrix File Suffix bni Unit 13 85 B 7 1 Exchange Information tor the Block 2 45 2 ASE 85 B 8 Temporary Exchange Matrix File Suffix mt Unit I 1 85 B 8 lt l Photon Number Maui EE EE 85 1v B 9 Block File Suffix blk Unit 14 List of Figures Figure 1 1 Example Geometry Which Can be Smulated AA 1 Fig t 2 1 Nodal eegene ge EA ege 6 Figure 2 2 E E ee ENN e 7 Figure 2 3 Three Dimensional Surface Details AAA 8 Figure 2 4 Planar Quadrilateral Divided into Two Overlapping Triangles oooocnnnncccinonccnnoccnonnss 9 Figure 2 5 Local Material Coordinate Systems i e ke a one ee BA 11 Figure
26. access the time and date of the run Requires that the Fortran 90 subroutine date_and_time be supported by the compiler Tested on the IBM RS 6000 and Microsoft Windows Microsoft FORTRAN platforms m3fdate f allows the code to access the time and date of the run Requires that the nonstandard subroutine fdate be supported by the compiler Tested on Sun SGI DEC Alpha Hewlett Packard and Macintosh Absoft FORTRAN platforms m3nodate f deactivates time and date information for platforms which do not support any date subroutine The date and time are set to the default value 16 53 49 on March 12 1970 5 1 5 Parallel Implementation Two stubs that control parallel implementation of MONT3D are available m3nopara f implements the single processor version of the code This has compiled on every plat form on which it has been tested m3pvm f implements a PVM version of MONT3D The file m3pvm inc contains the PVM specific parameters and common variables and is required The user s environment variables PVUM_ROOT and PVM_ARCH must be defined for this file to compile successfully The PVM version has been compiled on Sun Hewlett Packard IBM RS 6000 DEC Alpha and Linux NAG f90 compiler platforms More information about compiling is given in the below Also more information on running the parallel code is given in Section 5 6 below 52 5 2 Compiling MONT3D 5 2 1 Unix For Unix a Makefile that has been tested on several platfo
27. and unbiased and 4 the generator should be efficient In the past linear congruential generators LCG s were typically used to produce pseudo ran dom numbers However a new class of generators lagged Fibonacci generators LFG s have recently emerged LFG s have better properties than LCG s are more efficient and are readily amenable to parallelization An overview of these types of generators is presented followed by some implementation details Additional material may be found on line Burns and Pryor 1995 Zeeb and Burns 1997 and from other sources Anderson 1990 Brent 1992 Burns and Pryor 1999 Marsaglia 1985 2 11 1 Lagged Fibonacci Generators Lagged Fibonacci pseudo random number generators are based upon the Fibonacci sequence Golomb 1982 The Fibonacci sequence is generalized to a family of pseudo random number generators of the form Xa X _ X _ mod m gt k gt 0 2 7 where mod is the integer remainder function and f initial integer values Xo X are needed in order to compute the next element in the sequence In this expression the lags are k and so that the current value X is determined by the value of X k places ago and places ago In addition for most applications of interest m is a power of two That is m 2M Random real numbers amp are generated from the above integer numbers by dividing the integer X by m viz X Roos yielding 0 lt XK lt 1 2 8 Th
28. automatically reject a concave quadrilateral such as the one in the figure it may not catch all ill defined non planar split surfaces this will be discussed in greater detail below This problem has become more severe recently since due to user request the convexity test has been relaxed particularly for non planar surfaces If surfaces are non coplanar unpredictable results can occur The user is advised to examine split surfaces carefully Often the wisest course is to redefine the surfaces to make them planar and con vex Most of the potential problems mentioned above are closely related to the concepts of planar ity and convexity For this reason the planarity and convexity tests done by MONT3D and how split surfaces relate to them are described below There are also potential problem related to the number of photons emitted from each emission point which will also be described below Figure 2 4 Planar Quadrilateral Divided into Two Overlapping Triangles To assess the planarity of a surface the dot product of the surface normals of the two triangles defined by the nodes 1 2 3 and 1 3 4 is calculated If this dot product differs from one by more than a predefined tolerance SPLITOL see Section 3 2 3 for the input specification of this variable the surface is divided into two planar triangles It should be realized that this results in a geometry dif ferent from the original one i e a lack of consistency exists in the original
29. code The name of the MONT3D executable generated by the Makefile is specified by macros in the Makefile The name of the single processor version of the code is determined by the Makefile 53 macro M3DSERNAME which has a default value of mont3d The name of the PVM version is set by the macro M3DPARANAME which has a default value of m3dpvm For the worker processes to spawn correctly the name of the PVM version of executable must match the parameter m3dparaname which is declared in the file mont3d par The default value for m3dparaname is m3dpvm More detail is given in Sections 5 5 2 5 6 1 and 5 6 4 When compiling the parallel versions of the code the user s environment variables PVUM_ROOT and PVM_ARCH must be defined for this compilation to succeed When compiling the PVM version of the code on various heterogeneous architectures different executables can be used on different machines as long as they are the parallel versions of the exe cutables For example in the inhomogeneous network of the Suns and Linux workstation men tioned earlier the m3dpvm target was compiled on the Suns while the m3dpvmansi target was compiled under Linux Currently the command line timing and time and date functions are used only by the master in the parallel code Therefore the command line and time and date functions are supported if the master process s executable supports them To compile MONT3D on various architectures specifying the correct t
30. file is of course supplied by the user The block exchange matrix bni files are generated and used by both the master and the workers A lost photon Ist file and a trace trc file are generated by each worker Each file has the worker process s ID appended to the base name The ID number is a number between 1 and NWPROC that is supplied to the worker by the master For example 1f the base name of the run is fn the third worker process will create the files with names such as fn03 1st and fn03 trc The num ber of digits in the index is controlled by the parameter mag see Section 5 5 2 Each of these files can be viewed individually using MPLOT Nagesh and Burns 1994 A single output out file is generated by the master process but temporary output files indexed by worker ID i e fn03 out are also generated by each worker process These temporary output files are deleted at the end of a successful run Their main purpose is to provide information useful for tracking down problems if the run terminates due to errors 5 6 4 Errors While most errors from the master are very similar to that of the single processor version of the code PVM errors and some worker errors need some additional explanation Spawning errors have special error messages and may occur when the processes are trying to spawn The other types of worker errors described below have a generic error message which indicates the basic error type which worker had
31. first 48 characters are the title for the run which is entered on the first line of the input file see Section 3 1 for more details The last 24 charac 77 ters are three 8 character variables which are in order the version number of the code the date when the code was last modified and the language of the source code always f77 The header is the first line printed to the screen during a MONT3D run see the screen output in Chapter 4 for an example It is also used as a page header in the output file B 2 2 Control Information Format Integer Integer Integer 1 Record of Length 3 FORTRAN Format Specification 16i5 Entry Note s Number of surfaces including split surfaces NSPTR 1 Number of materials NUMMAT Number of wavelength bands NBANDS Notes 1 While split surfaces are transparent to the user the plot file contains information about them not the original unsplit surfaces B 2 3 Limiting Dimensions for the Geometry Format Real Real Real Real Real Real 1 Record of Length 6 FORTRAN Format Specification 6 1x f12 7 Entry Note s Minimum X value XLO Maximum X value XHI Minimum Y value YLO Maximum Y value YHI Minimum Z value ZLO Maximum Z value ZHI p bech bech bech bech Notes 1 Each of the hi values is slightly larger than the maximum value for the geometry and each lo value is slightly less than the minimum value for the geometry B 2 4 Surface Informa
32. for DELT then DELT is set to the default value of 0 01 It should be noted that very small values of DELT result in the consumption of excessive computer time For a detailed discussion of the emission algorithm see Burns and Pryor 1989 The range of acceptable SPLITOL values is 1E 20 lt SPLITOL lt 0 01 If a positive value out side this range is entered for SPLITOL SPLITOL is set to the default value of 0 0001 For more information about SPLITOL and split surfaces see Section 2 3 Itis possible to force the code to split all quadrilateral surfaces into triangles To turn this feature on enter a negative value of SPLITOL such that 0 01 lt SPLITOL lt 0 3 3 Grid Dimensions Shading Condition s NSHADE lt 0 entered in Section 3 2 2 otherwise omit card Cols Format Entry Note s 1 5 I5 Number of grid cells in the X direction NGX 1 6 10 I5 Number of grid cells in the Y direction NGY 1 11 15 I5 Number of grid cells in the Z direction NGZ 1 32 Notes 1 Cell divisions along each axis are uniform unless a negative number is entered for the NG vari able In that case the user must enter the grid coordinates for that axis as specified in Section 3 11 It should be noted that in versions of MONT3D prior to version 2 4 all axes must be user defined if NGX is negative otherwise all axes are uniformly divided Input files designed for versions of MONT3D prior to 2 4 may not be forwards compatible here 3 4 De
33. from the last state available to take advantage of previous work This prevents waste of computer resources in recom puting information already available A simulation may be restarted multiple times until the desired level of accuracy is attained To effect this the current state of the solution must periodically be written to disk so that it will be available for a restart run How often this is done is controlled by the input variable NEBLOCK All information required for restart is written to a restart file suffix rst after emission has been completed from each block of INEBLOCKI surfaces see Section 3 2 1 for more information Chapter 4 includes an example of a restart run 2 10 Parallel Version MONT3D now supports parallel execution implemented in PVM Greist et al 1994 The par allel version uses a master worker model The basic operation of the parallel code is as follows The master process reads the input file and checks it for errors If no errors are found the master spins off a user specified number of worker processes NWPROC See Section 3 2 2 and passes to them the input file name and other required information Next all the worker processes read the input file in an abbreviated input phase Since the input file has already been checked by the master many of the checks such as the time consuming check of the validity of the geometry can be skipped during the worker input stage As soon as a worker completes the
34. from the specular angle These features have been observed by Torrance and Sparrow 1966 and are shown conceptually in cross section in Figure 2 7 b Three components of reflectance are modelled weighted diffuse specular and semi specular Each is discussed below The weighted diffuse component exhibits a symmetric shape of revolution about the surface nor mal The weighting exponent rg controls how much the distribution tends toward the normal direction The probability distribution functions PDF s for energy not intensity for the weighted diffuse distribution are PDF 0 tg 1 cos 0 sin 0 2 2 PDF 0 1 27 2 3 13 Diffuse a Traditional Model A 0 Specular 0 A8 Weighted Diffuse Distribution Waisted Offset Semi specular Distribution y b Model in MONT3D Figure 2 7 Cross sectional Views of Reflectance Models 1 0 Isotropic g 0 5 Lambertian iO 05 0 0 0 5 1 0 Figure 2 8 Cross sectional View of Weighted Diffuse Normalized PDF s The coefficient r 1 in Equation 2 2 effects normalization of the distribution when integrated over O from 0 to 7 2 The normalized diffuse reflectance distributions are shown in Figure 2 8 with rq as a parameter Note that rg 1 represents the standard diffuse Lambertian distribution and rg 0 represents an isotropic distribution Values of ry exceeding 1 bias the distribution toward the
35. incident cone angle 0 within a wavelength band k At any particular value of incident cone angle 6 an incident photon has the 1 0 0 0 0 6 90 Incident Angle Degrees 1 Figure 2 6 Material Properties vs Incident Cone Angle 12 following probabilities Pal8 p 9 Pss 8 Tq 9 T 9 T 8 and 1 pa 0 P 0 Pss 9 Lat ks kal ll for diffuse specular and semi specular reflection diffuse specular and semi specular transmission and absorption or emission respectively Curves of material properties must be input for every wavelength band for each material In the old model these curves had to be input by point value as a function of cone angle The new material model allows each of these properties to be input as a single constant value or by reference to a curve which must subse quently be input by point value as a function of cone angle In the case of point value input the computer code parabolically interpolates between each three successive points entered In this case care must be taken to 1 include bounding points of 8 0 and O 90 since no extrapola tion is done and 2 to include enough points varying smoothly to result in good interpolation 1 e discontinuous jumps must be input as steep parabolas with three non coincident points used to define the jump If curves are input by point value then it is strongly suggested that the plot file
36. is intended to model beam or collumnated radiation Emission of this type is accomplished along the direction specified for this material by EBX EBY and EBZ the directional components in global coordinates of the emission vector Here emission is unidirectional all photons emitted from this material type travel in the direction specified by the global components only the point of emission changes Different material types must be defined for each global direction of emission desired When specifying a material of this type care must be taken to ensure that as discussed in Section 2 2 the beam emission will be from the front of the surface not the back In other words the dot product of the emission direction and the surface normal must be greater than 0 for all surfaces that use the material If this is not the case the code exits with an error Note that all interactions absorptions transmissions reflections will depend only on the incident material properties defined for this material Function Emission IETP 2 Here emission is accomplished using computer code supplied by the user more details are given in Section 3 8 2 Either EBX EBY and EBZ or both and q must be specified the example in the code supplies a function only for 6 emission is uniformly distrib uted md The user is cautioned that emission via this option is accomplished using the accept reject method and many trials may occur for each pho
37. mation is divided into three phases The input and solution phases are self explanatory The clean up phase is the time the program spends after the solution phase creating the exchange matrix file Finally upon completion of the run the Unix prompt is issued To find out more about the run at this point the output file box out is available Furthermore the plot file box p t can be used with the MPLOT program Nagesh and Burns 1994 to view the geometry and material properties etc For other more complicated geometries which have holes and other such problems the lost photon file file suffix st the leaks file file suffix ks and the optional trace file file suffix trc may 44 also be used with MPLOT to further analyze the geometry For more details see Sections 2 8 and 5 3 and the MPLOT documentation Section 4 4 contains the screen output generated by a restart run of box in The only modification to file box in was to change NEBLOCK from 2 for the initial run to 2 for the restart run It is pos sible to change a number of other variables before beginning a restart run Basically any variable that does not change the description of the geometry or material properties such as NPHTON can be changed for a restart run It should be noted that when doing the restart run the exchange factor file box nij and the restart file box rst must be present If the run restarted from a crash the block file box blk and any block
38. met after a full surface emission To explain this we first note that Equa tion 2 5 provides the confidence interval for only element ij of the exchange fraction matrix when emitting additional photons actually increases the accuracy of all elements in row i Equation 2 5 is modified to account for this with the rationale that exchange fractions affect the accuracy pro portional to their size Thus we weight each confidence interval by its exchange fraction sum and then average by dividing this amount by the total number of surfaces NSURF to yield the ad hoc NS o row confidence factor for row i C E 19 2 6 k 1 k k Z LF i NSURE i ij VUT J J If the confidence factor for emissions from surface 7 in band k is not met after a full surface emis sion loop then the program continues to perform full surface emission loops until either the spec ified confidence factor is achieved or a maximum number of loops over the surface NPLOOPS have occurred This feature can be used with the restart option to effect a specified accuracy for surfaces traded off against CPU usage The user has quite a bit of control over how many emissions occur for each surface While NDIVX NDIVY and NLOOPS are the same for all surfaces NPHTN and the confidence factor can be specified for each surface see Sections 3 2 3 4 and 3 6 for additional detail It should also be noted that the value of z used by the code for calculation of the
39. nij files file suffix bni must also be present The restart run in Section 4 4 also demonstrates MONT3D s command line interface The f family option specifies the name to be used for all files not specifically named by any other command option More details about the command line interface are given in Section 5 4 Convergence was achieved in the restart run 4 3 Screen Output During Execution of File box in czeeb 1 mont 3d KkKKKKK mont3d Enter prefix for disk files 20 characters or less input file MUST have extension in box 3 D BOX TEST PROBLEM v 2 4f1 04 15 99 77 in nodin3 in surfin3 in wavin in matinnew reading material property curves in curveset in cumdis in fileset in gridin Memory Allocation and Usage Category Allocated Used 1 Nodes inod 15000 words 8 words 0 2 Surfaces isrf 5000 words 6 words 0 3 Materials imat 30 words 2 words 7 4 Wavelength bands God 5 words 1 words 20 5 Restart surface block size iblk 200 words 2 words 1 6 Restart blocks itblk 1000 words 3 words 0 7 Index digits for filename iimag 4 words 1 words 25 8 Grid divisions per axis incg 60 words 1 words 2 45 9 Surfaces including split surfaces isrfs 7000 words 6 words 0 10 Surface segments in grid cells iseg 100000 words 6 words 0 in order in graf in bplane2d input phase comp
40. row confidence factor can be set by a parameter see Section 5 5 2 for more details The default value is 1 96 which represents 95 confidence A rough guess of the size of the exchange fractions is the reciprocal of the number of surfaces in the input file This yields the average exchange fraction size since the sum of any row of the exchange fraction matrix is 1 The number of photons required to be emitted to achieve an aver age level of accuracy may then be estimated from Equation 2 5 or obtained from Table 2 1 through interpolation or extrapolation Errors in the temperatures calculated from radiative flux balances are smaller than errors in the exchange fractions due to the fourth root dependence of temperature upon radiative flux For small errors one may expect the errors in temperatures to be about one fourth of the errors in fluxes Emitting an equal number of photons from each surface may result in a waste of computer time since some surfaces contribute little to the radiative exchange A better approach would be to apportion the numbers of emissions to each surface based upon its estimated power output This is an approach which requires judgement gained through experience with specific problems since the power outputs are generally not known a priori In any case the above approach provides a poten tiometer which can be used judiciously to adjust solution accuracy 2 8 Aid in Debugging and Visualizing MONT3D Geo
41. several numbers of photons To estimate the number of photons required to achieve a given level of accuracy Table 2 1 is pro vided The table gives for each exchange fraction F the number of photons N which must be emitted from a surface to achieve 95 confidence that the exchange fraction is within 1 2 5 10 and 50 of the exact answer The numbers of photon emissions per surface are calcu k lated from the formula for confidence intervals C ij for the exchange fraction from surface i to surface j in wavelength band k F derived by Maltby Maltby 1990 2 5 where z is taken from the standard normal tables Kreyszig 1993 and is 1 96 for 95 confidence Equation 2 5 yields the fractional accuracy in F k j n b 100 times this value is the percent accu racy 18 False Convergence Exchange Factor Convergence 1 10 10 10 107 10 10 Number of Photon Emissions Figure 2 11 Convergence vs Number of Photon Emissions Table 2 1 Accuracy in Exchange Fractions Exchange Level of Accuracy ge 1 2 5 10 50 10 38 377 584 9 594 396 1 535 103 383 776 15 351 10 3 803 184 950 796 152 127 38 032 1 521 10 345 744 86 436 13 830 3 457 138 MONT3D is formulated to attain a specified accuracy for each row i of the exchange factor matrix The program is constructed to loop over successive emissions from each surface if a preset accuracy tolerance is not
42. surface is found for a given photon NLOST specifies the number of such occurrences before the run is aborted For the parallel version of the code each worker process aborts when it loses this number of photons As in Note 5 above the other worker processes continue and the aborted block is fin ished by another worker 28 7 Each MONT3D run involves emitting from NBANDS NSURF emitters or surfaces After emission and tracing from every INEBLOCKI emitters the exchange matrix and the restart files are written to disk Thus it is possible to restart only from every INEBLOCKI states Selecting a small value of INEBLOCKI will ensure that restart information is written frequently to the out put file Still if NEBLOCK is set too low the file writing overhead may become significant If NEBLOCK is negative the previous state is read from the restart and exchange matrix files Restart may be of two types 1 where the previous state is incomplete e the previous run was interrupted or 2 the previous state is not converged More detail is given in Section 2 9 and Chapter 4 NEBLOCK in versions of MONT3D prior to version 2 4 was known as NINCR 8 For more details on the initial seed and the RNG in general see Sections 2 11 5 5 2 and 5 6 5 3 2 2 Card 2 Cols Format Entry Note s 1 5 I5 Type of geometry IGEOM 1 6 10 5I1 Output print control code toggles IPRINT 2 6 Il IPRINT 1 1 exchange fractions are written to output file 3 7
43. surfaces including split surfaces More detail on setting NPHTN and other such topics is given in Sections 2 7 and 2 2 2 4 Surface Concatenation Previous versions of MONT3D permitted surface concatenation Current versions do not due to the limitations associated with error checking and restart it is impossible to recover restart infor mation from concatenated information as some information is lost during the concatenation pro cess If it is desired concatenation can be done a posteriori by operating on the exchange factor matrices 2 5 Material Properties The current version of MONT3D has a new material model The new material model extends the older material model in two respects First semi specular outgoing directional distributions are included for both transmission and reflection Secondly material input has been simplified The input formats for the new and old material models are not compatible MONT3D will read material property input in either the new or the old input format The input control variable NUMMAT the number of materials is used to control the format of the material properties to be input If neg ative the new format is used if positive the old format is used See Section 3 2 1 for the input spec ification of NUMMAT The material properties are defined in terms of a local spherical coordinate system Figure 2 5 defines the cone angle 8 and the azimuthal angle d with d and y in the plane of the surface
44. the letter in the format specifies the type of the variable A for character E for floating point and I for integer It should be noted that floating point numbers may be entered in many formats including as integers 1 in decimal format 1 or 010 or 0 001 or in scientific notation 3 07e 3 or 0 307E 2 Default values marked as DEFAULT are used if the input file contains zeroes or blanks read as zero by FORTRAN If no default value is given then zero is the default value 3 1 Title Card Cols Format Entry Note s 1 48 DAN Heading to appear on output 3 2 Control Cards 3 2 1 Card 1 Cols Format Entry Note s 1 5 I5 Number of dimensions NDIM 1 6 10 I5 Number of nodal points NUMNP 11 15 I5 Number of surfaces NSURF 16 20 I5 Number of materials NUMMAT 2 21 25 I5 Number of wavelength bands NBANDS 26 30 I5 Number of photons emitted per band per subsurface NPHTON 4 27 31 35 36 40 41 45 46 50 I5 I5 I5 Maximum number of reflections allowed per photon before a warning is issued NREFS DEFAULT NREFS 100 Maximum number of warnings before the run is aborted NWARNS DEFAULT NWARNS 50 Maximum number of lost photons NLOST Surface emitter increment for writing restart information NEBLOCK NEBLOCK lt 0 Restart run from previously stored state or crash NEBLOCK gt 0 New run Restart information written to disk after every INEBLOCKI surfaces DEFAULT NEBLOCK 10 51
45. the top and bottom of the box uses the same curve for its diffuse reflec tance and has a constant value for the specular reflectance 0 1 Due to the simplicity of the geom etry and the small number of surfaces it contains grid shading is not used It should be noted that even moderately complex geometries will benefit from grid shading see Section 2 6 for more details A complete description of the input format is given in Chapter 3 Figure 4 1 3 D Geometry of File box in The input file is listed below and is also available at the MONT3D WWW site mentioned in Sec tion 1 1 It should be noted that comment cards are used throughout the input file to identify the input variables and where they should be entered As shown in Chapter 3 each variable is restricted 41 to being entered in a certain range of non overlapping columns on a certain card The last letter of each variable name on the comment cards marks the last column that can be used to input that vari able except for IGEOM If the code reads blanks as zeroes see the beginning of Chapter 3 for more detail then all variables should be right justified and should line up as shown in the file below For maximum compatibility all input files should be right justified
46. the user to ensure this All material incident radiative properties may be explicit functions of the incident photon angle and be dependent upon energy through the band wavelength formulation Donald L Brown of Lawrence Livermore National Laboratory LLNL and Katherine Bryan of Oak Ridge National Laboratory have exhaustively exercised the 3 D code checking it for validity 3 D Cartesian System Z Figure 1 1 Example Geometry Which Can be Simulated The code has recently been updated extensively The core of the code has been recoded improv ing the efficiency of the code by around 44 in test cases Zeeb 1997 Zeeb and Burns 1999 Also the 3 D code has been parallelized to run under the PVM Geist et al 1994 environment with very good success Furthermore a new material model which includes semi specular com ponents of reflectance and transmittance has been implemented in the 3 D code In order to use these enhanced capabilities to the greatest effectiveness additional detail is required in the input file which has been changed from the older format to the one described herein However input files in the old format will still work as the changes are backwards compatible The current version of the code can be run on any computer which possesses a fully featured FORTRAN 77 or Fortran 90 compiler and has been extensively tested on Sun Hewlett Packard IBM DEC SGI Intel and Macintosh archite
47. to identify these six message types for both the master and the workers If the error occurred while packing or unpacking data for communication the last number marked item indicates for which item from the first to the last data item the error occurred 5 6 5 Random Numbers As discussed in Section 2 11 2 each worker process is supplied with an unique seed generated by the master process which the worker then masks with the process number to obtain the initial seed for that processor for the run While the random number state is saved for single processor restart runs this is not the case for the parallel version Instead the workers receive a totally new seed from the master for each restart run The reason for this is that the runs are done asynchro nously under PVM Since exact reproduction is impossible a different set of random seeds is used for each parallel restart run and CPU time and disk space are saved by not saving the random states When parallel restart runs are done care must be taken to ensure that the random number streams are uncorrelated with those of the previous run Since MONT3D uses canonical seeds generated by a binary shift register if the initial seeds used by the processes differ by even one bit then good 63 statistical behavior between the sequences is assured If the default seed INSEED lt 0 see Section 3 2 1 1s used for two consecutive continuing runs then the same initial seeds will be used f
48. to switch to different machines change the number of worker pro cesses or even switch between the parallel and single processor versions of the code More detail is given in Section 4 5 5 6 2 Worker Processes It should be noted that in the parallel environment the master and workers are just Unix pro cesses While it is possible to have multiple worker processes on one CPU it is generally not rec ommended On a Unix workstation only one process is using the CPU at a time When more than one process is executed on a CPU CPU cycles are wasted in the overhead of switching between processes For the master worker model used in MONT3D one worker process on a CPU is always more efficient than two worker processes on the same CPU There is only one time when a user might want two processes on the same CPU Since the master process does so little work during the solution phase the minimum overall wall clock time may be obtained by placing a worker pro cess on the CPU that has the master process Research into the benefits of having a worker on the master CPU is currently being done The benefit is probably greater as the total number of CPU s used on a problem decreases PVM does not allow much control over which processes run on which CPU To determine the CPU on which to spawn a process PVM usually uses a list of the CPU s in the order that they were added to the virtual machine The master CPU is at the end of the list Multiple processes a
49. 2 6 Material Properties vs Incident Cone Angle 00 0 ceeeeseessecesecesceeeneecsaecnseenseeeeneees 12 Figure 2 7 Cross sectional Views of Reflectance Model 14 Figure 2 8 Cross sectional View of Weighted Diffuse Normalized PDP S cee eeeeeeeeeeeeees 14 Figure 2 9 Normalized Weighted Semi specular Directional Distributions cee eeeeeeeeees 15 Figure 2 10 2 D Illustration of the Grid Shading AlgorithM oooconnnnccnnoncccnonccnnonccononccnonnncnnnncnnns 17 Figure 2 11 Convergence vs Number of Photon Emissions cooocooccnoconooncnononanononononnncnnccnnccnannon 19 Fig re 2 12 Example of a Reversed Bd reas 21 Figure 2 13 Example Master Worker Architecture ici iii 23 Figure 2 14 Bit Structure of 32 Bit Initial Seed for Parallel Processes oooooocnccnnnnnnococonnnannnnnnnno 26 Figure 4 1 3 D Geometry of File bOX iIn isisicin tun ici dee 41 Figure 4 2 Material Property Curve for File DoxiA ui id dia 43 Figure 5 1 Contents of Script File submit EE 64 Figure A 1 Conventions for Outgoing ANgleS ooconnnococinococonaccconnnnononcnonnncnononcnonncnononoconnnccnnnncnnns 70 List of Tables Table 2 1 Accuracy in Exchange Fractions td 19 Ke E ER RE KEE 56 Table 5 2 Command Line File Control 100 id eo STE 57 Table A 1 Material Property Summary ege BEE Ri Ee 69 vi CHAPTER 1 INTRODUCTION This manual encompasses the 3 D Monte Carlo radiative exchange factor computer code MONT3D This chapter gives a qui
50. 5 2 3 Macintosh The Macintosh version has been compiled on a 233 MHz 604e PowerPC chip using the Absoft 77 and 90 compilers A full featured version of the code can be obtained by compiling the fol lowing files m30s f m311s f m312s f m313s f m32s f m3nopara f m3comline f m3etime f m3fdate f mont3d par and mont3d com The compilation also requires the Absoft unixlib o file which is usually in the AbsoftLibraries folder in the Libraries folder in the MPW folder The code must be compiled with the fold to uppercase option N109 The general optimization O and 604 PowerPC specific optimizations Q92 if applicable options both improve performance Best performance is obtained compiling the code as an MPW Tool so it can run in the MPW Shell pro gram Performance is further increased by using a minimum of extensions and control panels Many timings have been done of the 233 MHz 604e PowerPC Macintosh and performance has been found to be very good This particular Macintosh is almost 5 times faster than a 36 MHz Sun Sparc 10 workstation 5 3 Files Generated and Used by MONT3D This section briefly describes the files used by MONT3D For specificity a prefix of fn is used Table 5 1 gives the files used either pre existing or generated during execution by MONT3D Files listed as temporary are deleted by the end of a successful run most are deleted at the end of the run Almost all the files listed in Table 5 1 are ASCII files
51. ANSI compliant except for bitwise operations required for the random number generator as men tioned above m3dpvm creates the parallel PVM implementation of MONT3D with all features activated using m3comline f m3ctiming f and m3fdate f The timing results generated are clock time It has been compiled on Sun DEC Alpha and Hewlett Packard workstations m3dpvmibm creates the parallel PVM implementation of MONT3D and activates the command line and the Fortran 90 versions of the clock timing and time and date functions using the files m3comline f m3f90timing f and m3f90date f The timing results generated are clock time This version compiles on the IBM RS 6000 platform m3dpvmf90 creates the parallel PVM implementation of MONT3D activates the Fortran 90 ver sions of the clock timing and time and date functions but not the command line It uses using the files m3nocom f m3f90timing f and m3f90date f The timing results generated are clock time This version can be compiled on any full featured Fortran 90 compiler m3dpvmansi creates the parallel PVM implementation of MONT3D with all optional features deactivated It uses the files m3nocom f m3notiming f and m3nodate f clean deletes all the object files in the current directory This option should be used whenever the user wants to start the compilation over from scratch If code does not seem to compile correctly then the user should try using the clean target and then recompiling the
52. Il IPRINT 2 1 lost photons are written to console and output file 4 8 Il IPRINT 3 currently unused reserved for future use 9 Il IPRINT 4 1 complete material property information is 5 written to output file 10 Il IPRINT S5 1 surfaces wholly or partially in each grid cell are written to output file 11 15 ID Number of concats NUMCAT 6 16 20 I5 Data check code IDATA IDATA 0 Normal execution IDATA 1 Data check only execution stops after input phase 21 25 I5 Number of x emission points per surface NDIVX 7 DEFAULT NDIVX 5 26 30 I5 Number of vi emission points per subsurface NDIVY 7 DEFAULT NDIVY 5 31 35 I5 Shading in geometry NSHADE 8 NSHADE gt 0 Shading distance algorithm NSHADE lt 0 Shading grid shading algorithm 36 40 I5 Trajectory control code ITRACES 9 ITRACES gt 0 Trajectory information written to disk file trc extension 29 ITRACES 0 Trajectory information not written to disk file 41 45 I5 Number of worker processes NWPROC 10 46 50 I5 Maximum number of photon convergence loops NPLOOPS 11 12 DEFAULT NPLOOPS 1 51 55 SIL Parallel option code IPAROPT I as follows 13 51 Il IPAROPT 1 worker spawning options 14 IPAROPT 1 0 workers can spawn on any CPU IPAROPT 1 1 workers can not spawn on master CPU IPAROPT 1 2 xterms with debug sessions are created for each worker IPAROPT 1 3 IPAROPT 1 1 and 2 combined Other array elemen
53. PLOT description of this file Nagesh and Burns 1994 the last two numbers written to this record are supposed to be an integer MAT and a real EO Neither of these two variables apply to MONT3D so they are replaced by ND and LERT 4 LERT is the surface number of the last surface with which the photon was in contact whether that was as an emission a reflection or a transmission As described in Section 2 2 each surface 1s divided into NDIVX x NDIVY subdivisions ND gives the number of the subsection from which the lost photon was emitted It ranges from 0 to NDIVX x NDIVY 1 It should be real ized that if a photon is reflected or transmitted before it is lost LERT is generally not the surface that emitted the photon B 3 2 Photon Ray s Starting Point 1 Record of Length 3 FORTRAN Format Specification 3 2x e10 4 Format Entry Note s Real X coordinate of photon ray s starting point Real Y coordinate of photon ray s starting point Real Z coordinate of photon ray s starting point B 3 3 Photon Ray s Ending Point 1 Record of Length 3 FORTRAN Format Specification 3 2x e10 4 Format Entry Note s Real X coordinate of photon ray s ending point Real Y coordinate of photon ray s ending point Real Z coordinate of photon ray s ending point B 4 Exchange Matrix File Suffix nij Unit 8 As discussed in Section 1 4 thermal balance codes such as TOPAZ3D Shapiro 1985 require the exchange matrix information generated by
54. USERS MANUAL for MONT3D Code Version 2 4 by Charles N Zeeb Patrick J Burns and Klemens Branner Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 970 491 7479 5778 and 7479 E mail Addresses czeebOlamar colostate edu pburns colostate edu and klem lamar colostate edu and John Dolaghan Lawrence Livermore National Laboratory E mail Address dolaghan OlInl gov April 1999 Table of Contents CHAPTER 1 INTRODUCTION crios 1 ABU a ie co 1 12 Theoretical FOO a o e e o a Bs 2 1 3 View EE 4 1 4 MON FSD Implementation as E a E elit cat S 4 I Overview f the Manta Lit Bi A EE 5 CHAPTER 2 COMPUTER CODE BACKGROUND AAA 6 GN e 6 A ciel es x acai teehee doe a ds we scans poet a cat Ea dental a ae Aap S aiat 6 2 3 Split Surfaces Planarity and Convexity wiv sicisscccssalageecedsaccesasaceecsasvenscdesebencetuasactesssswesans 8 24 Surtace ONC ate AO Si CA A hae eee Nee Bae aes 10 OMA e EE 10 2 31 Material Property Curves taaan 11 2 5 2 Outgoing Directional Dist But OMS ies tgteegel 3s eedeTeeet E ieget dg dE 13 A O Sh Road eee de Olah Ges 16 2 5 4 Cases Where the Reciprocity Relations Do Not Hold 17 EE 17 2 7 Number of Photons Convergence and ACCUTACY EEN 18 2 8 Aid in Debugging and Visualizing MONT3D Geometries ccccoccnocononcnannnonnnononcnoncnanncnnnnon 20 ZO REA or 22 2 TO Parallel Vero dt nl tn 22 2 11 Pseudo Random Numbers vinil 24 SN BEN d 24 2112 Imp
55. Virtual Machine A User s Guide and Tutorial for Networked Parallel Computing MIT Press Cambridge MA Also available as a WWW document URL http www netlib org pvm3 book pvm book html Golomb S W 1982 Shift Register Sequences Revised Ed Aegean Park Press 66 Kreyszig E 1993 Advanced Engineering Mathematics 7th Ed John Wiley amp Sons New York Maltby J D Burns P J and Winn C B 1986 Monte Carlo Simulation of Radiative Heat Transport in Passive Solar Buildings Proceedings of the 1986 American Solar Energy Society Conference Boulder Colorado June 9 11 1986 Maltby J D 1987 Three Dimensional Simulation of Radiative Heat Transfer by the Monte Carlo Method M S Thesis Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Maltby J D 1990 Analysis of Electron Heat Transfer via Monte Carlo Simulation Ph D Disser tation Department of Mechanical Engineering Colorado State University Fort Collins CO 80523 Maltby J D and Burns P J 1991 Performance Accuracy and Convergence in a Three Dimen sional Monte Carlo Radiative Heat Transfer Simulation Numerical Heat Transfer Part B Fun damentals Vol 16 pp 191 209 Maltby J D Zeeb C N Dolaghan J and Burns P J 1994 User s Manual for MONT2D Version 2 6 and MONT3D Version 2 3 Department of Mechanical Engineering Colorado State University Fort Collins CO
56. W document URL http www colostate edu pburns monte documents html Zeeb C N and Burns P J 1999 Performance Enhancements of Monte Carlo Particle Tracing Algorithms for Large Arbitrary Geometries To be presented at the 1999 ASME National Heat Transfer Conference Albuquerque NM August 15 17 1999 Zeeb C N and Romero V J 1999 LAYMC A Monte Carlo Code for Modeling Photon Trans port in Layered Participating Media Theory and User Manual version 2A to be published as a Sandia National Laboratories report unlimited distribution Expected 1999 68 APPENDIX A OLD MATERIAL MODEL This appendix covers the old material model The first section of this appendix gives an overview of the old material model This is followed by a section on the specification of outgoing angles for diffuse and specular reflection and transmission The next four sections describe the seven material types supported by the old material model The last two sections cover the input card format for entering in the material type data and the material property curves using the old material model A 1 Overview The old material model is only used if NUMMAT the number of material input specification in Section 3 2 1 is greater than 0 If NUMMAT is less than 0 the new material model which is described in Sections 2 5 and 3 8 3 10 is used More detail about the input specifications for the old model are given below in Sections A 7 and
57. Z coordinate of photon ray s ending point B 6 Leaks File Suffix Iks Unit 11 The leaks file contains information about potential leaks It can be used with MPLOT Nagesh and Burns 1994 to display these potential leaks see Section 2 8 for more details All the code for the writing of this file can be found in the subroutine order in the file m313s f The following record is repeated as needed for each potential leak B 6 1 Leak Information Format Integer Integer Integer 1 Record of Length 3 FORTRAN Format Specification 1x i2 1x i5 1x i2 Entry Note s Type of leak ITYPEL 152 Number of the surface associated with the leak Number of the side associated with the leak 3 Notes 1 ITYPEL is 1 for a reversed edge 2 for no match found with any other surface 3 for a slip sur face If ITYPEL is equal to 4 then the line is a continuation card that contains additional infor mation about the last leak 2 The number of records required for each type of error varies While only one record is required for ITYPEL equal 2 two are required for ITYPEL equal since the reversed edge is shared by two surfaces For ITYPEL equal 3 up to 15 records may be required since a slip surface may 84 touch many surfaces The limit of 15 is a hardcoded limit in MONT3D itself When more sur faces than this are involved with the slip surface they are not written to the leaks file 3 Side n is between nodes n and n 1 for the surface
58. al and material property information fn Ist Contains lost photon trajectories if any This file can be viewed by MPLOT Nagesh and Burns 1994 For the parallel version a separate file fnxx Ist is generated for each worker process xx stdin Standard input keyboard stdout Standard output screen fn in Input file with comment cards in the format described in Chapter 3 This file is used to generate the file of unit 1 fn nij Exchange matrix file which contains the results used by the thermal analysis code TOPAZ3D Shapiro 1985 See Section 1 4 for more details fn trc Trajectory file written if ITRACES 0 see Section 3 2 2 To be used with MPLOT Nagesh and Burns 1994 to plot particle trajectories For the parallel version a separate trace file fnxx trc is generated for each worker process xx 10 fn out ASCII output file Contains echo of all input and other information as determined by IPRNT see Section 3 2 2 The parallel version also gen erates for each process xx a temporary output file fnxx out that is deleted at the end of a completed run If the run exits abnormally these files may be used for debugging 11 fn Iks Leaks file To be used with MPLOT Nagesh and Burns 1994 to iden tify potential leaks 12 fnxx bni Temporary ASCII file which contains the exchange matrix for the est block of surfaces The full exchange matrix nij file onl
59. and 70 The distributions shown in Figure 2 9 are revolved about the preferred outgoing direction spreading the distribution in cone and azimuthal angles It should be noted that as r approaches infinity the semi specular distribution approaches a specular distribution at the preferred outgoing angle Axis of Revolution 9 30 Axis of rss 10 ss 10 Revolution a Op 30 b Op 70 Figure 2 9 Normalized Weighted Semi specular Directional Distributions Shown in Cross section These same three distributions apply to transmission except that the distributions pass through the surface instead of being reflected from it These distributions for transmission allow approxi mate modelling of semi transparent materials such as glass and translucent materials such as lighting diffusers Although the material models in MONT3D permit accurate modelling of energy no refraction is modelled introducing an error in direction However in many instances the direc tional changes induced by refraction are small and may be neglected with good accuracy 15 Care should be taken when modelling transmission All exterior surfaces of a geometry must be totally non transmissive If this is not the case photons transmitted through the exterior surfaces will be lost MONT3D does not check for this and no warning will be issued during the input phase 1f this error occurs In addition to being reflected or transmitted the
60. and may be read and printed with no dif ficulty Files for unit 13 are binary files and are only read by MONT3D itself The Unix utility od octal dump may be used to examine binary files perform a man on od for instructions The description of the input file format is given in Chapter 3 and most of the other files are described in Appendix B 5 4 Specifying File Names MONT3D must have the names specified for all of the files shown in Table 5 1 This section explains the naming conventions and methods of specifying these file names There are two methods of specifying the file names default and command line If no name s are specified on the command line or the command line is disabled see Section 5 1 2 the code will query the user via the console for a base file name fn This base name is used as the prefix for all files in the run The command line method of specifying the file names allows the user more flex ibility in defining file names Most file names can be specified independently according to the con ventions in Table 5 2 55 Table 5 1 MONT3D Files Unit Name Function fn scr Temporary input file with comment cards stripped away File is gener ated by code This is the file actually read during the input phase fn rst Restart file required for restarting from a crash or a completed run fn plt Plot file to be used with the program MPLOT Nagesh and Burns 1994 Contains geometric
61. apiro Shapiro 1983 A number of related codes are available in the public domain These include the postprocessor SMOOTH Dolaghan et al 1992 which smooths the results and establishes reciprocity the graphical postprocessor MPLOT Nagesh and Burns 1994 which runs on Sun workstations and under Microsoft Windows MONT2D Maltby et al 1994 an older 2 D version of the MONT3D code which simulates 2 D and axisymmetric geometries MONT3E Crockett et al 1990 a code for simulating electron transport in three dimensions in the presence of a spatially nonuniform magnetic field SPUT3D Dolaghan 1991 a code for simulating molecular redistribution during sputtering in three dimensional enclosures and MONT3V Dolaghan 1996 a code for simulat ing rarefied gas dynamics Information on these codes may be obtained from the authors of this manual 1 2 Theoretical Formulation MONT3D is formulated in the Monte Carlo style where a large number of photons are emitted from each surface and traced until each is absorbed by another surface Using the subscripts 7 and j to denote the emitting and absorbing surfaces respectively and the superscript k to denote the wavelength band it can be shown that k ENG at apo IA Sek N i where k eg Ona j One way rate of radiative heat transfer emitted from surface i and absorbed by surface jin wavelength band k W e hemispherical emittance of surface i in wavelength band k N
62. arget may not be enough There are three macro definitions in the Makefile that may have to be set as well The Makefile lists default values for these macros for Sun SGI IBM RS 6000 DEC Alpha and Hewlett Packard platforms and for the NAG f90 compiler under Linux These macros are FC specifies the FORTRAN compiler This is usually set to f77 For the Hewlett Packard plat form this must be set to fort77 Of course if a Fortran 90 compiler is used this should be set to f90 FFLAGS specifies the FORTRAN compiler flags Some platforms require special flags Flags are specified in the Makefile to allow the user to compile the code on several platforms and control optimization If a person is knowledgeable about optimization options for his specific computers he may want to change the default settings for these flags FFLAGS can be used to compile the code with almost any options desired check the compiler s documentation for specifics Popular choices are optimizing O option debugging g option array bounds checking C option and profiling p or pg option LPVMFELAGS specifies the libraries for the PVM code which are used during linking The direc tory to search for the PVM libraries and the libraries pvm3 and fpvm3 must always be specified Some platforms may require other libraries For example the Sun version also requires the libraries nsl and socket Appropriate values of LPVMFLAGS are listed in the Make
63. called by subroutines in multiple source code files and other miscellaneous routines m311s f the main input routine and all the subroutines required to input nodes surfaces and wave length bands m312s f the input routines for entering material properties and material property curves 50 m313s f the input routines for entering and setting up the grid and post processing of the input data m32s f the solve routines mont3d par parameters that control the sizes of arrays and other quantities see Section 5 5 below mont3d com all common variables not specific to the parallel version of the code 5 1 2 Command Line The command line allows the user individually to specify file names for most of the files gener ated by MONT3D If the command line is disabled all command line input is ignored and the user must specify the base file name by entering it when prompted during program execution Addi tional detail is given in Section 5 4 Three stubs are available for the command line m3comline f activates the command line Requires the nonstandard subroutines iargc and getarg to be supported by the compiler Tested on Sun SGI DEC Alpha Hewlett Packard IBM RS 6000 and Macintosh Absoft FORTRAN platforms m3nocom f deactivates the command line for platforms such as the NAG f90 compiler under Linux which do not support the subroutines iargc and getarg m3pccom f activates the command line when compiling the code
64. ck overview of the code particularly its latest version 2 4 The chapter begins with the background of the code This is followed by a theoretical formulation of exchange factors calculated by the code Next is a brief discussion of view factors This is fol lowed by a short discussion of the MONT3D implementation The chapter ends with an overview of the rest of the manual 1 1 Background MONT3D was developed in the Department of Mechanical Engineering at Colorado State Uni versity CSU beginning with the work of Scott Statton in 1983 Statton 1983 continuing with the work of James D Maltby Maltby 1987 Maltby 1990 Charles N Zeeb Zeeb 1997 Zeeb and Burns 1999 and Klemens Branner Branner 1999 The code is used to calculate radiative exchange factors for enclosures with a nonparticipating medium The focus is complex geometries rather than sophisticated physics A simple geometry which may be simulated is shown in Figure 1 1 The 3 D code is capable of simulating geometries modeled as assemblages of generalized quadrilaterals and triangles which are constrained to be flat but may otherwise be in any orien tation Curved surfaces must be approximated by a sufficient number of flat surfaces sometimes termed faceting to capture the curvature Surfaces may absorb photons or they may reflect and or transmit them specularly semi specularly and or diffusely All exterior surfaces must be non transmissive 1t is left to
65. code using selected stubs All nonportable parts of the MONT3D code the command line the timing and the time and date functions have been separated into stubs If an architecture does not support a feature it can be compiled with a stub that omits the feature Alternatively it is possible to create a stub that imple ments that feature specifically for that platform The only potentially nonportable aspects of MONT3D are the bitwise operators used in the ran dom number generator The bitwise operator functions used are those defined in the Fortran 90 standard While these bitwise operations functions are not part of the ANSI FORTRAN 77 stan dard these subroutines have been supported on every platform tested so far and appear to be included in all current FORTRAN 77 compilers as extensions The parallel portion of the code is also implemented as a stub The only difference between the parallel and single processor versions of the code is which stub is used In the subsections below various files are described starting with the files common to all ver sions Next the stubs to support the nonportable features command line timing and date and time are covered Finally the parallel stubs are discussed Further detail is also be given in the next sec tion which covers compiling MONT3D for various platforms 5 1 1 Files Common to All Versions Every compilation of MONT3D requires the following files m30s f the main program routines
66. ctures A robust Makefile has been implemented which allows the code to be compiled on virtually any Unix platform although in some cases some nonessential functions will be lost More detail on compiling the code for Unix Microsoft Win dows and Macintosh platforms is provided in Chapter 5 Should compilation problems occur one of the authors should be contacted In order to serve users better a World Wide Web site for the code exists at http www colostate edu pburns monte html The WWW site will include general information about the code contact information for the authors the current version of the manual and other documents of interest A number of related publications exist wherein the code has been applied to various problems including a detailed test of the Separator Development Facility SDF Maltby 1987 the calcula tion of radiative exchange in passive solar enclosures Maltby et al 1986 and application to the Laser Isotope Separation LIS process Burns and Pryor 1989 Work has been done to include the modeling of combustion gases particularly carbon dioxide and water vapor in MONT2D Zeeb 1996 Five other publications of interest are Pryor and Burns 1986 Burns et al 1990 Maltby and Burns 1991 Burns et al 1992 and Schweitzer et al 1993 Also a comprehensive review article of the MONTE codes is in press Burns and Pryor 1999 Finally an alternative approach for diffuse view factors is the FACET code of Sh
67. diating surface is assigned a material number and all material properties are independent of spatial position on a single surface More detail on the material properties is given below in Sec tion 2 5 Referring to Figure 2 3 a one observes the local primed coordinate system with vertex at Ny and axes as shown Each surface is divided into equally spaced regions and emission occurs from the centroids of these subsurfaces The user determines how many subsurfaces each surface in the geometry will be divided into by specifying NDIVX and NDIVY the number of subdivisions in the x and y directions see Section 3 2 2 for the input specification of these variables Figure 2 3 b depicts this for four subdivisions in the y direction and three subdivisions in the x direction here editorial license has been taken as in general x is not aligned with the lines N N or N N3 as it is normal to the y and z axes The dots in Figure 2 3 b indicate the photon emission points The number of photons emitted from each point is scaled by the area of its subsurface to eliminate bias that would otherwise result in hot spots At least 10 divisions in x and y are rec ommended for uniform surface emission default is 5 Additionally at least 100 photons should be emitted from each emission point per loop specified by the variable NPHTN for each surface to render insignificant round off problems in scaling photon emissions to subsurface area
68. drilaterals The convexity test in MONT3D has two parts For the first convexity test a check is done that the sum of the lengths of each pair of non adjacent sides is shorter than the sum of the lengths of the two surface diagonals If this is not the case the surface is rejected whether it has been split or not and MONT3D exits with an error For the second convexity test a check is done of the sum of the areas of triangles comprising the surface for both the cases of splitting along the lines from node 1 to node 3 and from node 2 to node 4 For a planar surface if the areas do not match within a certain tolerance the quadrilateral is considered concave and MONT3D exits with an error The tolerance is given as the percent difference of the areas PDA being compared This tolerance pdamax is a parameter which can be set by the user see Section 5 5 2 for more details Its default value is 0 1 a 0 1 difference between the two areas Non planar split surfaces often fail this test but when they do only a warning is issued It should be realized that the PDA for a surface is a good measure of the lack of consistency involved in modelling the surface as two split surfaces or as convex The larger this value the greater the chance that the surface is modelled incorrectly for example as overlapping triangles Since MONT3D accepts any non planar set of split surfaces no matter how large their PDA value the user must make sure that the split su
69. e 6 Hereinafter we drop the explicit dependence upon wavelength band k and carry an implicit dependence It should be noted that all properties may be considered in terms of probability 1 e Pa 0 is the probability that a photon of incident angle O will be diffusely reflected p 8 is the probability that a photon of incident angle 8 will be specularly reflected etc Furthermore the total reflectance in band k is the sum of the specular semi specular and diffuse components and simi larly for the total transmittance The fundamental difference among the specular semi specular and diffuse components is the shape of the outgoing directional distributions for these components covered in Section 2 5 2 below Since material properties are both constant in each wavelength band and independent of o the emittance and absorptance for a given wavelength band and 0 are equal by virtue of Kirchoff s law The absorptance and emittance here are determined as the complement of the other properties Thus specification of the diffuse specular and semi specular reflectances and transmittances as functions of the incident angle uniquely defines the incident properties within one wavelength band for a material In the case of ordinary emission the directional emittance is determined from the absorptance However other possibilities for emission exist as described below in Section 2 5 3 Figure 2 6 depicts the material property curves as functions of the
70. e Condition s MTYPE 2 1 0 or 2 omit otherwise CARD 1 Cols Format Entry Note s 1 16 2A8 Name of curve e g specular trans CN1 CN2 17 21 I5 Material number MN 1 22 26 I5 Wavelength band number IB 1 72 27 31 32 36 Cols 1 10 11 20 I5 I5 Format E10 0 E10 0 Curve number NJ 1 2 Number of points to be input for this material NP CARDS 2 to NP 1 Entry Note s Cone angle O 3 Specular transmittance p 8 Notes 1 These values are used to check that the data are input properly by material number band num ber and curve number 2 A curve number of 1 must be input for specular transmittance 3 NP number of cards must be input for the curve A 8 2 Diffuse Transmittance Cols 1 16 17 21 22 26 27 31 32 36 Cols 1 10 11 20 Format 2A8 15 15 15 15 Format E10 0 E10 0 Condition s MTYPE 1 or 2 omit otherwise CARD 1 Entry Note s Name of curve e g diffuse trans CN1 CN2 Material number MN 1 Wavelength band number IB 1 Curve number NJ 1 2 Number of points to be input for this material NP CARDS 2 to NP 1 Entry Note Cone angle O 3 Diffuse transmittance Za Notes 1 These values are used to check that the data are input properly by material number band num ber and curve number 2 For diffuse transmittance curve number 1 for MT YPE 1 and curve number 2 for MTYPE 2 3 NP number of cards must be input for the curve
71. e previous card It should be noted that if the program generates nodes they should not be input elsewhere 3 6 Surface Data Cols Format Entry Notes 1 5 I5 Surface number N 1 33 6 10 ID Node N NODES 1 N 2 11 15 I5 Node Ny NODES 2 N 16 20 IS Node N3 NODES 3 N 21 25 ID Node Ny NODES 4 N 26 30 5X Skip 31 35 ID Number of surfaces to be generated after current surface NMISS 3 36 40 I5 Increment of generation INC 3 41 45 5X Skip 46 50 I5 Surface material number MATNUM N 51 60 10X Skip 61 65 I5 Number of photons NPHTN 4 66 70 I5 Photon increment INCP 5 71 80 E10 0 Convergence tolerance for surface ERRMAX N 6 DEFAULT for surface ERRMAX N ERRDEF 7 Notes Surfaces can be input in any order All surfaces from 1 to NSURF entered in Section 3 2 1 inclusive must be input or generated as described in the notes below The outward normal must be such that the right hand rule as explained in Section 2 2 applies Unpredictable and erroneous errors may result if this convention is not adhered to for all sur faces NMISS additional surfaces are generated by successively incrementing surface numbers by 1 and all 4 node numbers by INC NPHTN different from 0 overrides NPHTON entered in Section 3 2 1 the number of photons per subsurface division If NPHTN is negative no photons will be emitted from the surface For more details see Sections 2 2 and 2 7 Similar to INC in the node input above F
72. ed for the parallel version of the code Tested on Sun DEC Alpha IBM RS 6000 and Windows Microsoft FORTRAN platforms 51 m3etiming f allows the code to collect timing information about the run in CPU time Requires that the nonstandard subroutine efime be supported Mainly used for the single processor version of the code Tested on Sun SGI DEC Alpha Hewlett Packard and Macintosh Absoft FORTRAN platforms More detail on the use of this stub under Microsoft Windows Microsoft FORTRAN is given in Section 5 2 2 m3f90timing f allows the code to collect clock time using the Fortran 90 subroutine It is used by the parallel and single processor versions of the code on computers such as the IBM RS 6000 which do not support the subroutine etime It is also the preferred timing stub to use for Microsoft Windows Microsoft FORTRAN m3notiming f deactivates timing for platforms which do not support any of the timing routines listed above 5 1 4 Time and Date Information Time and date information is rather important because it is used to create time generated seeds for the random number generator see Sections 2 11 and 3 2 1 for additional detail If time and date information are disabled then the time generated seed is an internal constant To obtain different random number sequences the user must supply different initial seeds in the input file Three stubs are available for time and date information m3f0date f allows the code to
73. emporary binary file tni Now writing the exchange numbers from the temporary binary file tni to the nij file normal termination Convergence information for band 6 completed surfaces did not emit O out of the and 6 out of for the emitting Average error Minimum error Maximum error the surfaces 0 1957E 02 0 1938E 02 0 1984E 02 o LL ut iron time for input phase on surface on surface time 48 6 emitting surfaces converged log 0 16846E 00 secs time for solution phase 0 20285E 01 secs time for cleaning up 0 11734E 01 secs total run time 0 22087E 01 secs total number of photons emitted 0 12000E 06 total number of photons lost 0 photons per second solution phase 591 55 912 photons per second total run 54329 894 all results are given in CPU time czeeb 3 4 5 Machine Independence of MONT3D Much effort has been put into making MONT3D platform independent Of all the files used by MONT3D only one is binary the temporary binary exchange matrix file and it only exists during the input phase at the beginning of the run and clean up phase at the end of a run Since all results are stored as ASCII files runs started on one machine can be restarted on a different machine pro vided the files are available on the other machine usually accomplished via ftp This is true even 1f the run is restart
74. er for semi specular reflectance RRHOSS 8 DEFAULT 1 61 70 E10 0 Cosine power for weighted diffuse transmittance RTAUD 8 DEFAULT 1 71 80 E10 0 Cosine power for semi specular transmittance RTAUSS 8 DEFAULT 1 Notes If IB is 0 for the first band of the material then it is assumed that all material properties for that material are the same for all bands No cards are read for the other bands IETP must be between 0 and 2 inclusive More detail is given in Sections 2 5 3 and 2 5 4 Ifa material has O emittance for all values of 8 then no photons are emitted from surfaces of that type unless IETP 1 or 2 As explained in Section 2 5 4 if IETP equals 1 or 2 the reciprocity relations Equations 1 5 and 1 6 may no longer hold If IETP 2 emission is accomplished using computer code supplied by the user function fen in subroutine getang in the file m32s f For regular emission IETP 0 these values are ignored They are read in if IETP 1 beam emission or if IETP 2 the function for function emission may require them Values are nor malized internally to yield a magnitude of 1 If all components entered are equal to 0 and IETP does not equal 0 the program exits with an error 36 7 When using beam emission IETP 1 care must be taken to ensure that all emission is from the front of the surface 1 e the dot product of the emission vector and the surface normal for each s
75. er of Records in the Binary Exchange Matrix File 1 Record of Length 1 FORTRAN Format Specification i10 Format Entry Note s Integer Number of records in file 1 Notes 1 This value was used by MPLOT Nagesh and Burns 1994 to read the exchange matrix infor mation from older versions of MONT3D which used familied binary files Due to the new exchange matrix file format used by MONT3D this value no longer has any meaning and is always set to 1 B 3 Lost Photon File Suffix Jet Unit 4 The lost photon file contains the trajectory photon ray end point information for each lost pho ton and can be used with MPLOT Nagesh and Burns 1994 to display the trajectories see Section 2 8 for more details All the code for the writing of this file can be found in the subroutine grdint in the file m32s f The following series of records are repeat for each lost photon Records are written in order of lost photon number B 3 1 Header Card 1 Record of Length 5 FORTRAN Format Specification 5 3x 17 Format Entry Note s Integer Lost photon number LOST Integer Event number IEVENT 1 Integer Number of points to be plotted along the particle s trajectory NPNTS 2 Integer Subdivision number ND 3 4 Integer Number of surface where last emitted reflected or transmitted LERT 3 4 Notes 1 IEVENT is always set to 1 2 NPNTS is always 2 and indicates that the trajectory just includes the starting and ending points 80 3 In the M
76. erial model is equal to 1 at all angles It should also be noted that while the user enters offset angles A0 9 for the semi specular reflectance and transmittance the code stores these as the preferred outgoing angle 0 0 A 0 The thetar arrays are used to determine the outgoing cone angle of emission from a uniformly distributed random number between 0 and 100 For a detailed discussion of the emission algorithm see Burns and Pryor 1989 6 This option is not available in this version This space is being retained in the input file for back ward compatibility in format If present NUMCAT must be 0 or MONT3D will terminate with an error 30 7 The number of photons emitted per loop for each surface in each band is NPHTN NDIVX NDIVY See Sections 2 2 2 7 3 2 1 and 3 6 for more detail 8 Currently only the grid shading algorithm is used in this code If NSHADE is set to zero or greater a single grid cell is used which is equivalent to the distance algorithm for shading More details are given in Sections 2 6 3 3 and 3 11 9 The program outputs trajectory information to the trc file if this option is set This file is used to view the trajectories using the MPLOT program Nagesh and Burns 1994 useful in estab lishing physical intuition If chosen a copious amount of information is printed the user is therefore cautioned to select this option only for very few photon emissions per surface See Section 2 8 fo
77. erun However if view factors are calculated all properties black arbitrary diffuse reflectances may be included in the thermal analysis code since view factors are dependent on geometry alone Note that diffuse exchange with finite reflectances calculated from the present codes may yield different answers than those obtained using the radiosity irradiation approach as the assumption in the radiosity approach is uniform radiosity irradiation which is not a mandatory condition for the present code Specularity or material property dependence on inci dent angle may not be modeled using view factors In addition to radiation exchange this code can also be used to simulated some special cases of other transport problems in enclosures If the Knudsen number is much less than 1 rarefied gas dynamics problems can be simulated a vacuum vessel Also some simple cases of molecular sputtering in an enclosure can be simulated 1 5 Overview of the Manual In Chapter 2 the general background required to run MONT3D is presented Chapter 3 presents in great detail the format of the input file data deck that MONT3D requires A sample problem is used to demonstrate how to run MONT3D in Chapter 4 The more technical details about the MONT3D implementation are covered in Chapter 5 CHAPTER 2 COMPUTER CODE BACKGROUND This chapter presents the background information necessary to run MONT3D The first three sections define the geometry of a radiating encl
78. es which have been identified as potential problems or leaks The three types of errors identified are Error 1 Reversed Edge This error occurs when two surfaces share the same edge An example is given in Figure 2 12 In Figure 2 12 a the edge between the two surfaces is correct and both surfaces have normals pointing into the page In Figure 2 12 b the edge is reversed and the nor mals of the two surfaces point in opposite directions Recall from Section 2 2 that surfaces are transparent to photons which hit the back side of the surface This type of error usually results in the enclosure losing excessive photons resulting in an error termination a correct edge b reversed edge Arrows represent direction of increasing node number Figure 2 12 Example of a Reversed Edge Error 2 No Match Found This error occurs when no match is found connecting at least one side of that surface to the side of another surface This may or may not be acceptable Error 3 Slip Surface This error occurs when an edge goes through a node point instead of ter minating at it Although this is sometimes an actual error it often is not If the slip surface creates no holes in the geometry then it should not cause the enclosure to lose photons When photons are lost the endpoints of each photon ray are written to a separate file file suffix Ist which may then be read by the MPLOT program Then trajectories of the
79. etail is given in Section 2 5 4 It should be noted that unless the material type is 3 or 4 the curves listed in Table A 1 must be entered by point value as a function of angle The format is given in Section A 8 The computer code parabolically interpolates between each three successive points entered just as it does with curves entered in by point value for the new model Section 2 5 1 gives several tips about entering curves by point value 69 A 2 Outgoing Angles for Diffuse and Specular Interactions Figure A 1 shows the conventions for 8 and for diffuse and specular interactions The cone angle 8 is always defined from the surface normal and the azimuthal angle p is positive coun terclockwise when viewed from above from the surface x axis The x axis is defined perpendic ular to the ray joining nodes 1 and 2 y axis and the surface normal n z axis according to a right hand rule as shown in Figure A 1 Care should be taken to number the nodes of a surface correctly to achieve the desired emission direction This coordinate system is used by both the new and old material models Figure A 1 Conventions for Outgoing Angles A 3 Material Type 2 Emission According to a User Supplied Function For material type 2 emission occurs according to a user supplied function This is exactly the same as setting IETP in the new material model to 2 Photon material interactions are determined by the three input curves lis
80. fault Convergence Tolerance Condition s NPLOOPS gt 0 entered in Section 3 2 2 otherwise omit card Cols Format Entry Note s 1 10 E10 0 Default convergence tolerance for photon emissions ERRDEF 1 Notes 1 This is the default tolerance for convergence of the surface exchange fractions see Section 2 7 for more detail This may be overridden for a particular surface s during surface input see Section 3 6 If 0 is entered for ERRDEF then any surface using the default tolerance will com plete the full NPLOOPS surface emission loops If NPLOOPS is equal to 0 ERRDEF is set to 1x 1010 see Section 3 2 2 for details 3 5 Nodal Point Data Cols Format Entry Note s 1 5 I5 Node point number N 1 6 10 I5 Increment in number of points to be generated INC 2 11 30 E20 0 X coordinate X N 31 50 E20 0 Y coordinate Y N 51 70 E20 0 Z coordinate Z N Notes 1 Node points can be input in any order All nodes from 1 to NUMNP entered in Section 3 2 1 inclusive must be input or generated as described in the next note More detail on nodes is given in Section 2 1 2 Nodal points are generated in increments of INC from the previous node input to the current node The coordinates are obtained by linearly interpolating all coordinates between the ones input on the previous card and the present ones Care must be taken such that there are an integer number of generated nodes between the present node number and the one input on th
81. file for the Sun Hewlett Packard IBM RS 6000 and DEC platforms and for the NAG f90 compiler under Linux Values for other platforms can be found by compiling the sample programs that are included with the PVM distribution The authors have worked hard to make MONT3D as portable as possible They would like to be informed about troubles successes when compiling the code on other platforms 5 2 2 Microsoft Windows The code has been compiled under Microsoft Windows using Microsoft FORTRAN Powersta tion The files which are needed to compile the code under Windows are m30s f m311s f m312s f m313s f m32s f m3nopara f m3pccom f m3f90timing f m3f90date f mont3d par and mont3d com These files have compiled successfully on every Windows machine we have tested so 54 far However it is possible to use other timing stubs The code is essentially the same if either m3f90timing f or m3ctiming f is used Both stubs cause timing results to be given in clock time While m3etiming f compiles in all test cases sometimes the timing function does not work and zero seconds is reported for all the timings in the timing summary In our limited testing the etime func tion works when the code is compiled and run under Windows NT but not under Windows 95 or 98 It is highly likely that etime reports clock timing instead of CPU timing on most Windows machines so there is probably no advantage to using etime instead of one of the clock time func tions
82. file suffix plt and MPLOT Nagesh and Burns 1994 be used to view the curves created to ascer tain that the interpolation is physically reasonable 2 5 2 Outgoing Directional Distributions Photon material interactions of seven types may occur These outgoing directional distributions will be discussed briefly below A more detailed discussion of these distributions is given by Burns and Pryor 1999 In the current discussion for purposes of illustration these outgoing directional distributions will be presented graphically for reflection only and depicted in cross section To establish a basis for the ensuing discussion the definition of the bidirectional reflectance is recalled as P 0 0 Oo 0 where the double prime indicates that it is dependent upon two directions inci dent 8 and outgoing 0 9 Figure 2 7 a depicts the traditional model for reflection consisting of a purely specular compo nent and a purely diffuse component The current model in MONT3D includes three enhancements to the traditional model First the diffuse distribution may be weighted in cos 8 to allow control of the shape of the outgoing directional distribution Second a semi specular outgoing distribution is added The semi specular distribution is spread in space to represent more realistic materials Third the semi specular distribution may be modeled using an offset about the specular angle A 8 which usually tends toward the grazing
83. g split surfaces is specified by erte For a geometry with NBANDS NSUREF emitters NEMIT there are NEMIT NEBLOCKI restart blocks in a run round the result up This number can not be larger than itblk It is a fairly simple process for the user to compile MONT3D for each geometry so that it uses the smallest amount of memory possible If memory on a machine is limited this may allow the code to run without having to use virtual memory The way this is done is as follows The user should first run a data check only IDATA 1 see Section 3 2 2 which will only go through the input phase of the code As shown in Chapter 4 during the input phase a Memory Allocation and Usage section is printed All parameters listed in that section should be set to the value in the used column of that section and the code should be recompiled The newly compiled code will use the minimum memory required for the given geometry 5 5 2 Other Parameters The other parameters used in MONT3D and their default values are iflen maximum length of a file s base name 20 llarg maximum length of a command line argument 30 iseeddef default seed for RNG see Section 3 2 1 19 895 660 Iflen Iflag 1f1 lfs parameters for RNG see below m3dparaname name of the code s parallel version see Sections 5 2 1 and 5 6 m3dpvm pdamax maximum allowed value for percent area difference see Section 2 3 0 1 zee z value from normal tables default 95 c
84. he program with equally spaced grids or 2 a user defined grid For option 1 the user need specify only the number of grids along the axis while for option 2 the user must also specify the grid coordinate locations along the axis See Sections 3 3 and 3 11 for additional details 2 7 Number of Photons Convergence and Accuracy The number of photons emitted in each photon loop is specified for each surface in each band by the relation of photons NDIVX x NDIVY x NPHTN Multiple photon emission loops may be done per surface more detail is given below and in Sections 2 2 3 2 and 3 6 As Monte Carlo tech niques are statistical in nature enough photons must be emitted from each surface to yield a sta tistically accurate result This number depends upon the geometry and to some extent upon the material properties As a general rule greater numbers of surfaces require greater numbers of pho tons Execution time increases linearly with number of photons For small problems about 20 sur faces it has been found that on the order of 20 000 photons per surface not subsurface are required to achieve exchange factors accurate to within about 5 It is typical to observe conver gence in a particular exchange factor as shown in Figure 2 11 The user is cautioned that false con vergence may be indicated when comparing two values on the curve as shown It is therefore wise to check the entire matrix of exchange factors for consistency at
85. ile name The maximum length of the base name is set by the parameter iflen The default value is 20 characters Indices are always appended to the end of the base name The number of digits used for the indices are controlled by the parameter iimag More details on these parameters is given in Section 5 5 To help clarify the command line conventions the following examples and explanations are offered Example 1 mont3d i alakazam Okaboom e ardvark M toasted MONT3D will expect the input file named alakazam to exist MONT3D will create the following files the lost photon trajectory file named toasted toastedO1 toasted02 up to the number of worker processes if this is the parallel version the absorption exchange matrix file named ardvark the output file named kaboom additional temporary files named kaboom01 kaboom02 up to the number of worker processes for the parallel version All other files will use alakazam for their base name Example 2 mont3d f calendar MONT3D will expect the input file calender in to exist MONT3D will create all files using the base name calendar Example 3 mont3d f box e miSrun MONT3D will expect the input file box in to exist The exchange matrix files will use the base name miSrun All the other files will use the base name box 57 5 5 Parameter Statements and Memory Allocation MONT3D uses static common blocks for storage making the code more robust and easier to edit Unfor
86. in the grid To our knowledge this error has never occurred for any geometry If it does occur there may be serious problems in the geometry specification Maximum Number of Photons Lost per Worker Process This error occurs when more then NLOST input format described in Section 3 2 1 photons are lost per worker process Maximum Number of Reflection Warnings per Process This error occurs for a process when there are more then NWARNS warnings of a photon reflecting more than NREFS times both described in Section 3 2 1 PVM Error A PVM error occurs when a PVM function exits with an error If no worker process is mentioned then the error occurred on the master To our knowledge this type of error has not yet occurred Quite a bit of information is printed for this type of error but it is mainly intended to be given to the code s authors so they can determine the problem For any one trying to track down the problems themselves the error message includes the following information First it gives the PVM function that caused the error Second the item marked error code specifies which PVM error condition occurred The error code numbers are described in fpvm h as discussed above in spawning errors The mestag item gives the message tag ID Each mestag number is equivalent to a message tag parameter defined in the file m3pvm inc The PVM version of the code passes six different types of messages The message tag parameters are used
87. ine one executes mont3d and redirects standard output to the file run The second line causes the script to pause until line one has finished When the first run has completed the process continues with line three etc mont3d f tcl gt runl wait mont3d f tc2 gt run2 walt mont3d f tc3 gt run3 Figure 5 1 Contents of Script File submit The script file can be created with any ASCII editor and given any valid Unix name here the file is named submit The files referred to in the script here tc run etc can also have any valid Unix name The files tc 1 tc2 and tc3 must be the MONT3D input files all must have the in exten sion to be used for the run Once the script is created it must have execute permission before it can be run This is accom plished for the file submit with the Unix command chmod Schmod 744 submit 64 where is the Unix prompt The script can be run in the background by typing the script name followed by 82 If commands are run in the C shell then to run submit in the background and redirect all its output to standard output and standard error to the file submit out type Ssubmit gt amp submit out amp where the gt amp redirects both standard output and standard error to the file submit out Alternately it can be submitted using the Unix commands at or batch The syntax of any of these Unix com mands can be obtained by referring to the Unix man ual pages
88. ing from a crash Furthermore the code can switch between single processor and parallel execution or even change the number of worker processes being used in a parallel run even if restarting from a crash 49 CHAPTER 5 IMPLEMENTATION DETAILS This chapter covers how MONT3D is implemented The first two sections describe the MONT3D source code and explain how to compile it on various platforms The next two sections cover the files generated and used by MONT3D and the command line used to name several of these files The fifth section discusses the use of parameter statements in the code including how they affect memory allocation The sixth section discusses the parallel version of the code Unix batch execution by scripts is the subject of the seventh section The last section briefly discuss pre cision in MONT3D If any problems with the code are encountered one of the authors should be contacted 5 1 MONTS3D Source Files In this section the various files included in the MONT3D source code are described Much work has been done recently to increase the portability of MONT3D Furthermore the ability to compile a parallel version of the code implemented in PVM Geist et al 1994 has been added Both of these features have been implemented through the use of stubs Stubs are multiple files which contain the same subroutine and function names each with or without certain options Features can be turned on and off by compiling the
89. input phase it sends a worker ready message to the master The master then sends a block of INEBLOCKI surfaces to the worker The worker performs the work associated with emissions from these surfaces Once it completes these emissions it writes the results to the disk and sends a message to the master indi cating it has completed that block and the master issues another block of surfaces to the worker if any are left This cycle continues until all emissions have been completed If a worker encounters a fatal error it aborts and the block it is working on is done later by another worker If all workers abort due to fatal errors or if a block of surfaces results in fatal errors for two different workers the 22 entire run is aborted and the program terminates After all emissions are done the master combines the results from the workers into one exchange matrix file and the program terminates The parallel version of MONT3D has been tested on a wide variety of platforms PVM Parallel Virtual Machine was originally designed to combine a number of heterogeneous computers into a parallel virtual machine using the TCP IP networking protocol The master and the workers can be totally different types of machines and each machine must be accessible via the network A dia gram of this topology is shown in Figure 2 13 Each of the switches in the diagram may be either Switch Switch Switch Figure 2 13 Example Master Worke
90. is type of pseudo random number generator has been extensively tested for randomness prop erties using Marsaglia s 1985 DIEHARD tests and has been given high marks The only defi ciency found is related to what Marsaglia terms the Birthday Spacings test Preliminary work by Brent 1992 suggests that LFG s pass the Birthday Spacings test if is greater than 100 It should be noted that LCG s did not do nearly as well on the tests A firm theoretical understanding of the cycle structure of these generators has been established in a series of two papers by a group at the Center for Computing Sciences Pryor et al 1994 Mascagni et al 1995 With proper choice of k L and the first values of X the period P of this generator is equal to 2 L 1 x 2M D For example for a small generator with 17 and M 31 the period P is huge 1 4x 101 The only condition on the first values is that at least one of them must be odd Still for some applications one should refrain from using more than 2 1 of the numbers generated by 24 these generators because for a generator with period PX and XK y 4 py differ by at most i bits 0 lt i lt M Brent 1992 Examples of four commonly used versions of these generators LFG l k M are 1 LFG 17 5 31 P 247 1 4 x 10 4 2 1 3 x 10 2 LFG 55 24 31 P 28 3 9 x 102 2f 3 6 x 101 3 LFG 127 97 31 P 21 1 8 x 104 2 1 7 x 10 8 4 LFG 607 273 31
91. lementation Details ia e 25 2 11 3 Effect of Different Random Sequences on Results 26 CHAPTERS INPUT DECK eege ee 27 e et 27 3 2 Control Cards iia 27 O EE 27 3 22 EE 29 ICAO EE 31 2 Grid Dimensions Shading ee 32 34 D t ult Convergence RE 33 3 5 Nodal ER siessen aig n eE a i ES 33 Strada Data o cauati ds 33 A MVE O NK BGs ich IG Si a a E IA aa Se ela 35 3 0 Material Type Datta acs ina iii tad 35 DBL WEE 35 SIPA EE 36 O eects asst 37 3 9 Material Property Curves Tree EE 38 SE WEE 38 3 9 2 Cards 2 to NPFL eebe hroir ene EE See 38 3 10 Semi specular Offset Angle Curves EE 38 IIO Card A a en a E 38 SUEZ Cards EE 39 O 39 AUS A A a 39 311 2 User Y grid Coordinates vinilos EEN sotana 39 UA Z orid eg A O tei cascags Seas cot ade age ews 40 CHAPTER 4 PROGRAM BX UY BION ten 41 del Inp t File EEN 41 4 2 EXE CUA O OF File DORIA ea a AEE AOA AARETE 44 4 3 Screen Output During Execution of File box me 45 4 4 Screen Output During Restart Execution of File box 97 47 4 5 Machine Independence of MONT3D EE 49 CHAPTER 5 IMPLEMENTATION DETAILS al 50 5S LMONT3D ENEE 50 51 1 Files C mmon to All VersiOn asia iii 50 A IN AAA EN 51 5 1 3 Timing Information EE 51 5 14 Time and RE Ee EE 52 ii 5 1 5 Parallel Implementation ii 52 52 COMPA MONTI e EE ee 53 ILN UDIR aes EE 53 5 2 2 Microsoft ee 54 3 2 3 AC EE 55 5 3 Files Generated and Used by MONT3D a oda 55 5 4 Specifying File Narmes 2 nuiis ii radica rae EE edad 55 5 5
92. lete band surf iter npht error EOL not converged 1 1 10 100000 0O 2173E 02 0 2000E 02 not converged 1 2 10 100000 0 2175E 02 0 2000E 02 restart file written not converged 1 3 10 100000 0 2125F 02 0 2000E 02 not converged 1 4 10 100000 0 2123F 02 0 2000E 02 restart file written not converged I 5 10 100000 0 2136E 02 0 2000E 02 not converged ih 6 10 100000 0 2136EF 02 0 2000E 02 restart file written Now writing exchange numbers from each block nij file bni to a temporary binary file tni Now writing the exchange numbers from the temporary binary file tni to the nij file normal termination Convergence information for band 1 O out of the 6 completed surfaces did not emit and D out of the 6 emitting surfaces converged for the emitting surfaces Average error 0 2145E 02 Minimum error 0 2123E 02 on surface 4 Maximum error 0 2175E 02 on surface 2 46 total total total solution time for input phase time for solution phase time for cleaning up run time number of photons emitted number of photons lost photons per second solution phase photons per second total run all results are given in CPU time czeeb 2 time 59567 793 58563 584 SECS SECS secs SECS 4 4 Screen Output During Restart Execution of File box in czeeb 2 mont3d f box
93. lost photons may be displayed on the geometry Because there is no terminus of the ray a fictitious endpoint is used 21 An option is also available to write trajectory information to an output file file suffix trc which may be subsequently read and plotted by the program MPLOT see Section 3 2 2 for more details This feature is useful in obtaining a feel for the underlying physical processes and to ascertain that the simulation is proceeding as planned There is a copious amount of information written to the output file during the exercise of this option so it is suggested that the number of photons emit ted per surface be less than about 100 Recent versions of MPLOT allow the user to view convergence information on the exchange matrix values for a specified surface Unfortunately MPLOT can not read the new exchange matrix file format used by latest version of MONT3D and this feature is not available for MONT3D ver sions 2 4 and later For more information the reader is urged to consult the MPLOT documentation Nagesh and Burns 1994 2 9 Restart Capability The code has been designed to be restarted from a previously computed state For example the code may experience a crash during execution for any of a host of reasons Alternatively the code may run to completion and subsequent examination of the answers indicates that they are not sufficiently accurate In either case it is desirable to begin a new simulation
94. lus at least one other intermediate angle 3 10 2 Cards 2 to NP 1 Cols Format Item Note s 1 10 E10 0 Angle for curve value in degrees ANGLE 12 11 20 E10 0 Semi specular offset angle value in degrees VALUE 1 3 Notes 1 Values must be given for O and 90 degrees 2 ANGLE values must be between 0 and 90 inclusive 3 VALUE must be between ANGLE and 90 ANGLE so that the preferred outgoing angle is between 0 and 90 degrees inclusive 3 11 User Grid Input It should be noted that depending on the values of NGX NGY and NGZ entered forwards com patibility may not exist for input files create for versions of MONT3D earlier than 2 4 For addi tional explanation of the variables NSHADE and NGX NGY and NGZ see Sections 3 2 2 and 3 3 respectively 3 11 1 User X grid Coordinates Condition s NSHADE lt 0 and NGX lt 0 otherwise omit card s Cols Format Entry Note s 1 80 8E10 0 X grid coordinates XG N 1 Notes 1 For N 1 to NGX 1 No more than eight values should be input per card 10 columns per value More than one card may be required 3 11 2 User Y grid Coordinates Condition s NSHADE lt 0 and NGY lt 0 otherwise omit card s Cols Format Entry Note s 1 80 8E10 0 Y grid coordinates YG N 1 Notes 1 For N 1 to NGY 1 No more than eight values should be input per card 10 columns per value More than one card may be required 39 3 11 3 User Z grid Coordinates Condition s NSHADE lt
95. machine is created on the machine on which the master process will run After the parallel virtual machine is created the user just executes MONT3D executable usually called m3dpvm on the master machine Just like the single processor version the parallel version can be run interactively or using the command line as explained in Section 5 4 Once the input file is checked for errors the master then spawns NWPROC see Section 3 2 2 worker processes on the virtual machine The PVM daemon on the master selects the CPU s on which to spawn the pro cesses more on this below To run the parallel version of MONT3D successfully it is important that certain directories be correctly specified The path for the executable file must be known For the master the path for the executable must be in the user s path or must be explicitly given on the command line The path for executables for each of the worker processes is set to 5HHOME pvm3 bin PVM_ARCH by default HOME is the user s home directory and PVM_ARCH is an environment variable describing the platform being used One way to change the directories for executables for each CPU in the virtual machine is to use the ep option executable path in the PVM hostfile The working directory where the code will execute and look for files must also be specified For the code to run properly all processes must use the same directory so they can share disk files For the master the working direc
96. metries MONT3D generates several files useful in debugging and visualizing geometries These files are the plot file the leaks file the lost photon file and the trajectory file The various files are described below All can be visualized using the stand alone graphics program MPLOT Nagesh and Burns 1994 The actual formats of each of these files are presented in detail in Appendix B The plot file file suffix plt containing all the information in the input file geometry and mate rial properties is written to disk during the input phase This file may be used with MPLOT to dis play the geometry and the material property curves This file must be read by MPLOT before viewing the results from any of the other files listed above otherwise MPLOT will have no geom etry over which to display the results An error in the specification of the geometry often results in a leak or hole in the enclosure through which photons may be transmitted and lost Leaks may be caused due to disjoint sur faces missing surfaces incorrect node numbering on a surface misplaced nodal points or insuffi 20 cient precision in specifying coordinates During the input phase the geometry is checked for leaks and results are written to the output file Additionally an ASCII file of potential leaks file suffix lks identified by type severity of leak is also created This file may be used with MPLOT to highlight surfaces and sides of surfac
97. nsitive and is invoked by typing its name shown at the first prompt czeeb 1 All subsequent output up to the czeeb 2 prompt is from the program MONT3D The user types in only the prefix of the input file which MUST have the extension in In this case the file is box in and the user enters box If the program cannot find the input file an error diagnostic is printed and the program exits Additional detail on the files used by MONT3D can be found in Chapter 5 The program proceeds with reading of the input file The run s title is printed here 3 D BOX TEST PROBLEM along with the version number here 2 4f1 the date of last modification here 04 15 99 and the language of the source code always f77 Next the control portion of the input is read This establishes the numbers of nodes surfaces sometimes referred to as ele ments or surface elements wavelength bands materials grids etc which are to be read by suc ceeding subroutines Then the input subroutines are executed one by one As each subroutine is entered the name of the subroutine is printed to the output file This assists in debugging input files For example if the program crashes after the message in nodin3 is printed there is almost cer tainly a problem with the nodal input or possibly the cards are out of order Another item that should be noted is the Memory Allocation and Usage secti
98. o the different intersection points must then be computed and the closest point chosen as the true intersection point the surface first encountered For large prob lems this results in significant expense To reduce execution time for large problems with shading the grid shading algorithm Margolies 1986 has been implemented Here the geometry is divided into a series of grid cells resulting in rectangular parallelepipeds The photon is traced from grid cell to grid cell and a search is done within each grid cell only over those surfaces which exist either wholly or partly within that cell The situation is depicted in Figure 2 10 for a 2 D geometry SCH Enclosure Photon Trajectory Grid Figure 2 10 2 D Illustration of the Grid Shading Algorithm 17 In the recent recoding of MONT3D Zeeb 1997 Zeeb and Burns 1999 the grid tracing routine was further optimized and use of this algorithm has resulted in speed ups in execution time in trac ing compared to no grid of factors of 18 to factors of 81 for large geometries 1 000 to 5 000 sur faces The optimum grid differs from problem to problem and must be empirically determined by the user However a good starting guess for a large geometry 1 000 to 5 000 surfaces is about 15 000 grid cells Grid coordinates are defined separately for each axis Two options exist for defining the grid coordinates along each axis 1 a uniform grid generated by t
99. of a MONT3D run and deleted at the end of a successful MONT3D run To restart from a crashed run the block file must be present as it is now how MONT3D realizes that a restart from a crash is occurring All the code for the reading and writing of this file can be found in the subroutine blkfile in the file m313s f The block file was mainly cre ated to keep track of the surfaces in blocks for load balancing which has not been implemented yet Without load balancing there is not much need for the information in this file This file contains several variables used internally by MONT3D for restart It has little or no usefulness outside of MONT3D and requires quite a bit of explanation If the user needs to know about this file one of the authors should be contacted 86
100. on listed between the subroutines gri din and order By setting the memory allocation parameters to the used values it is possible to run the code using the smallest memory allocation possible More details on changing the code s parameters are given in Section 5 5 Finally the successful completion of the entire input phase is indicated by the message input phase complete The solution phase occurs next After the specified number of full surface emission loops for each surface are completed a message is printed indicating whether the exchange fractions have converged see Section 2 7 In addition the wavelength band surface number total number of emitted photons summed over all full surface emissions and the calculated error are printed Here none of the surfaces converge to the stringent error tolerance of 0 002 but all come close Next after all the surfaces emissions have been completed the code creates the exchange matrix file file suffix nij as shown by the two statements that both start with Now writing This phase is usually fast unless there is a large number of surfaces Next overall program statistics are printed including the error statistics various timings for the run in seconds of CPU time total number of photons emitted and traced to absorption and the performance metrics number of photons per CPU second for both the entire run and just for the solution phase The timing infor
101. onfidence 1 96 There are a few parameters controlling file name length and input that should be explained iflen 1s the maximum possible length for the base name file name without indices or suffix for a file ilarg is the maximum length of a single argument on a command line or the base name entered interactively If the base file name obtained this way is longer than en the base name is clipped to iflen Having ilarg larger than iflen may prevent possible array bounds errors on some systems iimag is another file parameter that needs explanation In creating the block exchange matrix bni files MONT3D must append the block number to the file s base name Furthermore several files generated in the parallel version of the code need the worker process number appended to the base name imag specifies the maximum number of digits which can be appended to the base name For example for 50 processes imag should be 2 while for 100 blocks imag should be 3 The length of the lagged Fibonnaci generator can be changed if desired As shown by Pryor et al 1994 it takes four constants to describe a LFG fully Besides fand kmentioned in Section 2 11 two constants L and S are needed to specify the format of the canonical seed The code defines these four constants in the file mont3d par as Iflen for LF length lflag Ifl and Ifs Several sets of k L S are given by Pryor et al 1994 Popular values are 55 24 1 11 127 97 1
102. or each run and the same set of random number sequences will be used in both runs which may cause prob lems Similarly if the user specifies a specific random number seed for INSEED INSEED gt 0 a different seed must be entered for each run On the other hand a different time generated seed is produced for nominally every second in a 32 year period Therefore if time generated seeds INSEED 0 are used independent streams of random numbers are virtually assured It should be noted that time generated seeds vary only with time if the code supports the time and date functions see Section 5 1 4 If time and date functions are not supported the user must enter different values of INSEED for each restart run It should be noted that the time generated seed is generated on the master process only If the master s version of MONT3D supports time and date functions then time generated seeds will work properly 5 7 Unix Batch Execution Using Scripts This section describes the use of a Unix shell script to submit multiple MONT3D runs to be exe cuted sequentially This has the advantage of running only one job at a time thereby avoiding the overhead involved with swapping jobs in memory in and out of the CPU our tests have shown that the overhead under Unix in so doing is prohibitively large The shell script in Figure 5 1 is an example which runs MONT3D three times for three separate problems input files tc tc2 and tc3 In this example l
103. or each missing surface i i 1 to NMISS generated 1 INCP additional photons emissions are added to NPHTN ERRMAX N is used as explained in Section 2 7 Loops over full surface emissions are done until either the specified number of loops NPLOOPS entered in Section 3 2 2 have occurred or convergence to within tolerance C defined in Equation 2 6 is achieved whichever comes first If no value of ERRMAX N is input or a value less than or equal to 0 is read then this defaults to the global value ERRDEF input as described in Section 3 4 34 3 7 Wavelength Band Data CARDS 1 to NBANDS 1 8 Condition s NBANDS gt 1 entered in Section 3 2 1 otherwise omit card s Cols Format Entry Note s 1 80 8El0 0 Wavelength breakpoint N micrometers 1 Notes 1 The first 1 and last NBANDS 1 wave breakpoints are assumed to be 0 0 and 1 x 1019 in micrometers and should not be input The remaining breakpoints between 0 and 1 x ICH should be input in order from 2 to NBANDS No more than eight breakpoints should be input per card 10 columns per value More than one card may be required 3 8 Material Type Data Material type data cards are input by band for each material in order For example 1f three mate rials are used in two bands then all material type data are read in for material 1 band 1 then mate rial 1 band 2 then material 2 band 1 etc MN and IB are used as checks to ensure that the values are ente
104. osure in terms of nodes and radiating surfaces Next there is a note on the surface concatenation option The material interactions supported by the code and how materials are specified by the user is the subject of the fifth section The sixth section explains the available shading algorithms while the seventh discusses accuracy versus the number of photons emitted Next debugging and visualization information generated by the program is covered This is followed by information on the restart capability whereby a run may proceed from a previously calculated state In the tenth section the parallel execution of MONT3D is covered The chapter concludes with a discussion of the pseudo random number generator 2 1 Nodes The description of the geometry of the radiating enclosure begins with the specification of the nodes also called nodal points of the enclosure A node is a point in three dimensional space defined by three coordinates in a Cartesian coordinate system X Y Z as depicted in Figure 2 1 Each node N in the enclosure is assigned a node number which must be positive and a member of the closed full set Ne 1 NUMNP where NUMNP is the total number of nodes for the problem Once the nodes of the enclosure have been specified radiating surfaces can be defined by specify ing sets of nodal points See Sections 3 2 1 and 3 5 for additional detail on the node input format Node N X Z Figure 2 1 Nodal Coordinate System
105. photon may be absorbed In summary seven possibilities for incident photon disposition exist three components of reflection three compo nents of transmission and absorption For each material in each band the diffuse and semi specu lar weighting coefficients ry and r for both reflection and transmission must be input Furthermore for semi specular reflection and transmission the offset angle as a function of inci dent angle A 8 must also be input More details on the input format are given in Sections 3 8 3 10 2 5 3 Emission In the new material model emission type is defined using the variable IETP Emission of one of three types may be specified depending on the whether IETP is 0 the default 1 or 2 as discussed below See Section 3 8 2 for additional details Emission is specified quite differently in the old material model Appendix A specifying old material model and input format is provided for ref erence Hereinafter in this section only the new material model will be presented Standard Emission IETP 0 This is the type of emission deriving from Kirchoff s Law At each angle the emittance is equal to the absorptance determined as the complement of the reflectance and transmittance This type of emission adheres to the second law of thermodynamics and is rec ommended for radiative transfer If this type of emission is used no additional input for emission is required Beam Emission IETP 1 This type
106. r Architecture a switch between subnets or a gateway router between different networks The parallel code has been shown to work on a homogeneous network of Hewlett Packard workstations and a heteroge neous network of three Sun workstations and a Linux workstation Excellent results running the code on a tightly couple cluster of eight DEC Alpha CPU s have also been obtained The only requirement for the parallel version of the code is that all CPU s must use a common file system such as NES as the workers must be able to access the scratch file suffix scr file created by the master and the master and the workers must be able to access the block exchange matrix file suffix bni files More information about the parallel version of the code is given in Section 5 6 23 2 11 Pseudo Random Numbers Random Number Generators RNG s are fundamental components of Monte Carlo analyses without which Monte Carlo simulation would be virtually impossible In the codes described herein uniformly distributed pseudo random also termed just random numbers are used to deter mine 1 outgoing directions of particles and 2 interactions of particles with surfaces Mathe matically the sequence of random numbers used to effect a Monte Carlo model should possess the following properties 1 the sequences of random numbers should be serially uncorrelated 2 the generator should be of long period 3 the sequence of random numbers should be uniform
107. r more detail 10 This option is used only by the parallel version of the code it is ignored in the single processor version of the code If NWPROC is less than 1 for the parallel code a single processor run is done More detail about the parallel code is given in Sections 2 10 and 5 6 11 NPLOOPS is the maximum number of full surface photon convergence loops done per surface In each full surface emission NPHTN photons are emitted from each subsurface see Sections 2 2 and 2 7 and the description of NDIVX and NDIVY above If convergence to the specified tolerance for the surface see Sections 2 7 3 4 and 3 6 is not attained within NPLOOPS full surface emissions then a warning is printed to the screen and execution continues with the next surface 12 If 0 is entered for NPLOOPS an extremely large default convergence tolerance is established 1x 10 thereby ensuring that convergence occurs after one full surface emission loop Sur faces that have their convergence tolerance set to this large value will not emit any photons in any restart runs since they are converged 13 The IPAROPT array is used only in the parallel version of the code Currently only IPA ROPT 1 is used the other array elements are reserved for future enhancements of the code 14 IPARAOPT 1 controls how workers are spawned If the value entered for this option is less than 0 or greater than 3 MONT3D will terminate with an error For more details see Section 5
108. rably 3 0 must be input Offset angle del theta curves are read after all material property curves have been read see Section 3 10 below 3 9 Material Property Curves Input Condition s NMACV gt 0 entered in Section 3 2 2 otherwise omit card s Material property curves must be entered in order from 1 to NMACV using the format given below 3 9 1 Card 1 Cols Format Item Note s 1 5 I5 Material property curve number NCMA 6 10 I5 Number of points to be read in for the curve NP 1 Notes 1 Atleast three points must be input Points must be input at angles of 0 and 90 degrees plus at least one other intermediate angle 3 9 2 Cards 2 to NP 1 Cols Format Item Note s 1 10 E10 0 Angle for curve value in degrees ANGLE 1 2 11 20 E10 0 Material property curve value VALUE 1 3 Notes 1 Values must be given for O and 90 degrees 2 ANGLE values must be between 0 and 90 inclusive 3 VALUE must be between 0 and 1 inclusive 3 10 Semi specular Offset Angle Curves Input Condition s NDTCV gt 0 entered in Section 3 2 2 otherwise omit card s Semi specular offset angle curves must be entered in order from 1 to NDTCV using the format given below 3 10 1 Card 1 Cols Format Item Note s 1 5 ID Semi specular offset angle curve number NCDT 6 10 I5 Number of points to be read in for the curve NP 1 38 Notes 1 At least three points must be input Points must be input at angles of O and 90 degrees p
109. radiation PHISET MN IB 1 26 35 El0 0 R dependence of diffuse reflectance RDIFFR MN IB 5 6 DEFAULT RDIFFRD 1 8 36 45 E10 0 R dependence of diffuse transmittance RDIFFT MN IB 5 6 DEFAULT RDIFFT 1 8 46 50 I5 Material number MN 5 6 51 55 I5 Wavelength band number IB 5 6 Notes 1 THSET and PHISET are ignored unless MTYPE 1 or MTYPE 2 and the user supplied func tion requires them 71 2 If MTYPE N 2 then emission occurs according to the user supplied function fen in subrou tine getang in the file m32s f 3 If a material has 0 emittance for all values of 6 then no photons are emitted from surfaces of that type unless MTYPE 1 or 2 4 Material property curves are required for all material types except 3 and 4 5 If the values of MN and IB are 0 or blank for the first band of a material then RDIFFR and RDIFFT are set to 1 standard diffuse re emission and the material type data values are used for all bands in that material and no other material type data cards are read in for that material This has been done for compatibility with earlier versions which do not support r dependence or multiple material types 6 If MN is not 0 but IB is for the first band of the material then it is assumed that the material type data are constant for this material for all bands and no other material type data cards are read in for this material The material property curves must still be entered for each band 7 A
110. re put on one CPU only if NWPROC the number of worker processes specified by the user is greater than the number of CPU s in the virtual machine Since having more than one worker process on a CPU is inefficient NWPROC should always be less than or equal to the number of CPU s in the virtual machine If NWPROC is equal to the number of CPU s then a worker process will spawn on the master CPU If the user wants to insure that a worker does not spawn on the master CPU he should set the input variable IPAROPT 1 to 1 use IPAROPT 1 3 if debugging see Section 3 2 2 for more detail It is possible to do batch jobs as described in Section 5 7 with the parallel version of the code It should be noted that if more than one run is done in succession using the same virtual machine it will rotate through the list of CPU s and sooner or later a worker process will spawn on the master CPU If the user wishes to prevent this IPAROPT 1 should be set to 1 5 6 3 Files The file structure for the parallel version of the code requires a bit of explanation Most of the files listed Table 5 1 are generated and used by the master process This includes the restart rst 61 file the plot plt file the exchange matrix nij file the leaks Iks file the temporary binary exchange matrix tni file and the block blk file The scratch scr file is generated by the mas ter but used by both the master and worker processes The input in
111. red in the right order If the information is not entered in the correct order the program detects an error and terminates All material type data cards must be input before any material prop erty curves are input Sections 3 8 3 10 describe the new material model which is used if NUM MAT entered in Section 3 2 1 is less than 0 Otherwise the old material model is used with input as described in Appendix A More detail on the material model is given in Section 2 5 A sample input file using the new material model is given in Section 4 1 3 8 1 Card 1 Condition s Repeat for every material Cols Format Item Note s 1 5 I5 Material number MN 1 6 37 A20 Material name Note 1 The material number must be between 1 and INUMMATI inclusive 35 3 8 2 Card 2 Condition s Repeat the pair of cards 2 and 3 for every band for each material unless IB 0 in which case the information is only entered once See Note 1 below Cols Format Item Note s 1 5 I5 Band numter IB 1 6 10 ID Emission type IETP 2 3 4 IETP 0 standard emission according to e 0 IETP 1 beam emission IETP 2 function emission 5 11 20 E10 0 Global X component of beam emission vector EBX 6 7 21 30 E10 0 Global Y component of beam emission vector EBY 6 7 31 40 E10 0 Global Z component of beam emission vector EBZ 6 7 41 50 E10 0 Cosine power for weighted diffuse reflectance RRHOD 8 DEFAULT 1 51 60 E10 0 Cosine pow
112. reflectances independent of inci dent angle To do so all reflectances and transmittances must be set to 0 0 resulting in an emittance of 1 0 black for all surfaces In this limiting case exchange factors for blackbody surfaces are equal to view factors 1 4 MONT3D Implementation MONT3D is typically used as a preprocessor for thermal balance studies As such the matrix of exchange factors output from the program is used as input to a thermal analysis code MONT3D is designed to be compatible with the thermal analysis code TOPAZ3D Shapiro 1985 developed at Lawrence Livermore National Laboratory by Art Shapiro SMOOTH Dolaghan et al 1992 is a postprocessor designed to take advantage of reciprocity to improve the accuracy of the exchange factors SMOOTH operates on the output of MONT3D and produces output compatible with TOPAZ3D Fundamentally the geometry and the material properties are the only quantities necessary to establish the exchange factors The exchange factors result from the interaction between the geom etry and the material properties in a complex fashion and are unique to a particular geometry mate rial property combination Therefore it is not possible to extend a set of exchange factors calculated for a particular geometry material property combination to another geometry material property combination even if only the geometry or only the material properties vary After any changes the problem must be r
113. rfaces particularly those with high PDA values are prop erly defined The MONT3D output file does include a warning that lists all split surfaces with a PDA greater than pdamax and their PDA values The user should consult this list to determine which surfaces may require redefinition When a planar surface fails the second convexity test there are three ways to fix the problem The only safe way to fix the problem is to redefine the surface so that it is convex More dangerous solutions are to lower SPLITOL enough to mark the surface as non planar or to increase pdamax enough that the surface is marked as convex Neither solution is recommended When a surface is split it should emit as many photons per loop as it would if it were not split To ensure this while the number of subdivisions in the x and y directions are the same for each split surface the number of photons emitted per emission point per loop NPHTN is divided between the two surfaces weighted by the area of each surface Frequently this causes at least one of the split surfaces to emit many fewer than the suggested 100 photons per emission point leading to round off errors There may even be significant round off error in the division of the photons per emission point between the two split surfaces Therefore for split surfaces the user should set NPHTN to values greater than 100 The MONT3D output file lists the area and the number of pho tons emitted per emission point for all
114. rms is available to compile the code Different instances of the program can be created by typing make target in the directory that con tains the source code files and the Makefile where target is a keyword that determines which ver sion of MONT3D is created Currently there are nine options for target m3d creates the single processor version of MONT3D with all optional features command line timing and time and date enabled using m3comline f m3etiming f and m3fdate f The timing results generated are CPU time This has been compiled on Sun SGI DEC Alpha and Hewlett Packard architectures m3dibm creates the single processor version of MONT3D and activates the command line and the Fortran 90 versions of the clock timing and time and date functions using the files m3comline f m3f90timing f and m3f90date f The timing results generated are clock time This version compiles on the IBM RS 6000 platform m3df90 creates the single processor version of MONT3D and activates the Fortran 90 versions of the clock timing and time and date functions but not the command line It uses the files m3nocom f m3f90timing f and m3f90date f The timing results generated are clock time This version can be compiled on any full featured Fortran 90 compiler m3dansi creates the single processor version of MONT3D with all optional features listed above turned off The files used are m3nocom f m3notiming f and m3nodate f We believe it to be mostly
115. rounded absolute value must be between 1 and NMACV entered in Section 3 2 2 inclusive For example if the values for this property are included in curve 3 a value that rounds to 3 preferably 3 0 must be input Material property curves are read after all material information has been read see Section 3 9 below Positive val ues must be between 0 and 1 inclusive For more detail see Section 2 5 1 As explained in Section 2 5 4 if semi specular properties are used the reciprocity relations Equations 1 5 and 1 6 may no longer hold The reciprocity relations also do not hold if the diffuse reflectance varies as a function of angle They DO hold if the specular reflectance varies as a function of angle No tests have been done to see if reciprocity relations hold when the specular or diffuse transmittance vary as a function of angle The user enters the offset angle which is the A 0 quantity defined in Equation 2 4 Values are in degrees The code stores the results internally as 0 If O is entered A8 8 is O Other positive values can not be entered because A0 0 must be between 6 and 90 O for all angles 37 0 If a negative value is input it is taken as the negative of the curve index for this offset angle curve and the rounded absolute value must be between 1 and NDTCV entered in Section 3 2 2 inclusive For example if the values for this property are included in curve 3 a value that rounds to 3 prefe
116. s 30 incg maximum number of grid divisions along any axis see Section 3 3 60 inod maximum value for NUMNP the number of nodes 15 000 iseg maximum number of surfaces segments in all grid cells 100 000 isrf maximum value for NSURF the number of surfaces 5 000 isrfs maximum number of surfaces including split surfaces 7 000 itblk maximum number of restart blocks in a run 1 000 iwproc maximum value for NWPROC the number of worker processes 64 Most of the parameters listed above are rather straightforward The value of several input vari ables most of which are defined in Sections 3 2 and 3 3 must be compatible with the memory lim 1ts set by the values of the above parameters Results in MONT3D are stored in memory for a block of INEBLOCKI surfaces before being written to disk see Sections 2 9 and 3 2 1 INEBLOCKI can not be larger than iblk When the grid shading option is used in MONT3D see Section 2 6 the program stores in one long array a list of all surfaces which are completely or partially in each grid cell The length of this array cannot be larger than seg 58 As explained in Section 2 3 if the nodes of a quadrilateral surface are not coplanar MONT3D may have to split the surface into two planar triangles Every time a surface is split storage is required for an additional split surface While the maximum number of surfaces that can be spec ified is srf the maximum number of surfaces includin
117. s Integer Photon number IHIST 1 Integer Event number IEVENT 2 Integer Number of points to be plotted along the particle s trajectory NPNTS 3 Integer Material number of emitting surface 4 Integer Wavelength band number in which the photon is being traced 4 Notes 1 THIST starts at 1 and is incremented 1 for each new photon emitted It is not incremented when a photon is lost and re emitted 2 IEVENT is set to 1 when a photon is emitted and is incremented by 1 every time it is reflected or transmitted IEVENT is reset to 1 when a photon is lost and re emitted 3 NPNTS is always 2 and indicates that the trajectory includes just the starting and ending points 4 In the MPLOT description of this file Nagesh and Burns 1994 the last two number written to this record are supposed to be an integer MAT and a real EO Neither of these two variables apply to MONT3D so they are replaced by the values listed above 83 B 5 2 Photon Ray s Starting Point Format Real Real Real 1 Record of Length 3 FORTRAN Format Specification 3 2x e10 4 Entry Note s X coordinate of photon ray s starting point Y coordinate of photon ray s starting point Z coordinate of photon ray s starting point B 5 3 Photon Ray s Ending Point Format Real Real Real 1 Record of Length 3 FORTRAN Format Specification 3 2x e10 4 Entry Note s X coordinate of photon ray s ending point Y coordinate of photon ray s ending point
118. s More detail about specifying the number of photons to emit from a surface is given in Section 2 7 Z Y a Global Local Coordinate Systems b Photon Emission Points Figure 2 3 Three Dimensional Surface Details 2 3 Split Surfaces Planarity and Convexity As mentioned above while surfaces in MONT3D are supposed to be planar and convex a con vex surface is usually defined as one with no interior angles greater than 180 the code can handle non planar surfaces It does this by dividing non planar quadrilaterals into two triangles which are planar and convex by definition Since the photons emitted by the original surface are proportioned to the two split surfaces and the results for the two split surfaces are combined in the final output this division is totally transparent to the user In fact it is often easy for split surfaces to go unno ticed by the user because MONT3D only issues warnings for these surfaces not errors This is unfortunate because while there is little harm in splitting a slightly non planar surface extremely non planar surfaces may be modelled very badly they may even be modelled as two overlapping triangles An example for a planar surface is shown in Figure 2 4 where the quadrilat eral in the figure is split into the triangles defined by nodes 1 2 3 and 1 3 4 The triangle 1 2 3 is not part of the original quadrilateral and the triangle 1 3 4 completely covers the triangle 1 2 3 While MONT3D would
119. s discussed in Section 2 5 4 if MTYPE 1 or 2 the reciprocity relations Equations 1 5 and 1 6 may no longer hold 8 If either RDIFFR or RDIFFT 0 then it will be set to 1 standard diffuse distribution If either RDIFFR or RDIFFT are lt 0 then it will be set to 0 isotropic distribution Note that as dis cussed in Section 2 5 4 if either of these variables do not equal 1 standard diffuse distribution the reciprocity relations Equations 1 5 and 1 6 may no longer hold A 8 Material Property Curves Cards The material property curves should be entered right after the material property cards described above These cards do have a different format than the curve cards used by the new material model and should be used instead of them Material property curves are input by band for each material except for materials of type 3 and 4 where no curves are input Curves must be input in order For example if three materials are used in two bands then all material type data are read in for material 1 band 1 then material 1 band 2 then material 2 band 1 etc MN and IB are used as checks to ensure that the values being entered are in the right order If the information is not entered in the correct order the program detects an error and terminates As discussed in Section 2 5 4 if any curve except the specular reflectance varies as a function of angle the reciprocity relationships may not hold A 8 1 Specular Transmittanc
120. seed is gen erated from the time and date then the following formula is used 25 Xo isec 2 imin 2 ihr 21 iday 2 imon 2 gt mod iyr 2 2 9 where mod is the integer remainder function and the integer variables on the right hand side are the second of the minute 0 59 the minute of the hour 0 59 the hour of the day 0 23 the day of the month 1 31 the month of the year 1 12 and the year of the century 00 99 More detail on specifying the initial seed is given in Section 3 2 1 Next the initial seed is used in the binary shift register to fill the initial state of the LFG according to the canonical form as described by Burns and Pryor 1999 Also each binary shift register is stepped through 64 bits before starting to fill the rectangular region in the canonical form to avoid starting at a flat spot on the cycle See Pryor et al 1994 for a discussion of these flat spots When executing the code in parallel the lowest order bits of the initial 32 bit seed usually obtained from Equation 2 9 above are masked with the worker process number 1 as shown in Figure 2 14 In the figure ten bits which are enough bits for up to 1 024 worker processes are masked The exact number masked depends on the number of worker processes being used Note that when a time generated seed is used the most significant bits derive from the time and are the same for all tasks but vary from run to run as does the time a
121. set to zero For material type 2 all four curves are input A 6 Material Types 3 and 4 Perfect Mirrors Material types 3 and 4 are perfect mirrors perfect reflectors Material type 3 is completely specular and material type 4 is completely diffuse For surfaces of this material type no emission occurs and zero exchange numbers are written into the exchange matrix file A 7 Material Type Data Cards If the old material property model is used the material type data cards should be entered right after the wavelength band data which is where the new material model property curve information is currently entered See Chapter 3 for more details Material type data cards are input by band for each material in order For example if three mate rials are used in two bands then all material type data are read in for material 1 band 1 then mate rial 1 band 2 then material 2 band 1 etc MN and IB are used as checks to ensure that the values being entered are in the right order If the information is not entered in the correct order the pro gram detects an error and terminates All cards must be input before any material property curves are input these cards control which material property curves are read Cols Format Entry Note s 1 5 I5 Material type MTYPE N IB domain 4 2 1 2 3 4 5 6 7 6 15 E10 0 Outgoing cone angle 0 for beam radiation THSET MN IB 1 16 25 E10 0 Outgoing surface azimuth angle po for beam
122. st be input for the curve 75 APPENDIX B FILE FORMATS As discussed in Section 5 3 MONT3D generates a large number of files This appendix gives the format of most of these files The files are presented in order of their unit numbers see Section 5 3 for more detail This appendix should only be of interest to those who plan to write programs that work with the files created by MONT3D The input file format which is of much more general interest is described in Chapter 3 Files are ASCII unless otherwise specified The ASCH FORTRAN format specifications given below are for a single record Each record starts on a new line and if the record is larger than the specification the format repeats as needed starting on a new line each time B 1 Restart File Suffix rst Unit 2 The restart file contains the information MONT3D requires to restart from a completed or crashed run If the program is restarting from a crash additional information stored in the block blk file described below is also required All the code for the reading and writing of this file can be found in the subroutine rstfile in the file m30s f B 1 1 IPARFLG 1 Record of Length 1 FORTRAN Format Specification 7 110 1x Format Entry Note s Integer Parallel run flag IPARFLG 1 Notes 1 IPARFLG is 0 for a single processor run for a parallel run B 1 2 Photon Emission Counts 1 Record of Length NSURF NBANDS FORTRAN Format Specification 7 110 1x Format Entr
123. t the start of the run Since all RNG s are initialized using the binary shift register this methodology produces parallel independent streams of very high quality random numbers on each worker process bit 31 bit 0 m s b Base Usually Time Identical for All Tasks Task No 22 bits shown 10 bits shown lt 1 024 tasks Figure 2 14 Bit Structure of 32 Bit Initial Seed for Parallel Processes 2 11 3 Effect of Different Random Sequences on Results Every different initial seed creates a different sequence of random numbers so different answers are obtained However if enough photons are emitted to achieve convergence then the answers whatever the initial seed will be within statistical convergence error It should be noted that it is not possible to traverse the same sequence of random numbers restarting from a completed run involving emission from more than one surface Thus if a run is done with 20 000 photons emitted initially from each surface the answers will be different than if an initial run is done with 10 000 photons per surface followed by a restart with 10 000 additional photons emitted However the comments above pertaining to convergence do apply If enough photons are emitted then the answers will converge within a statistical tolerance to a final state independent of the order of emissions
124. ted in Table A 1 above A 4 Material Type 1 Beam Emission An option material type 1 is available in the code to simulate beam radiation with all primary photon emissions from a specified material occurring in a fixed direction To use this option fixed values of and 0 for a material must be entered by the user in a format described below It should be noted that this is very different than the beam emission defined by the new material model The new material model defines the beam direction by an emission vector in GLOBAL coordinates The Do and 6 defined in the old material model are relative to the LOCAL coordinate system for the surface For the old material model the emission direction for the beam depends on the orientation of the surface Just as with the new material model all interactions absorptions transmissions reflections will depend only on the material property curves defined for that material Again the user should be cautious when specifying the beam radiation option since the reciprocity relations Equations 1 5 and 1 6 may no longer be valid The other conservation relations still hold 70 A 5 Material Types 0 Thorough 2 Normal Emission For material type 0 through 2 emission is a function of 6 so all of the photon material inter actions are determined by the input curves For material 0 three curves are read and T 0 is set to zero Material type 1 also requires three input curves with T 8
125. the error on which block and other information If a worker encounters any error it terminates As stated in Section 2 10 the first time a block of surfaces fails the block is sent to another worker The second time the block fails the entire run is aborted As described above if the run terminates from errors output files for each process are generated These can be used to get further information about the errors Spawning errors Errors in spawning often means that one or more machines or the communica tion between them are down The error can either occur on the master which is called a system error or it can occur on one or more workers when they fail to start their copy of MONT3D If a system error occurs or all the workers fail to start MONT3D the run exits with an error If some of the workers fail to start the program a serious warning is issued but the run continues with the remaining workers To help identify the spawning problem s the code prints out the PVM error code s for either the system error or for each failing worker Each error code is a number that rep resents a PVM error condition Which code specifies which condition is given in the file fpvm3 h which can usually be found in the directory PVM_ROOT include More detail of these spawning errors can be found in the PVM documentation about the function pvmfspawn A particularly common spawning error is when all the workers fail to start their copy of MONT3D This usuall
126. tion The following records are repeated for each of the NSPTR surfaces The surfaces are listed in order of surface number 78 Material Information 1 Record of Length 2 FORTRAN Format Specification 16i5 Format Entry Note s Integer Surface number Integer Surface s material number Node Information 4 Records of Length 3 FORTRAN Format Specification 6 1x f12 7 Format Entry Note s Real X value of node 1 1 Real Y value of node i 1 Real Z value of node i 1 Notes 1 The X Y and Z coordinates are listed for each of the four nodes of the surface One node is listed per line B 2 5 Material Information The following records are repeated 4 NUMMAT NBANDS times The records are repeated for the four cumulative property types from the old material model in the following order specular transmittance T diffuse transmittance Tq T specular reflectance P Tg T and diffuse reflectance Pa Ps Ta Ts This series of material property records is repeated from 1 to NUM MAT times in each band in order of material number which in turn is repeated from 1 to NBANDS for each band in order of band number Curve Name 1 Record of Length 16 FORTRAN Format Specification a16 Format Entry Note s Character Curve name Curve Values 1 Record of Length 91 FORTRAN Format Specification f10 7 Format Entry Note s Real Curve values 1 79 Notes 1 Curve values are listed in order from 0 to 90 degrees B 2 6 Numb
127. ton emission if the magnitude of the user supplied function is small Photon material interactions are determined by the incident material properties defined for this material 16 2 5 4 Cases Where the Reciprocity Relations Do Not Hold Care must be taken when using some of the more advanced material property features of MONT3D Unless the directional model for emission is consistent with the directional model for surface properties the reciprocity relations Equations 1 5 and 1 6 may no longer hold The other conservation relations still hold however Conditions in which the two models do not match include function and beam emission diffuse reflectance and transmittance with r not equal to 1 and any case involving semi specular reflectance or transmittance When modelling radiative trans fer it is suggested that the user avoid the above conditions The reciprocity relations also are not observed when the diffuse reflectance varies as a function of angle Surprisingly they DO hold when the specular reflectance varies as a function of angle No tests have been done to assess if reciprocity holds when diffuse or specular transmittance varies by angle In the future investiga tions will be done to determine how MONT3D can be modified to observe reciprocity relations under the above conditions 2 6 Shading If any shading exists in the geometry a photon s path may intersect a number of surfaces The distance from the emission point t
128. tory is the directory in which the program is run For the worker pro cesses the default value is HOME The working directory for each CPU in the virtual machine can be changed using the wd option in the PVM hostfile If HOME is different for the user s accounts on different machines the user must change the working directory for the machines so that all use the same directory When each worker spawns it attempts to run a specifically named executable It is very impor tant that the executable be named properly or the executable will not be found and the process will 60 exit in error The default name for the executable is m3dpvm but it can be changed by changing the parameter m3dparaname and recompiling the code More detail is given in Sections 5 2 1 5 5 2 and 5 6 4 When debugging the code it is helpful to have separate debugging sessions for each worker pro cess If IPAROPT 1 see Section 3 2 2 is set to 2 or 3 then an xterm with a dbx session on some systems 1t may be some other debugger is created for each worker process For this to work the DISPLAY variable must be set properly for each worker process To accomplish this the DISPLAY environment variable on the master must be set correctly and the variable PVUM_EXPORT on the master must be set to include the DISPLAY environment variable When running the parallel version of the code it should be remembered that even when restart ing from a crash it is possible
129. ts are reserved for future use 56 60 I5 Number of material property curves NMACV 15 61 65 I5 Number of semi specular offset angle curves NDTCV 15 Notes 1 This option is not available in this version This space is being retained in the input file for back ward compatibility in format Any value entered will be ignored 2 If IPRNT D 1 the specified information is written Otherwise if IPRNT 0 the informa tion is not written 3 If IPRNT 1 1 then exchange fractions are printed in the output file If IPRNT 1 0 they are written only to the exchange matrix file 4 Lost photon information is always written to the lost photon file file suffix lst where it can be viewed using the MPLOT program see Section 2 8 for more detail If IPRNT 2 1 informa tion about the lost photons is also written to the console and the output file 5 When IPRNT 4 is equal to 1 all material information the material property curves the semi specular preferred angle curves and the thetar arrays are printed to the output file in the form in which they are stored internally Angles are always displayed in degrees even if they are stored internally as radians Material property curves are stored so that each property includes the cumulative sum of all properties below it The order in which the properties are stored is amp Da Ps Pss Td Ts aNd Tss The cumulative sum of all the material properties Tss T for the old mat
130. tunately this also requires that the sizes of arrays be pre specified The sizes of various arrays are pre specified with parameter statements Several other features of the code are also spec ified by parameter statements All parameters in MONT3D are stored in one file mont3d par To change a parameter the value need be changed only in the file mont3d par and all files must be recompiled MONT3D has many parameters any parameters not listed in this section should not be altered 5 5 1 Parameters Specifying Array Sizes These parameters establish the maximum sizes of various arrays such as number of surfaces number of wavelength bands number of materials etc If the numbers are set too low MONT3D will issue an error message informing the user that insufficient storage space is available and ter minate It should be noted that the larger the arrays the more memory the program uses If the arrays become too large the program may exceed available physical memory and the execution speed will severely degrade because virtual memory is used where the program is swapped to and from disk The array sizing parameters used in MONT3D and their default values are iblk maximum value for INEBLOCKI the number of surfaces in a restart block 200 ibnd maximum value for NBANDS the number of wavelength bands 5 iimag maximum number of index digits for file names see Section 5 5 2 4 imat maximum value for NUMMAT the number of material
131. under Microsoft Windows Microsoft FORTRAN 5 1 3 Timing Information As shown in Chapter 4 MONT3D prints some timing information at the end of each run There are two types of timing information that can be collected For single processor runs the timing information desired is usually the CPU time The CPU time includes both the user time which is the time the program itself uses in execution and the system time which is the time the system uses for activities such as I O and swapping the program in and out of memory The CPU time does not include the time the processor spends on other programs or processes For parallel runs the most useful timing information is clock time which is the actual time recorded from the clock The clock time includes the time spent on other processes besides MONT3D If timing is disabled then MONT3D reports no timing information On Unix systems the clock user and system times for the run can be obtained using the Unix time command perform a man on time for more information All these stubs work to some degree with the Microsoft Windows Microsoft FORTRAN ver sion of the code The suggest stub for compiling the Windows version of the code is m3f90timing f For more details on Windows timing see Section 5 2 2 Four stubs are available for timing m3ctiming f allows the code to collect timing information about the run in clock time Requires that the nonstandard subroutine time be supported Mainly us
132. urface that uses this material must be greater than 0 If this is not the case the code will exit with an error No check is made when the beam emission variables are used for function emission IETP 2 These are the coefficients rg and r s described in Section 2 5 2 If one of these variables equals 0 then it will be set to 1 standard diffuse distribution If any of these variables is less than 0 then it is set to 0 isotropic distribution Note that as discussed in Section 2 5 4 if ry does not equal 1 standard diffuse distribution or semi specular properties are used the reciprocity rela tions Equations 1 5 and 1 6 may no longer hold 3 8 3 Card 3 Condition s Repeat the pair of cards 2 and 3 for every band input for every material Cols Format Item Note s 1 10 E10 0 Diffuse reflectance RHOD 1 2 11 20 E10 0 Specular reflectance RHOS 1 2 21 30 E10 0 Semi specular reflectance RHOSS 1 2 31 40 E10 0 Diffuse transmittance TAUD 1 2 41 50 E10 0 Specular transmittance TAUS 1 2 51 60 E10 0 Semi specular transmittance TAUSS 152 61 70 E10 0 Semi specular offset angle for reflectance DTHRSS 3 71 80 E10 0 Semi specular offset angle for transmittance DTHTSS 3 Notes Ifa positive definite value 0 or greater is input then this is taken as the constant value for this material property for all values of 6 If a negative value is input it is taken as the negative of the curve index for this property and the
133. versus simulated geom etry Indeed greater differences in non planarity result in greater inconsistencies with the original geometry If these aberrations are large unpredictable and unintended results may occur Indeed there is no substitute for a well defined geometry On the other hand it should be realized that if the value of SPLITOL is too high non planar surfaces will not be split and excessive lost photons and other such problems can occur When splitting a surface MONT3D arbitrarily splits the quad rilateral along the line from node 1 to node 3 While in certain cases it may be better to split the quadrilateral along the line from node 2 to node 4 there is no known way for MONT3D to deter mine which way is better so the surface always splits along the line from node 1 to node 3 MONT3D also tests for convexity A common definition for convexity is that no interior angle can exceed 180 but a complete definition is much more complex see Schorn and Fisher 1994 By definition a convex polygon is planar so the convexity tests are not totally applicable to non planar quadrilaterals This is unfortunate because it is possible to split a concave quadrilateral into two overlapping triangles perhaps similar to those shown in Figure 2 4 To try to prevent this MONT3D applies modified convexity tests to non planar surfaces These tests probably do not catch all overlapping triangles but we know of no foolproof test for non planar qua
134. xcellent ran domness properties across parallel sequences with this method even when the initial seeds for each sequence are very similar This is the method employed in MONT3D Additional detail may be found in Burns and Pryor 1999 and Zeeb and Burns 1997 2 11 2 Implementation Details Experience has shown that using LFG 17 5 31 can lead to about 0 1 systematic error in some applications Zeeb and Burns 1997 Zeeb and Romero 1999 probably due to the fact that as mentioned above correlations appear after about 130 000 or 1 random numbers are generated This error is generally well below the accuracy inherent in Monte Carlo simulations Furthermore these correlations probably have little effect on all but the most simple of problems However to ensure high accuracy runs we have chosen to implement LFG 127 97 31 which has the smallest value of hat passes all of Marsaglia s DIEHARD tests including the Birthday Spacings test Correlations do not appear among the random numbers until after about 1 7 x 10 random numbers have been generated which is more than adequate for any problem in the fore seeable future It is possible to compile the code so that it implements a different length LFG gen erator see Section 5 5 2 for more details The RNG is initialized as follows First the initial seed Xo which is either given by the user generated from the time and date or set to the default value is obtained If the initial
135. y Note s Integer Number of photons emitted from each surface in each band 1 Notes 1 The photon counts are written in order from 1 to NSURF for each band 1 to NBAND 76 B 1 3 Random Number Generator Information Only Written Read if IPARFLG 0 1 Record of Length flen 2 FORTRAN Format Specification 7 i10 1x Format Entry Note s Integer The ISEED array of seeds which is of length flen 1 Integer First tap value 1 Integer Second tap value 1 Notes 1 The code uses a lagged Fibonnaci RNG of length flen The parameter flen is usually 127 but can be changed see Sections 2 11 and 5 5 2 for more details B 1 4 Block Information 1 Record of Length NBLOCKS FORTRAN Format Specification 7 i10 1x Format Entry Note s Integer NBKFIN array 1 Notes 1 The NBKFIN array is NBLOCKS long where NBLOCKS is the number of surface emission blocks for the run see Sections 2 9 and 3 2 1 for more details NBKFIN is 1 if the block has been successfully completed otherwise it is 0 B 2 Plot File Suffix plt Unit 3 The plot file contains the basic information MPLOT Nagesh and Burns 1994 requires to plot the geometry see Section 2 8 for more details All the code for the writing of this file can be found in the subroutine graf in the file m313s f B 2 1 Header 1 Record of Length 72 FORTRAN Format Specification 10a8 Format Entry Note s Character File header 1 Notes 1 This is a character string of 72 characters The
136. y exists at the beginning and end of a run During the run the block exchange matrix files are used instead 13 fn tni Temporary binary exchange matrix file used to convert back and forth between the exchange matrix nij file and the block exchange matrix bni files 14 fn blk Temporary ASCII file containing block information required for restart ing from a crash 56 Table 5 2 Command Line File Control File name to be specified Preceded on command line by Restart file name r R r or R Plot file name p P p or P Lost photon trajectory file name m M m or M Input file name i L i or I Absorption exchange matrix file name e E e or E Trajectory file name t T t or T Output file name 0 O o or O Leaks file name 1 L l or L Family file name f F f or F Several conventions bear emphasizing If even one file name is specified on the command line the code will not query the user for a base file name If the f option is used any file not explicitly specified will assume the naming convention indicated in Table 5 1 Those file names explicitly specified will override this default If the foption is not used then as a minimum the names of the input file output file and exchange matrix file must be specified independently on the command line with the other files deriving their base name from the input f
137. y occurs due to one of three causes First the MONT3D executable may not be in the directory PVM searches for executables see Section 5 6 1 for more detail Second the worker process may not be able to start the MONT3D executable because the executable is named incorrectly When each worker spawns it attempts to run the executable with the name specified by the parameter m3dparaname Therefore for the parallel code to run the executable must be named as specified by m3dparaname parameter which has a default value of m3dpvm For more 62 detail see Sections 5 2 1 5 5 2 and 5 6 1 Third the executable can be compiled for a platform other than the one on which the worker process is spawned General error General errors are a catch all category If the block number is 0 the error occurred during the input phase for the worker Check the process s output file for more details Not Enough Memory Allocated on Worker When working on a heterogeneous architecture at least some of the workers will use a different version of the executable than the master In those cases it is possible for a worker executable not to have enough memory allocated even if the master executable does If this error occurs check the worker process s output file to determine which parameters defining memory allocation need to be increased For more detail see Section 5 5 Emission Point Not in Grid This error occurs when an emission point from a surface is not with

USERS` MANUAL for MONT3D - Code Version 2.4 by Charles N

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