stardis.1.in (22914B)
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If not, see <http://www.gnu.org/licenses/>. 15 .Dd July 18, 2024 16 .Dt STARDIS 1 17 .Os 18 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 19 .Sh NAME 20 .Nm stardis 21 .Nd statistical solving of coupled thermal systems 22 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 23 .Sh SYNOPSIS 24 .Nm 25 .Op Fl eghiv 26 .Op Fl a Ar diff_algo 27 .Op Fl D Ar path_type , Ns Ar files_name_prefix 28 .Op Fl d Ar file_base_name 29 .Op Fl F Pa surface Ns Op , Ns Ar time Ns Op , Ns Ar time 30 .Op Fl f Ar x , Ns Ar y , Ns Ar z Ns Op , Ns Ar time Ns Op , Ns Ar time 31 .Op Fl G Pa green_bin Ns Op , Ns Pa green_ascii 32 .Op Fl I Ar initial_time 33 .Op Fl L Pa interface_probes 34 .Op Fl l Pa interface_probes 35 .Op Fl m Ar medium_name Ns Op , Ns Ar time Ns Op , Ns Ar time 36 .Op Fl n Ar samples_count 37 .Op Fl o Ar picard_order 38 .Op Fl P Ar x , Ns Ar y , Ns Ar z Ns Oo , Ns Ar time Ns Oo , Ns Ar time Oc Oc \ 39 Ns Op : Ns Ar side_indicator 40 .Op Fl p Ar x , Ns Ar y , Ns Ar z Ns Op , Ns Ar time Ns Op , Ns Ar time 41 .Op Fl R Ar rendering_opt Ns Op : Ns Ar rendering_opt No ... 42 .Op Fl S Pa surface Ns Op , Ns Ar time Ns Op , Ns Ar time 43 .Op Fl s Pa surface Ns Op , Ns Ar time Ns Op , Ns Ar time 44 .Op Fl t Ar threads_count 45 .Op Fl V Ar verbosity_level 46 .Op Fl X Pa output_rng 47 .Op Fl x Pa input_rng 48 .Fl M Pa system 49 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 50 .Sh DESCRIPTION 51 .Nm 52 solves coupled thermal systems: conductive, convective and radiative transfers 53 are solved together. 54 The physical model used for conduction is the local unstationary heat conduction 55 equation. 56 Convection fluxes are assumed to be linear with temperature, and radiation 57 is assumed to be integrated over the whole thermal spectral range, 58 therefore radiative heat fluxes are proportionnal to a difference of 59 temperatures to the power 4. 60 .Nm 61 can deal with complex geometries as well as high-frequency external 62 solicitations over a very long period of time, relative to the characteristic 63 time of the system. 64 The provided system description should comply with the 65 .Xr stardis-input 5 66 format. 67 .Pp 68 .Nm 69 can compute a thermal observable, like temperature or flux, at a probe point and 70 date or the mean value of an observable over a given surface, volume, or time 71 range. 72 When a time range 73 .Ar t1 , Ns Ar t2 74 is provided, the computed value is the mean value over the time range. 75 To compute the value at a given time, simply provide a single value 76 .Ar t . 77 In addition, 78 .Nm 79 gives access to the evaluation of the propagator (a.k.a the Green function). 80 The propagator is of great value for thermicist engineers as it gives some 81 crucial information to analyse heat transfers in the system. 82 It helps engineers answer questions like 83 .Dq Where from does the heat come at this location? . 84 Propagators seamlessly aggregate all the provided geometrical and physical 85 information on the system in an unbiased and very-fast statistical model. 86 .Pp 87 .Nm 88 also provides two additional functionalities: converting the 89 .Xr stardis-input 5 90 geometry into a VTK file and rendering an infrared image of 91 the submitted system. 92 .Pp 93 .Nm Ns ' 94 algorithms are based on state-of-the-art Monte Carlo method applied to radiative 95 transfer physics (Delatorre et al. 2014) combined with conduction's 96 statistical formulation (Kac 1949 and Muller 1956). 97 Monte Carlo algorithms associated with convective and conductive processes 98 consist in sampling heat paths: this can be seen as an extension of Monte Carlo 99 algorithms that solve monochromatic radiative transfer. 100 The radiative transfer algorithm, based on the Picard method, is also based on 101 sampling radiative paths. 102 However, since 103 .Nm 104 solves the spectrally integrated radiative transfer, the process can be 105 recursive: secondary heat paths (convective, conductive and radiative) may be 106 necessary along the sampling of an initial radiative path. 107 The solution may not be sufficiently converged with a Picard order equal to 1 in 108 the presence of high temperature gradients. 109 Increasing the Picard order may be necessary in this case, until the required 110 convergence is reached. 111 .Pp 112 One of the key features of 113 .Nm 114 is that its algorithms are not based on a volumetric mesh of the system: 115 only the representation of its interfaces is required. 116 And these are used only as a description of the system, not as a basis 117 for calculation, whose discretization would have an impact on the 118 accuracy of estimates. 119 .Pp 120 .Nm 121 implements mixed parallelism. 122 On a single computer (that is, a node), it uses shared memory parallelism while 123 it relies on Message Passing Interface (MPI) to parallelize calculations between 124 multiple nodes. 125 .Nm 126 can therefore be launched either directly or via a process launcher such as 127 .Xr mpirun 1 128 to distribute the calculation on several computers. 129 .Pp 130 The options are as follows: 131 .Bl -tag -width Ds 132 .It Fl a Ar diff_algo 133 Define the diffusion algorithm to be used when sampling a conductive 134 path. 135 The default diffusion algorithm is 136 .Cm dsphere . 137 .Pp 138 The diffusion algorithms are as follows: 139 .Bl -tag -width Ds 140 .It Cm dsphere 141 Use the delta sphere algorithm, in which Brownian motion is approximated 142 by a random walk of random delta steps. 143 The algorithm is consistent with respect to the 144 .Ar delta 145 parameter, i.e. Brownian motion is estimated exactly with 146 .Ar delta 147 tending towards 0. 148 This numerical parameter 149 .Ar delta 150 is defined by solid and can be varied in 151 time and space to handle the spatio-temporal temperature gradient 152 without prohibitively increasing computation time 153 .Pq see Xr stardis-input 1 . 154 .It Cm wos 155 Use the Walk on Sphere algorithm to estimate Brownian motion. 156 Although a numerical parameter is required to define the distance at 157 which the random walk is considered to have reached the boundary, it can 158 be assumed that this algorithm estimates Brownian motion without any 159 bias with respect to numerical uncertainty. 160 Indeed, the aforementioned distance can be set to the computer's 161 numerical accuracy without any significant impact on performance. 162 .El 163 .It Fl D Ar path_type , Ns Ar files_name_prefix 164 Write sampled heat paths of the given 165 .Ar path_type 166 to files in VTK format, one file per path. 167 Possible values for 168 .Ar path_type 169 are 170 .Cm error 171 .Pq write paths ending in error , 172 .Cm success 173 .Pq write successful paths , 174 and 175 .Cm all 176 .Pq write all paths . 177 Actual file names are produced by appending 178 .Ar files_name_prefix 179 and the path rank starting at index 180 .Ql 00000000 , 181 and possibly followed by 182 .Ql _err 183 for failure paths 184 .Pq e.g. Pa prefix00000000.vtk , Pa prefix00000001_err.vtk 185 .Pp 186 Can only be used in conjunction with some options that sample heat paths 187 .Pq Fl m , Fl p , Fl P , Fl R, Fl s No or Fl S . 188 .It Fl d Ar file_base_name 189 Write the geometry to a file in VTK format along with various properties, 190 including possible errors. 191 Also possibly write some problematic parts of the geometry (if any) in OBJ 192 format. 193 Possible parts are overlapping triangles, riangles with property conflicts, and 194 triangles with merge errors. 195 The various file are all named after the provided base name. 196 If this option is used, no computation occurs. 197 .Pp 198 Using this option in conjunction with an option that 199 specifies a compute region 200 .Pq i.e. Fl F , Fl S , Fl s 201 has the effect to include the region in the VTK output. 202 .It Fl e 203 Use extended format to output Monte Carlo results. 204 Can only be used in conjunction with options that compute a single Monte-Carlo 205 .Pq Fl F , Fl m , Fl P , Fl p No or Fl s No without options Fl g No or Fl G . 206 .It Fl F Pa surface Ns Op , Ns Ar time Ns Op , Ns Ar time 207 Compute the flux through a given 2D surface at a given time, the surface being 208 defined by the triangles in a STL file. 209 The flux can only be computed on a solid-fluid interface and is accounted 210 positive from the solid to the fluid. 211 These triangles are not added to the geometry, but must be part of it. 212 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 213 The surface does not need to be connex. 214 .It Fl f Ar x , Ns Ar y , Ns Ar z Ns Op , Ns Ar time Ns Op , Ns Ar time 215 Compute the flux density at a given probe on an interface at a given time. 216 The probe is supposed to be on an interface and is moved to the closest point of 217 the closest interface before the computation starts. 218 The flux density can only be computed on a solid-fluid interface and is 219 accounted positive from the solid to the fluid. 220 The probe coordinates must be in the same system as the geometry. 221 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 222 .It Fl G Pa green_bin Ns Op , Ns Pa green_ascii 223 Compute the Green function at the specified time and write it to a binary file. 224 If a 225 .Pa green_ascii 226 file name is provided, information on heat paths' ends is also written in this 227 second file in ascii csv format. 228 .Pp 229 This option can only be used in conjunction with one these options: 230 .Fl p , Fl P , Fl m , Fl s 231 and cannot be used in conjunction with option 232 .Fl D . 233 .Pp 234 The resulting file can be further used through the 235 .Xr sgreen 1 236 command to apply different temperature, flux or volumic power values. 237 .It Fl g 238 Compute the Green function at the specified time and write it in ASCII to 239 standard output. 240 This option can only be used in conjunction with one these options: 241 .Fl p , Fl P , Fl m , Fl s 242 and cannot be used in conjunction with option 243 .Fl D . 244 .It Fl h 245 Output short help and exit. 246 .It Fl I Ar initial_time 247 Define initial time in seconds. 248 It can take any value between +/- infinity. 249 The default initial time is 0. 250 .It Fl i 251 Disable internal radiative exchanges. 252 External radiative exchanges are still processed, i.e. the external 253 source. 254 .It Fl L Pa interface_probes 255 Defines a set of interface probes for which 256 .Nm 257 calculates the temperature. 258 The argument file lists the interface probe points. 259 Each line of this file describes a probe point using the same grammar as 260 that used to describe a single interface probe 261 .Pq see Fl P No option . 262 In addition to this syntax, characters behind the hash mark 263 .Pq Ql # 264 are considered comments and are therefore ignored, as are empty lines, 265 i.e. lines with no characters at all or composed solely of spaces and 266 tabs. 267 .Pp 268 Note that this option parallelizes the calculation of the probe list, 269 and not the calculation of each individual probe. 270 Its use is therefore more advantageous in terms of load distribution 271 when the number of probes to be evaluated is large, compared with the 272 cost of calculating a single probe point. 273 .It Fl l Pa interface_probes 274 Defines a set of interface probes for which 275 .Nm 276 calculates the flux density. 277 The argument file lists the interface probe points. 278 Each line of this file describes a probe point using the same grammar as 279 that used to describe a single interface probe 280 .Pq see Fl f No option . 281 In addition to this syntax, characters behind the hash mark 282 .Pq Ql # 283 are considered comments and are therefore ignored, as are empty lines, 284 i.e. lines with no characters at all or composed solely of spaces and 285 tabs. 286 .Pp 287 This option allows the calculation of the probe list while reading and 288 constructing the system only once. 289 .It Fl M Pa system 290 Read a text file containing a possibly partial description of the system. 291 Can include programs, media enclosures and boundary conditions. 292 Media and boundaries can appear in any order, but programs must be defined 293 before their first reference. 294 Refer to 295 .Xr stardis-input 5 296 for a full description of the file format. 297 Can be used more than once if the description is split across different files. 298 .It Fl m Ar medium_name Ns Op , Ns Ar time Ns Op , Ns Ar time 299 Compute the mean temperature in a given medium at a given time. 300 The medium name must be part of the 301 .Pa system 302 description. 303 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 304 The medium region does not need to be connex. 305 .It Fl n Ar samples_count 306 Number of Monte Carlo realisations. 307 By default, the number of realisations is 308 @STARDIS_ARGS_DEFAULT_SAMPLES_COUNT@. 309 .It Fl o Ar picard_order 310 Determine the iteration level used with the Picard method to deal with 311 non-linear radiative transfer accross the model. 312 By default 313 .Ar picard_order 314 is set to @STARDIS_ARGS_DEFAULT_PICARD_ORDER@. 315 Note that a Picard order greater than 1 is incompatible both with Green 316 computations and systems including volumic power sources or non zero flux at a 317 boundary. 318 .It Fl P Ar x , Ns Ar y , Ns Ar z Ns Oo , Ns Ar time Ns Oo , Ns Ar time Oc Oc \ 319 Ns Op : Ns Ar side_indicator 320 Compute the temperature at the given probe on an interface at a given time. 321 If the probe is on an interface where a thermal contact resistance is defined, 322 it is mandatory to provide a side indicator 323 .Pq either Cm FRONT , Cm BACK , No or a medium name , 324 as the temperature differs between the two sides. 325 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 326 The probe is supposed to be on an interface and is moved to the closest point of 327 the closest interface before the computation starts. 328 The probe coordinates must be in the same system as the geometry. 329 .It Fl p Ar x , Ns Ar y , Ns Ar z Ns Op , Ns Ar time Ns Op , Ns Ar time 330 Compute the temperature at the given probe at a given time. 331 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 332 The probe must be in a medium. 333 The probe coordinates must be in the same system as the geometry. 334 .It Fl R Ar rendering_opt Ns Op : Ns Ar rendering_opt No ... 335 Render an infrared image of the system through a pinhole camera. 336 One can use all-default sub-options by simply providing the colon character 337 .Pq Ql \&: 338 alone as an argument. 339 Please note that the camera position must be outside the geometry or in a fluid. 340 .Pp 341 The rendering options are as follows: 342 .Bl -tag -width Ds 343 .It Cm file= Ns Pa output_file 344 File name to use to write the infrared image to. 345 If no file name is provided, the result is written to standard output. 346 .It Cm fmt= Ns Ar image_file_format 347 Format of the image file in output. 348 Can be 349 .Cm VTK , 350 or 351 .Cm HT 352 .Pq see Xr htrdr-image 5 No and Xr htpp 1 . 353 Default 354 .Ar image_file_format 355 is @STARDIS_ARGS_DEFAULT_RENDERING_OUTPUT_FILE_FMT@. 356 .It Cm fov= Ns Ar angle 357 Vertical field of view of the camera in [30,120] degrees. 358 The default field of view is @STARDIS_ARGS_DEFAULT_RENDERING_FOV@ degrees. 359 .It Cm img= Ns Ar width Ns x Ns Ar height 360 Image definition. 361 Default is 362 @STARDIS_ARGS_DEFAULT_RENDERING_IMG_WIDTH@x@STARDIS_ARGS_DEFAULT_RENDERING_IMG_HEIGHT@. 363 .It Cm pos= Ns Ar x , Ns Ar y , Ns Ar z 364 Camera position. 365 Default is @STARDIS_ARGS_DEFAULT_RENDERING_POS@ unless 366 .Cm tgt 367 is not defined, in which case the position is automatically calculated to ensure 368 that the entire scene is visible. 369 .It Cm spp= Ns Ar samples_per_pixel 370 Number of samples to solve the Monte Carlo estimation of each pixel. 371 Default is @STARDIS_ARGS_DEFAULT_RENDERING_SPP@. 372 .It Cm t= Ns Ar time , Ns Op Ns Ar time 373 Rendering time. 374 Default is @STARDIS_ARGS_DEFAULT_RENDERING_TIME@. 375 .It Cm tgt= Ns Ar x , Ns Ar y , Ns Ar z 376 Targeted position. 377 Default is @STARDIS_ARGS_DEFAULT_RENDERING_TGT@ unless 378 .Cm pos 379 is not defined, in which case the targeted position is automatically calculated 380 to ensure that the entire scene is visible. 381 .It Cm up= Ns Ar x , Ns Ar y , Ns Ar z 382 Upward vector that the top of the camera is pointing towards. 383 Default is @STARDIS_ARGS_DEFAULT_RENDERING_UP@. 384 .El 385 .It Fl S Pa surface Ns Op , Ns Ar time Ns Op , Ns Ar time 386 Compute the by-triangle mean temperature on a given 2D 387 .Pa surface 388 at a given time, 389 the 390 .Pa surface 391 defined as the front sides of the triangles in the provided STL file. 392 These triangles are not added to the geometry, but must be part of it. 393 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 394 The 395 .Pa surface 396 does not need to be connex. 397 .It Fl s Pa surface Ns Op , Ns Ar time Ns Op , Ns Ar time 398 Compute the mean temperature on a given 2D 399 .Pa surface 400 at a given time, the 401 .Pa surface 402 being defined as the front sides of the triangles in the provided STL file. 403 By default the compute time is @STARDIS_ARGS_DEFAULT_COMPUTE_TIME@. 404 These triangles are not added to the geometry, but must be part of it. 405 The 406 .Pa surface 407 does not need to be connex. 408 .It Fl t Ar threads_count 409 Advice on the number of threads to use. 410 By default, 411 .Nm 412 uses many threads as processor cores. 413 .It Fl V Ar verbosity_level 414 Set the verbosity level. 415 Possible values are 416 .Ql 0 417 .Pq no message , 418 .Ql 1 419 .Pq error messages only , 420 .Ql 2 421 .Pq error and warning messages , 422 and 423 .Ql 3 424 .Pq error, warning and informative messages . 425 All the messages are written to standard error. 426 Default is @STARDIS_ARGS_DEFAULT_VERBOSE_LEVEL@. 427 .It Fl v 428 Output version information and exit. 429 .It Fl X Pa output_rng 430 Write the random generator's internal state, as it is at the end of the 431 computation, to the provided file. 432 .It Fl x Pa input_rng 433 Read the provided file and use its content to initialize the random generator's 434 internal state. 435 Used in conjunction with the 436 .Fl X 437 option, this can be used to ensure statistical independence between subsequent 438 computations. 439 .El 440 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 441 .Sh EXIT STATUS 442 .Ex -std 443 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 444 .Sh EXAMPLES 445 Preprocess the system as described in 446 .Pa scene 5.txt 447 when intending to compute the mean flux on the triangles from the file 448 .Pa edge.stl , 449 and write its geometry in the file 450 .Pa scene.vtk . 451 Verbosity level is set to 452 .Ar 3 : 453 .Bd -literal -offset Ds 454 stardis -M "scene 5.txt" -F edge.stl -d -V 3 > scene.vtk 455 .Ed 456 .Pp 457 Compute the temperature at the probe point 458 .Ar 0 , Ns Ar 0.5 , Ns Ar 0 459 at steady state. 460 The system is read from the file 461 .Pa model.txt 462 and the number of samples is set to 463 .Ar 1000000 : 464 .Bd -literal -offset Ds 465 stardis -M model.txt -p 0,0.5,0 -n 1000000 466 .Ed 467 .Pp 468 Compute the mean temperature in the medium 469 .Ar med05 470 at 471 .No t= Ns Ar 100 Ns s . 472 The system is read from the file 473 .Pa model.txt 474 and the result is output with extended format 475 .Pq option Fl e : 476 .Bd -literal -offset Ds 477 stardis -M model.txt -m med05,100 -e 478 .Ed 479 .Pp 480 Compute the temperature at the probe point 481 .Ar 0 , Ns Ar 0 , Ns Ar 0 482 at 483 .No t= Ns Ar 2500 . 484 The system is read from the 2 files 485 .Pa media.txt 486 and 487 .Pa bounds.txt , 488 and the number of samples is set to 489 .Ar 1000000 : 490 .Bd -literal -offset Ds 491 stardis -M media.txt -M bounds.txt -p 0,0,0,2500 -n 1000000 492 .Ed 493 .Pp 494 Compute the mean temperature at the probe point 495 .Ar 1 , Ns Ar 2.5 , Ns Ar 0 496 over the 497 .Ar 50 , Ns Ar 5000 498 time range. 499 The system is read from the file 500 .Pa model.txt : 501 .Bd -literal -offset Ds 502 stardis -M model.txt -p 1,2.5,0,50,5000 503 .Ed 504 .Pp 505 Compute 3 probe temperatures, ensuring statistical independence: 506 .Bd -literal -offset Ds 507 stardis -M model.txt -p 1,1.5,0,50,5000 -Xstate1 508 stardis -M model.txt -p 1,2.5,0,50,5000 -xstate1 -Xstate2 509 stardis -M model.txt -p 1,3.5,0,50,5000 -xstate2 510 .Ed 511 .Pp 512 Use 513 .Xr mpirun 1 514 to launch 515 .Nm 516 on several hosts defined in the my_hosts file. 517 Render the system as described in 518 .Pa scene.txt 519 with default settings: 520 .Bd -literal -offset Ds 521 mpirun --hostfile my_hosts stardis -M scene.txt -R\&: 522 .Ed 523 .Pp 524 Render the system as described in 525 .Pa scn.txt 526 at 527 .Ar 100 528 seconds 529 Using 2 samples per pixel 530 for an image of 531 .Ar 800 No by Ar 600 532 pixels 533 saved in 534 .Xr htrdr-image 5 535 format 536 and all other settings set to their default values. 537 The output is redirected to the 538 .Pa img.ht 539 file. 540 If the computation encounters erroneous heat paths, they will be dumped to VTK 541 files named 542 .Pa err_path_00000000.vtk , err_path_00000001.vtk , 543 etc. 544 The image file is then post-processed using 545 .Xr htpp 1 546 with default settings to obtain a png file: 547 .Bd -literal -offset Ds 548 stardis -M scn.txt \\ 549 -R t=100:spp=2:img=800x600:fmt=ht \\ 550 -D error,err_path_ \\ 551 > img.ht 552 htpp -o img.pgn -v -m default img.ht 553 .Ed 554 .Pp 555 Compute the Green function that computes the temperature at the probe point 556 .Ar 0 , Ns Ar 0 , Ns Ar 0 557 at steady state. 558 The system is read from the file 559 .Pa model.txt 560 and the Green function is written to the 561 .Pa probe.green 562 file and the heat paths' ends are written to the 563 .Pa probe_ends.csv 564 file: 565 .Bd -literal -offset Ds 566 stardis -M model.txt -p 0,0,0 -G probe.green,probe_ends.csv 567 .Ed 568 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 569 .Sh SEE ALSO 570 .Xr htpp 1 , 571 .Xr mpirun 1 , 572 .Xr sgreen 1 , 573 .Xr htrdr-image 5 , 574 .Xr stardis-input 5 , 575 .Xr stardis-output 5 576 .Rs 577 .%A Léa Penazzi et al. 578 .%T Path integrals formulations leading to propagator evaluation for coupled \ 579 linear physics in large geometric models 580 .%J Computer Physics Communications 581 .%V 294 582 .%D 2024 583 .%U https://doi.org/10.1016/j.cpc.2023.108911 584 .Re 585 .Rs 586 .%A Mégane Bati et al. 587 .%T Coupling Conduction, Convection and Radiative Transfer in a Single \ 588 Path-Space: Application to Infrared Rendering 589 .%J ACM Transactions on Graphics 590 .%V 42 591 .%N 4 592 .%D August 2023 593 .%U https://doi.org/10.1145/3592121 594 .Re 595 .Rs 596 .%A Jean Marc Tregan et al. 597 .%T Coupling radiative, conductive and convective heat-transfers in a single \ 598 Monte Carlo algorithm: A general theoretical framework for linear situations 599 .%J PLOS ONE 600 .%V 18 601 .%N 4 602 .%D 2023 603 .%U https://doi.org/10.1371/journal.pone.0283681 604 .Re 605 .Rs 606 .%A Jérémie Delatorre et al. 607 .%T Monte Carlo advances and concentrated solar applications 608 .%J Solar Energy 609 .%V 103 610 .%P 653--681 611 .%D 2014 612 .%U https://doi.org/10.1016/j.solener.2013.02.035 613 .Re 614 .Rs 615 .%A Abdolhossein Haji-Sheikh 616 .%A Ephraim Maurice Sparrow 617 .%T The floating random walk and its applications to Monte-Carlo \ 618 solutions of heat equations 619 .%J SIAM Journal on Applied Mathematics 620 .%V 14 621 .%N 2 622 .%P 370--389 623 .%D 1966 624 .Re 625 .Rs 626 .%A Mervin E Muller 627 .%T Some continuous Monte Carlo methods for the Dirichlet problem 628 .%J The Annals of Mathematical Statistics 629 .%P 569--589 630 .%D 1956 631 .Re 632 .Rs 633 .%A Mark Kac 634 .%T On distributions of certain Wiener functionals 635 .%J Transactions of the American Mathematical Society 636 .%V 65 637 .%N 1 638 .%P 1--13 639 .%D 1949 640 .Re 641 .\"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""" 642 .Sh STANDARDS 643 .Rs 644 .%B The VTK User's Guide 645 .%O Simple Legacy Formats 646 .%I Kitware, Inc 647 .%N 11 648 .%D 2010 649 .%P 470--482 650 .Re 651 .Pp 652 .Rs 653 .%A OpenMP Architecture Review Board 654 .%D March 2002 655 .%T OpenMP C and C++ Application Interface 656 .%O version 2.0 657 .Re 658 .Pp 659 .Rs 660 .%A Message Passing Interface Forum 661 .%D July 1997 662 .%T MPI-2: Extensions to The Message-Passing Interface 663 .Re 664 .Pp 665 .Rs 666 .%T The StL Format: Standard Data Format for Fabbers 667 .%A Marshall Burns 668 .%D 1993 669 .%U https://www.fabbers.com/tech/STL_Format 670 .Re