1 // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at 2 // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights 3 // reserved. See files LICENSE and NOTICE for details. 4 // 5 // This file is part of CEED, a collection of benchmarks, miniapps, software 6 // libraries and APIs for efficient high-order finite element and spectral 7 // element discretizations for exascale applications. For more information and 8 // source code availability see http://github.com/ceed. 9 // 10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC, 11 // a collaborative effort of two U.S. Department of Energy organizations (Office 12 // of Science and the National Nuclear Security Administration) responsible for 13 // the planning and preparation of a capable exascale ecosystem, including 14 // software, applications, hardware, advanced system engineering and early 15 // testbed platforms, in support of the nation's exascale computing imperative. 16 17 // libCEED + PETSc Example: Surface Area 18 // 19 // This example demonstrates a simple usage of libCEED with PETSc to calculate 20 // the surface area of a simple closed surface, such as the one of a cube or a 21 // tensor-product discrete sphere via the mass operator. 22 // 23 // The code uses higher level communication protocols in DMPlex. 24 // 25 // Build with: 26 // 27 // make area [PETSC_DIR=</path/to/petsc>] [CEED_DIR=</path/to/libceed>] 28 // 29 // Sample runs: 30 // Sequential: 31 // 32 // ./area -problem cube -petscspace_degree 3 -dm_refine 2 33 // 34 // ./area -problem sphere -petscspace_degree 3 -dm_refine 2 35 // 36 // In parallel: 37 // 38 // mpiexec -n 4 ./area -probelm cube -petscspace_degree 3 -dm_refine 2 39 // 40 // mpiexec -n 4 ./area -problem sphere -petscspace_degree 3 -dm_refine 2 41 // 42 // The above example runs use 2 levels of refinement for the mesh. 43 // Use -dm_refine k, for k levels of uniform refinement. 44 // 45 //TESTARGS -ceed {ceed_resource} -test -petscspace_degree 3 46 47 /// @file 48 /// libCEED example using the mass operator to compute a cube or a cubed-sphere surface area using PETSc with DMPlex 49 static const char help[] = 50 "Compute surface area of a cube or a cubed-sphere using DMPlex in PETSc\n"; 51 52 #include <string.h> 53 #include <petscdmplex.h> 54 #include <ceed.h> 55 #include "qfunctions/area/areacube.h" 56 #include "qfunctions/area/areasphere.h" 57 58 #ifndef M_PI 59 # define M_PI 3.14159265358979323846 60 #endif 61 62 // Auxiliary function to define CEED restrictions from DMPlex data 63 static int CreateRestrictionPlex(Ceed ceed, CeedInt P, CeedInt ncomp, 64 CeedElemRestriction *Erestrict, DM dm) { 65 PetscInt ierr; 66 PetscInt c, cStart, cEnd, nelem, nnodes, *erestrict, eoffset; 67 PetscSection section; 68 Vec Uloc; 69 70 PetscFunctionBegin; 71 72 // Get Nelem 73 ierr = DMGetSection(dm, §ion); CHKERRQ(ierr); 74 ierr = DMPlexGetHeightStratum(dm, 0, &cStart,& cEnd); CHKERRQ(ierr); 75 nelem = cEnd - cStart; 76 77 // Get indices 78 ierr = PetscMalloc1(nelem*P*P, &erestrict); CHKERRQ(ierr); 79 for (c=cStart, eoffset = 0; c<cEnd; c++) { 80 PetscInt numindices, *indices, i; 81 ierr = DMPlexGetClosureIndices(dm, section, section, c, &numindices, 82 &indices, NULL); CHKERRQ(ierr); 83 for (i=0; i<numindices; i+=ncomp) { 84 for (PetscInt j=0; j<ncomp; j++) { 85 if (indices[i+j] != indices[i] + (PetscInt)(copysign(j, indices[i]))) 86 SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, 87 "Cell %D closure indices not interlaced", c); 88 } 89 // NO BC on closed surfaces 90 PetscInt loc = indices[i]; 91 erestrict[eoffset++] = loc/ncomp; 92 } 93 ierr = DMPlexRestoreClosureIndices(dm, section, section, c, &numindices, 94 &indices, NULL); CHKERRQ(ierr); 95 } 96 97 // Setup CEED restriction 98 ierr = DMGetLocalVector(dm, &Uloc); CHKERRQ(ierr); 99 ierr = VecGetLocalSize(Uloc, &nnodes); CHKERRQ(ierr); 100 101 ierr = DMRestoreLocalVector(dm, &Uloc); CHKERRQ(ierr); 102 CeedElemRestrictionCreate(ceed, nelem, P*P, nnodes/ncomp, ncomp, 103 CEED_MEM_HOST, CEED_COPY_VALUES, erestrict, 104 Erestrict); 105 ierr = PetscFree(erestrict); CHKERRQ(ierr); 106 107 PetscFunctionReturn(0); 108 } 109 110 // Utility function taken from petsc/src/dm/impls/plex/examples/tutorials/ex7.c 111 static PetscErrorCode ProjectToUnitSphere(DM dm) { 112 Vec coordinates; 113 PetscScalar *coords; 114 PetscInt Nv, v, dim, d; 115 PetscErrorCode ierr; 116 117 PetscFunctionBeginUser; 118 ierr = DMGetCoordinatesLocal(dm, &coordinates); CHKERRQ(ierr); 119 ierr = VecGetLocalSize(coordinates, &Nv); CHKERRQ(ierr); 120 ierr = VecGetBlockSize(coordinates, &dim); CHKERRQ(ierr); 121 Nv /= dim; 122 ierr = VecGetArray(coordinates, &coords); CHKERRQ(ierr); 123 for (v = 0; v < Nv; ++v) { 124 PetscReal r = 0.0; 125 126 for (d = 0; d < dim; ++d) r += PetscSqr(PetscRealPart(coords[v*dim+d])); 127 r = PetscSqrtReal(r); 128 for (d = 0; d < dim; ++d) coords[v*dim+d] /= r; 129 } 130 ierr = VecRestoreArray(coordinates, &coords); CHKERRQ(ierr); 131 PetscFunctionReturn(0); 132 } 133 134 int main(int argc, char **argv) { 135 PetscInt ierr; 136 MPI_Comm comm; 137 char filename[PETSC_MAX_PATH_LEN], 138 ceedresource[PETSC_MAX_PATH_LEN] = "/cpu/self"; 139 PetscInt lsize, gsize, xlsize, 140 qextra = 1, // default number of extra quadrature points 141 ncompx = 3, // number of components of 3D physical coordinates 142 ncompu = 1, // dimension of field to which apply mass operator 143 topodim = 2, // topological dimension of manifold 144 degree = 3; // default degree for finite element bases 145 PetscBool read_mesh = PETSC_FALSE, 146 test_mode = PETSC_FALSE; 147 PetscSpace sp; 148 PetscFE fe; 149 Vec X, Xloc, V, Vloc; 150 DM dm, dmcoord; 151 Ceed ceed; 152 CeedInt P, Q; 153 CeedOperator op_setupgeo, op_apply; 154 CeedQFunction qf_setupgeo, qf_apply; 155 CeedBasis basisx, basisu; 156 CeedElemRestriction Erestrictx, Erestrictu, Erestrictxi, 157 Erestrictqdi; 158 PetscFunctionList geomfactorlist = NULL; 159 char problemtype[PETSC_MAX_PATH_LEN] = "sphere"; 160 161 ierr = PetscInitialize(&argc, &argv, NULL, help); 162 if (ierr) return ierr; 163 comm = PETSC_COMM_WORLD; 164 165 // Set up problem type command line option 166 ierr = PetscFunctionListAdd(&geomfactorlist, "cube", &SetupMassGeoCube); 167 CHKERRQ(ierr); 168 ierr = PetscFunctionListAdd(&geomfactorlist, "sphere", &SetupMassGeoSphere); 169 CHKERRQ(ierr); 170 171 // Read command line options 172 ierr = PetscOptionsBegin(comm, NULL, "CEED surface area problem with PETSc", 173 NULL); 174 CHKERRQ(ierr); 175 ierr = PetscOptionsFList("-problem", "Problem to solve", NULL, geomfactorlist, 176 problemtype, problemtype, sizeof problemtype, NULL); 177 CHKERRQ(ierr); 178 ierr = PetscOptionsInt("-qextra", "Number of extra quadrature points", 179 NULL, qextra, &qextra, NULL); CHKERRQ(ierr); 180 ierr = PetscOptionsString("-ceed", "CEED resource specifier", 181 NULL, ceedresource, ceedresource, 182 sizeof(ceedresource), NULL); CHKERRQ(ierr); 183 ierr = PetscOptionsBool("-test", 184 "Testing mode (do not print unless error is large)", 185 NULL, test_mode, &test_mode, NULL); CHKERRQ(ierr); 186 ierr = PetscOptionsString("-mesh", "Read mesh from file", NULL, 187 filename, filename, sizeof(filename), &read_mesh); 188 CHKERRQ(ierr); 189 ierr = PetscOptionsEnd(); CHKERRQ(ierr); 190 191 // Setup function pointer for geometric factors 192 int (*geomfp)(void *ctx, const CeedInt Q, const CeedScalar *const *in, 193 CeedScalar *const *out); 194 ierr = PetscFunctionListFind(geomfactorlist, problemtype, 195 (void(* *)(void))&geomfp); CHKERRQ(ierr); 196 const char *str; 197 if (geomfp == SetupMassGeoCube) 198 str = SetupMassGeoCube_loc; 199 else if (geomfp == SetupMassGeoSphere) 200 str = SetupMassGeoSphere_loc; 201 else 202 return CeedError(ceed, 1, "Function not found in the list"); 203 204 // Setup DM 205 if (read_mesh) { 206 ierr = DMPlexCreateFromFile(PETSC_COMM_WORLD, filename, PETSC_TRUE, &dm); 207 CHKERRQ(ierr); 208 } else { 209 // Create the mesh as a 0-refined sphere. This will create a cubic surface, not a box. 210 PetscBool simplex = PETSC_FALSE; 211 ierr = DMPlexCreateSphereMesh(PETSC_COMM_WORLD, topodim, simplex, &dm); 212 CHKERRQ(ierr); 213 // Set the object name 214 ierr = PetscObjectSetName((PetscObject)dm, problemtype); CHKERRQ(ierr); 215 // Distribute mesh over processes 216 { 217 DM dmDist = NULL; 218 PetscPartitioner part; 219 220 ierr = DMPlexGetPartitioner(dm, &part); CHKERRQ(ierr); 221 ierr = PetscPartitionerSetFromOptions(part); CHKERRQ(ierr); 222 ierr = DMPlexDistribute(dm, 0, NULL, &dmDist); CHKERRQ(ierr); 223 if (dmDist) { 224 ierr = DMDestroy(&dm); CHKERRQ(ierr); 225 dm = dmDist; 226 } 227 } 228 // Refine DMPlex with uniform refinement using runtime option -dm_refine 229 ierr = DMPlexSetRefinementUniform(dm, PETSC_TRUE); CHKERRQ(ierr); 230 ierr = DMSetFromOptions(dm); CHKERRQ(ierr); 231 if (!strcmp(problemtype, "sphere")) 232 ierr = ProjectToUnitSphere(dm); CHKERRQ(ierr); 233 // View DMPlex via runtime option 234 ierr = DMViewFromOptions(dm, NULL, "-dm_view"); CHKERRQ(ierr); 235 } 236 237 // Create FE 238 ierr = PetscFECreateDefault(PETSC_COMM_SELF, topodim, ncompu, PETSC_FALSE, NULL, 239 PETSC_DETERMINE, &fe); 240 CHKERRQ(ierr); 241 ierr = DMSetFromOptions(dm); CHKERRQ(ierr); 242 ierr = DMAddField(dm, NULL, (PetscObject)fe); CHKERRQ(ierr); 243 ierr = DMCreateDS(dm); CHKERRQ(ierr); 244 ierr = DMPlexSetClosurePermutationTensor(dm, PETSC_DETERMINE, NULL); 245 CHKERRQ(ierr); 246 247 // Get basis space degree 248 ierr = PetscFEGetBasisSpace(fe, &sp); CHKERRQ(ierr); 249 ierr = PetscSpaceGetDegree(sp, °ree, NULL); CHKERRQ(ierr); 250 ierr = PetscFEDestroy(&fe); CHKERRQ(ierr); 251 if (degree < 1) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, 252 "-petscspace_degree %D must be at least 1", degree); 253 254 // Create vectors 255 ierr = DMCreateGlobalVector(dm, &X); CHKERRQ(ierr); 256 ierr = VecGetLocalSize(X, &lsize); CHKERRQ(ierr); 257 ierr = VecGetSize(X, &gsize); CHKERRQ(ierr); 258 ierr = DMCreateLocalVector(dm, &Xloc); CHKERRQ(ierr); 259 ierr = VecGetSize(Xloc, &xlsize); CHKERRQ(ierr); 260 ierr = VecDuplicate(X, &V); CHKERRQ(ierr); 261 ierr = VecDuplicate(Xloc, &Vloc); CHKERRQ(ierr); 262 263 // Set up libCEED 264 CeedInit(ceedresource, &ceed); 265 266 // Print summary 267 P = degree + 1; 268 Q = P + qextra; 269 const char *usedresource; 270 CeedGetResource(ceed, &usedresource); 271 if (!test_mode) { 272 ierr = PetscPrintf(comm, 273 "\n-- libCEED + PETSc Surface Area of a Manifold --\n" 274 " libCEED:\n" 275 " libCEED Backend : %s\n" 276 " Mesh:\n" 277 " Number of 1D Basis Nodes (p) : %d\n" 278 " Number of 1D Quadrature Points (q) : %d\n" 279 " Global nodes : %D\n", 280 usedresource, P, Q, gsize/ncompu); 281 CHKERRQ(ierr); 282 } 283 284 // Setup libCEED's objects: 285 // Create bases 286 CeedBasisCreateTensorH1Lagrange(ceed, topodim, ncompu, P, Q, 287 CEED_GAUSS, &basisu); 288 CeedBasisCreateTensorH1Lagrange(ceed, topodim, ncompx, 2, Q, 289 CEED_GAUSS, &basisx); 290 291 // CEED restrictions 292 ierr = DMGetCoordinateDM(dm, &dmcoord); CHKERRQ(ierr); 293 ierr = DMPlexSetClosurePermutationTensor(dmcoord, PETSC_DETERMINE, NULL); 294 CHKERRQ(ierr); 295 296 CreateRestrictionPlex(ceed, 2, ncompx, &Erestrictx, dmcoord); CHKERRQ(ierr); 297 CreateRestrictionPlex(ceed, P, ncompu, &Erestrictu, dm); CHKERRQ(ierr); 298 299 CeedInt cStart, cEnd; 300 ierr = DMPlexGetHeightStratum(dm, 0, &cStart, &cEnd); CHKERRQ(ierr); 301 const CeedInt nelem = cEnd - cStart; 302 303 // CEED identity restrictions 304 const CeedInt qdatasize = 1; 305 CeedElemRestrictionCreateIdentity(ceed, nelem, Q*Q, nelem*Q*Q, 306 qdatasize, &Erestrictqdi); 307 CeedElemRestrictionCreateIdentity(ceed, nelem, Q*Q, nelem*Q*Q, 1, 308 &Erestrictxi); 309 310 // Element coordinates 311 Vec coords; 312 const PetscScalar *coordArray; 313 PetscSection section; 314 ierr = DMGetCoordinatesLocal(dm, &coords); CHKERRQ(ierr); 315 ierr = VecGetArrayRead(coords, &coordArray); CHKERRQ(ierr); 316 ierr = DMGetSection(dmcoord, §ion); CHKERRQ(ierr); 317 318 CeedVector xcoord; 319 CeedElemRestrictionCreateVector(Erestrictx, &xcoord, NULL); 320 CeedVectorSetArray(xcoord, CEED_MEM_HOST, CEED_COPY_VALUES, 321 (PetscScalar *)coordArray); 322 ierr = VecRestoreArrayRead(coords, &coordArray); 323 324 // Create the vectors that will be needed in setup and apply 325 CeedVector uceed, vceed, qdata; 326 CeedInt nqpts; 327 CeedBasisGetNumQuadraturePoints(basisu, &nqpts); 328 CeedVectorCreate(ceed, qdatasize*nelem*nqpts, &qdata); 329 CeedVectorCreate(ceed, xlsize, &uceed); 330 CeedVectorCreate(ceed, xlsize, &vceed); 331 332 // Create the Q-function that builds the operator for the geomteric factors 333 // (i.e., the quadrature data) 334 CeedQFunctionCreateInterior(ceed, 1, geomfp, str, &qf_setupgeo); 335 CeedQFunctionAddInput(qf_setupgeo, "x", ncompx, CEED_EVAL_INTERP); 336 CeedQFunctionAddInput(qf_setupgeo, "dx", ncompx*topodim, CEED_EVAL_GRAD); 337 CeedQFunctionAddInput(qf_setupgeo, "weight", 1, CEED_EVAL_WEIGHT); 338 CeedQFunctionAddOutput(qf_setupgeo, "qdata", qdatasize, CEED_EVAL_NONE); 339 340 // Set up the mass operator 341 CeedQFunctionCreateInterior(ceed, 1, Mass, Mass_loc, &qf_apply); 342 CeedQFunctionAddInput(qf_apply, "u", ncompu, CEED_EVAL_INTERP); 343 CeedQFunctionAddInput(qf_apply, "qdata", qdatasize, CEED_EVAL_NONE); 344 CeedQFunctionAddOutput(qf_apply, "v", ncompu, CEED_EVAL_INTERP); 345 346 // Create the operator that builds the quadrature data for the operator 347 CeedOperatorCreate(ceed, qf_setupgeo, NULL, NULL, &op_setupgeo); 348 CeedOperatorSetField(op_setupgeo, "x", Erestrictx, CEED_TRANSPOSE, 349 basisx, CEED_VECTOR_ACTIVE); 350 CeedOperatorSetField(op_setupgeo, "dx", Erestrictx, CEED_TRANSPOSE, 351 basisx, CEED_VECTOR_ACTIVE); 352 CeedOperatorSetField(op_setupgeo, "weight", Erestrictxi, CEED_NOTRANSPOSE, 353 basisx, CEED_VECTOR_NONE); 354 CeedOperatorSetField(op_setupgeo, "qdata", Erestrictqdi, CEED_NOTRANSPOSE, 355 CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 356 357 // Create the mass operator 358 CeedOperatorCreate(ceed, qf_apply, NULL, NULL, &op_apply); 359 CeedOperatorSetField(op_apply, "u", Erestrictu, CEED_TRANSPOSE, 360 basisu, CEED_VECTOR_ACTIVE); 361 CeedOperatorSetField(op_apply, "qdata", Erestrictqdi, CEED_NOTRANSPOSE, 362 CEED_BASIS_COLLOCATED, qdata); 363 CeedOperatorSetField(op_apply, "v", Erestrictu, CEED_TRANSPOSE, 364 basisu, CEED_VECTOR_ACTIVE); 365 366 // Compute the quadrature data for the mass operator 367 CeedOperatorApply(op_setupgeo, xcoord, qdata, CEED_REQUEST_IMMEDIATE); 368 369 PetscScalar *v; 370 ierr = VecZeroEntries(Vloc); CHKERRQ(ierr); 371 ierr = VecGetArray(Vloc, &v); 372 CeedVectorSetArray(vceed, CEED_MEM_HOST, CEED_USE_POINTER, v); 373 374 // Compute the mesh volume using the mass operator: vol = 1^T \cdot M \cdot 1 375 if (!test_mode) { 376 ierr = PetscPrintf(comm, 377 "Computing the mesh area using the formula: area = 1^T M 1\n"); 378 CHKERRQ(ierr); 379 } 380 381 // Initialize u and v with ones 382 CeedVectorSetValue(uceed, 1.0); 383 384 // Apply the mass operator: 'u' -> 'v' 385 CeedOperatorApply(op_apply, uceed, vceed, CEED_REQUEST_IMMEDIATE); 386 CeedVectorSyncArray(vceed, CEED_MEM_HOST); 387 388 // Gather output vector 389 ierr = VecRestoreArray(Vloc, &v); CHKERRQ(ierr); 390 ierr = VecZeroEntries(V); CHKERRQ(ierr); 391 ierr = DMLocalToGlobalBegin(dm, Vloc, ADD_VALUES, V); CHKERRQ(ierr); 392 ierr = DMLocalToGlobalEnd(dm, Vloc, ADD_VALUES, V); CHKERRQ(ierr); 393 394 // Compute and print the sum of the entries of 'v' giving the mesh surface area 395 PetscScalar area; 396 ierr = VecSum(V, &area); CHKERRQ(ierr); 397 398 // Compute the exact surface area and print the result 399 CeedScalar exact_surfarea = 4 * M_PI; 400 if (!strcmp(problemtype, "cube")) { 401 PetscScalar l = 1.0/PetscSqrtReal(3.0); // half edge of the cube 402 exact_surfarea = 6 * (2*l) * (2*l); 403 } 404 405 if (!test_mode) { 406 ierr = PetscPrintf(comm, "Exact mesh surface area : % .14g\n", 407 exact_surfarea); CHKERRQ(ierr); 408 ierr = PetscPrintf(comm, "Computed mesh surface area : % .14g\n", area); 409 CHKERRQ(ierr); 410 ierr = PetscPrintf(comm, "Area error : % .14g\n", 411 fabs(area - exact_surfarea)); CHKERRQ(ierr); 412 } 413 414 // PETSc cleanup 415 ierr = DMDestroy(&dm); CHKERRQ(ierr); 416 ierr = VecDestroy(&X); CHKERRQ(ierr); 417 ierr = VecDestroy(&Xloc); CHKERRQ(ierr); 418 ierr = VecDestroy(&V); CHKERRQ(ierr); 419 ierr = VecDestroy(&Vloc); CHKERRQ(ierr); 420 421 // libCEED cleanup 422 CeedQFunctionDestroy(&qf_setupgeo); 423 CeedOperatorDestroy(&op_setupgeo); 424 CeedVectorDestroy(&xcoord); 425 CeedVectorDestroy(&uceed); 426 CeedVectorDestroy(&vceed); 427 CeedVectorDestroy(&qdata); 428 CeedBasisDestroy(&basisx); 429 CeedBasisDestroy(&basisu); 430 CeedElemRestrictionDestroy(&Erestrictu); 431 CeedElemRestrictionDestroy(&Erestrictx); 432 CeedElemRestrictionDestroy(&Erestrictxi); 433 CeedElemRestrictionDestroy(&Erestrictqdi); 434 CeedQFunctionDestroy(&qf_apply); 435 CeedOperatorDestroy(&op_apply); 436 CeedDestroy(&ceed); 437 return PetscFinalize(); 438 } 439