1 // Copyright (c) 2017-2018, Lawrence Livermore National Security, LLC. 2 // Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-734707. 3 // All Rights 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 Example 1 18 // 19 // This example illustrates a simple usage of libCEED to compute the volume of a 20 // 3D body using matrix-free application of a mass operator. Arbitrary mesh and 21 // solution orders in 1D, 2D and 3D are supported from the same code. 22 // 23 // The example has no dependencies, and is designed to be self-contained. For 24 // additional examples that use external discretization libraries (MFEM, PETSc, 25 // etc.) see the subdirectories in libceed/examples. 26 // 27 // All libCEED objects use a Ceed device object constructed based on a command 28 // line argument (-ceed). 29 // 30 // Build with: 31 // 32 // make ex1-volume [CEED_DIR=</path/to/libceed>] 33 // 34 // Sample runs: 35 // 36 // ./ex1-volume 37 // ./ex1-volume -ceed /cpu/self 38 // ./ex1-volume -ceed /gpu/cuda 39 // ./ex1-volume -m ../../../mfem/data/fichera.mesh 40 // ./ex1-volume -m ../../../mfem/data/star.vtk -o 3 41 // ./ex1-volume -m ../../../mfem/data/inline-segment.mesh -o 8 42 // 43 // Next line is grep'd from tap.sh to set its arguments 44 // Test in 1D-3D 45 //TESTARGS -ceed {ceed_resource} -d 2 -t 46 //TESTARGS -ceed {ceed_resource} -d 3 -t 47 //TESTARGS -ceed {ceed_resource} -d 1 -t -g 48 //TESTARGS -ceed {ceed_resource} -d 3 -t -g 49 50 /// @file 51 /// libCEED example using mass operator to compute volume 52 53 #include <ceed.h> 54 #include <stdlib.h> 55 #include <math.h> 56 #include <string.h> 57 58 #include "ex1-volume.h" 59 60 // Auxiliary functions. 61 int GetCartesianMeshSize(int dim, int order, int prob_size, int nxyz[3]); 62 int BuildCartesianRestriction(Ceed ceed, int dim, int nxyz[3], int order, 63 int ncomp, CeedInt *size, CeedInt num_qpts, 64 CeedElemRestriction *restr, 65 CeedElemRestriction *restr_i); 66 int SetCartesianMeshCoords(int dim, int nxyz[3], int mesh_order, 67 CeedVector mesh_coords); 68 CeedScalar TransformMeshCoords(int dim, int mesh_size, CeedVector mesh_coords); 69 70 71 int main(int argc, const char *argv[]) { 72 const char *ceed_spec = "/cpu/self"; 73 int dim = 3; // dimension of the mesh 74 int ncompx = 3; // number of x components 75 int mesh_order = 4; // polynomial degree for the mesh 76 int sol_order = 4; // polynomial degree for the solution 77 int num_qpts = sol_order+2; // number of 1D quadrature points 78 int prob_size = -1; // approximate problem size 79 int help = 0, test = 0, gallery = 0; 80 81 // Process command line arguments. 82 for (int ia = 1; ia < argc; ia++) { 83 int next_arg = ((ia+1) < argc), parse_error = 0; 84 if (!strcmp(argv[ia],"-h")) { 85 help = 1; 86 } else if (!strcmp(argv[ia],"-c") || !strcmp(argv[ia],"-ceed")) { 87 parse_error = next_arg ? ceed_spec = argv[++ia], 0 : 1; 88 } else if (!strcmp(argv[ia],"-d")) { 89 parse_error = next_arg ? dim = atoi(argv[++ia]), 0 : 1; 90 ncompx = dim; 91 } else if (!strcmp(argv[ia],"-m")) { 92 parse_error = next_arg ? mesh_order = atoi(argv[++ia]), 0 : 1; 93 } else if (!strcmp(argv[ia],"-o")) { 94 parse_error = next_arg ? sol_order = atoi(argv[++ia]), 0 : 1; 95 } else if (!strcmp(argv[ia],"-q")) { 96 parse_error = next_arg ? num_qpts = atoi(argv[++ia]), 0 : 1; 97 } else if (!strcmp(argv[ia],"-s")) { 98 parse_error = next_arg ? prob_size = atoi(argv[++ia]), 0 : 1; 99 } else if (!strcmp(argv[ia],"-t")) { 100 test = 1; 101 } else if (!strcmp(argv[ia],"-g")) { 102 gallery = 1; 103 } 104 if (parse_error) { 105 printf("Error parsing command line options.\n"); 106 return 1; 107 } 108 } 109 if (prob_size < 0) prob_size = test ? 8*16 : 256*1024; 110 111 // Print the values of all options: 112 if (!test || help) { 113 printf("Selected options: [command line option] : <current value>\n"); 114 printf(" Ceed specification [-c] : %s\n", ceed_spec); 115 printf(" Mesh dimension [-d] : %d\n", dim); 116 printf(" Mesh order [-m] : %d\n", mesh_order); 117 printf(" Solution order [-o] : %d\n", sol_order); 118 printf(" Num. 1D quadr. pts [-q] : %d\n", num_qpts); 119 printf(" Approx. # unknowns [-s] : %d\n", prob_size); 120 printf(" QFunction source [-g] : %s\n", gallery?"gallery":"header"); 121 if (help) { 122 printf("Test/quiet mode is %s\n", (test?"ON":"OFF (use -t to enable)")); 123 return 0; 124 } 125 printf("\n"); 126 } 127 128 // Select appropriate backend and logical device based on the <ceed-spec> 129 // command line argument. 130 Ceed ceed; 131 CeedInit(ceed_spec, &ceed); 132 133 // Construct the mesh and solution bases. 134 CeedBasis mesh_basis, sol_basis; 135 CeedBasisCreateTensorH1Lagrange(ceed, dim, ncompx, mesh_order+1, num_qpts, 136 CEED_GAUSS, &mesh_basis); 137 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_order+1, num_qpts, 138 CEED_GAUSS, &sol_basis); 139 140 // Determine the mesh size based on the given approximate problem size. 141 int nxyz[dim]; 142 GetCartesianMeshSize(dim, sol_order, prob_size, nxyz); 143 144 if (!test) { 145 printf("Mesh size: nx = %d", nxyz[0]); 146 if (dim > 1) { printf(", ny = %d", nxyz[1]); } 147 if (dim > 2) { printf(", nz = %d", nxyz[2]); } 148 printf("\n"); 149 } 150 151 // Build CeedElemRestriction objects describing the mesh and solution discrete 152 // representations. 153 CeedInt mesh_size, sol_size; 154 CeedElemRestriction mesh_restr, sol_restr, sol_restr_i; 155 BuildCartesianRestriction(ceed, dim, nxyz, mesh_order, ncompx, &mesh_size, 156 num_qpts, &mesh_restr, NULL); 157 BuildCartesianRestriction(ceed, dim, nxyz, sol_order, 1, &sol_size, 158 num_qpts, &sol_restr, &sol_restr_i); 159 if (!test) { 160 printf("Number of mesh nodes : %d\n", mesh_size/dim); 161 printf("Number of solution nodes : %d\n", sol_size); 162 } 163 164 // Create a CeedVector with the mesh coordinates. 165 CeedVector mesh_coords; 166 CeedVectorCreate(ceed, mesh_size, &mesh_coords); 167 SetCartesianMeshCoords(dim, nxyz, mesh_order, mesh_coords); 168 169 // Apply a transformation to the mesh. 170 CeedScalar exact_vol = TransformMeshCoords(dim, mesh_size, mesh_coords); 171 172 // Context data to be passed to the 'f_build_mass' Q-function. 173 CeedQFunctionContext build_ctx; 174 struct BuildContext build_ctx_data; 175 build_ctx_data.dim = build_ctx_data.space_dim = dim; 176 CeedQFunctionContextCreate(ceed, &build_ctx); 177 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, 178 sizeof(build_ctx_data), &build_ctx_data); 179 180 // Create the Q-function that builds the mass operator (i.e. computes its 181 // quadrature data) and set its context data. 182 CeedQFunction build_qfunc; 183 switch (gallery) { 184 case 0: 185 // This creates the QFunction directly. 186 CeedQFunctionCreateInterior(ceed, 1, f_build_mass, 187 f_build_mass_loc, &build_qfunc); 188 CeedQFunctionAddInput(build_qfunc, "dx", ncompx*dim, CEED_EVAL_GRAD); 189 CeedQFunctionAddInput(build_qfunc, "weights", 1, CEED_EVAL_WEIGHT); 190 CeedQFunctionAddOutput(build_qfunc, "qdata", 1, CEED_EVAL_NONE); 191 CeedQFunctionSetContext(build_qfunc, build_ctx); 192 break; 193 case 1: { 194 // This creates the QFunction via the gallery. 195 char name[13] = ""; 196 snprintf(name, sizeof name, "Mass%dDBuild", dim); 197 CeedQFunctionCreateInteriorByName(ceed, name, &build_qfunc); 198 break; 199 } 200 } 201 202 // Create the operator that builds the quadrature data for the mass operator. 203 CeedOperator build_oper; 204 CeedOperatorCreate(ceed, build_qfunc, CEED_QFUNCTION_NONE, 205 CEED_QFUNCTION_NONE, &build_oper); 206 CeedOperatorSetField(build_oper, "dx", mesh_restr, mesh_basis, 207 CEED_VECTOR_ACTIVE); 208 CeedOperatorSetField(build_oper, "weights", CEED_ELEMRESTRICTION_NONE, 209 mesh_basis, CEED_VECTOR_NONE); 210 CeedOperatorSetField(build_oper, "qdata", sol_restr_i, CEED_BASIS_COLLOCATED, 211 CEED_VECTOR_ACTIVE); 212 213 // Compute the quadrature data for the mass operator. 214 CeedVector qdata; 215 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 216 CeedInt num_elem = 1; 217 for (int d = 0; d < dim; d++) 218 num_elem *= nxyz[d]; 219 CeedVectorCreate(ceed, num_elem*elem_qpts, &qdata); 220 if (!test) { 221 printf("Computing the quadrature data for the mass operator ..."); 222 fflush(stdout); 223 } 224 CeedOperatorApply(build_oper, mesh_coords, qdata, 225 CEED_REQUEST_IMMEDIATE); 226 if (!test) { 227 printf(" done.\n"); 228 } 229 230 // Create the Q-function that defines the action of the mass operator. 231 CeedQFunction apply_qfunc; 232 switch (gallery) { 233 case 0: 234 // This creates the QFunction directly. 235 CeedQFunctionCreateInterior(ceed, 1, f_apply_mass, 236 f_apply_mass_loc, &apply_qfunc); 237 CeedQFunctionAddInput(apply_qfunc, "u", 1, CEED_EVAL_INTERP); 238 CeedQFunctionAddInput(apply_qfunc, "qdata", 1, CEED_EVAL_NONE); 239 CeedQFunctionAddOutput(apply_qfunc, "v", 1, CEED_EVAL_INTERP); 240 break; 241 case 1: 242 // This creates the QFunction via the gallery. 243 CeedQFunctionCreateInteriorByName(ceed, "MassApply", &apply_qfunc); 244 break; 245 } 246 247 // Create the mass operator. 248 CeedOperator oper; 249 CeedOperatorCreate(ceed, apply_qfunc, CEED_QFUNCTION_NONE, 250 CEED_QFUNCTION_NONE, &oper); 251 CeedOperatorSetField(oper, "u", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 252 CeedOperatorSetField(oper, "qdata", sol_restr_i, CEED_BASIS_COLLOCATED, 253 qdata); 254 CeedOperatorSetField(oper, "v", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 255 256 // Compute the mesh volume using the mass operator: vol = 1^T \cdot M \cdot 1 257 if (!test) { 258 printf("Computing the mesh volume using the formula: vol = 1^T.M.1 ..."); 259 fflush(stdout); 260 } 261 262 // Create auxiliary solution-size vectors. 263 CeedVector u, v; 264 CeedVectorCreate(ceed, sol_size, &u); 265 CeedVectorCreate(ceed, sol_size, &v); 266 267 // Initialize 'u' and 'v' with ones. 268 CeedVectorSetValue(u, 1.0); 269 270 // Apply the mass operator: 'u' -> 'v'. 271 CeedOperatorApply(oper, u, v, CEED_REQUEST_IMMEDIATE); 272 273 // Compute and print the sum of the entries of 'v' giving the mesh volume. 274 const CeedScalar *v_host; 275 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_host); 276 CeedScalar vol = 0.; 277 for (CeedInt i = 0; i < sol_size; i++) { 278 vol += v_host[i]; 279 } 280 CeedVectorRestoreArrayRead(v, &v_host); 281 if (!test) { 282 printf(" done.\n"); 283 printf("Exact mesh volume : % .14g\n", exact_vol); 284 printf("Computed mesh volume : % .14g\n", vol); 285 printf("Volume error : % .14g\n", vol-exact_vol); 286 } else { 287 CeedScalar tol = (dim==1? 1E-14 : dim==2? 1E-7 : 1E-5); 288 if (fabs(vol-exact_vol)>tol) 289 printf("Volume error : % .1e\n", vol-exact_vol); 290 } 291 292 // Free dynamically allocated memory. 293 CeedVectorDestroy(&u); 294 CeedVectorDestroy(&v); 295 CeedVectorDestroy(&qdata); 296 CeedVectorDestroy(&mesh_coords); 297 CeedOperatorDestroy(&oper); 298 CeedQFunctionDestroy(&apply_qfunc); 299 CeedQFunctionContextDestroy(&build_ctx); 300 CeedOperatorDestroy(&build_oper); 301 CeedQFunctionDestroy(&build_qfunc); 302 CeedElemRestrictionDestroy(&sol_restr); 303 CeedElemRestrictionDestroy(&mesh_restr); 304 CeedElemRestrictionDestroy(&sol_restr_i); 305 CeedBasisDestroy(&sol_basis); 306 CeedBasisDestroy(&mesh_basis); 307 CeedDestroy(&ceed); 308 return 0; 309 } 310 311 312 int GetCartesianMeshSize(int dim, int order, int prob_size, int nxyz[dim]) { 313 // Use the approximate formula: 314 // prob_size ~ num_elem * order^dim 315 CeedInt num_elem = prob_size / CeedIntPow(order, dim); 316 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 317 while (num_elem > 1) { 318 num_elem /= 2; 319 s++; 320 } 321 CeedInt r = s%dim; 322 for (int d = 0; d < dim; d++) { 323 int sd = s/dim; 324 if (r > 0) { sd++; r--; } 325 nxyz[d] = 1 << sd; 326 } 327 return 0; 328 } 329 330 int BuildCartesianRestriction(Ceed ceed, int dim, int nxyz[dim], int order, 331 int ncomp, CeedInt *size, CeedInt num_qpts, 332 CeedElemRestriction *restr, 333 CeedElemRestriction *restr_i) { 334 CeedInt p = order, pp1 = p+1; 335 CeedInt nnodes = CeedIntPow(pp1, dim); // number of scal. nodes per element 336 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 337 CeedInt nd[3], num_elem = 1, scalar_size = 1; 338 for (int d = 0; d < dim; d++) { 339 num_elem *= nxyz[d]; 340 nd[d] = nxyz[d]*p + 1; 341 scalar_size *= nd[d]; 342 } 343 *size = scalar_size*ncomp; 344 // elem: 0 1 n-1 345 // |---*-...-*---|---*-...-*---|- ... -|--...--| 346 // nnodes: 0 1 p-1 p p+1 2*p n*p 347 CeedInt *el_nodes = malloc(sizeof(CeedInt)*num_elem*nnodes); 348 for (CeedInt e = 0; e < num_elem; e++) { 349 CeedInt exyz[3] = {1, 1, 1}, re = e; 350 for (int d = 0; d < dim; d++) { exyz[d] = re%nxyz[d]; re /= nxyz[d]; } 351 CeedInt *loc_el_nodes = el_nodes + e*nnodes; 352 for (int lnodes = 0; lnodes < nnodes; lnodes++) { 353 CeedInt gnodes = 0, gnodes_stride = 1, rnodes = lnodes; 354 for (int d = 0; d < dim; d++) { 355 gnodes += (exyz[d]*p + rnodes%pp1) * gnodes_stride; 356 gnodes_stride *= nd[d]; 357 rnodes /= pp1; 358 } 359 loc_el_nodes[lnodes] = gnodes; 360 } 361 } 362 CeedElemRestrictionCreate(ceed, num_elem, nnodes, ncomp, scalar_size, 363 ncomp*scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, 364 el_nodes, restr); 365 if (restr_i) 366 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, 367 ncomp, ncomp*elem_qpts*num_elem, 368 CEED_STRIDES_BACKEND, restr_i); 369 free(el_nodes); 370 return 0; 371 } 372 373 int SetCartesianMeshCoords(int dim, int nxyz[dim], int mesh_order, 374 CeedVector mesh_coords) { 375 CeedInt p = mesh_order; 376 CeedInt nd[3], num_elem = 1, scalar_size = 1; 377 for (int d = 0; d < dim; d++) { 378 num_elem *= nxyz[d]; 379 nd[d] = nxyz[d]*p + 1; 380 scalar_size *= nd[d]; 381 } 382 CeedScalar *coords; 383 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 384 CeedScalar *nodes = malloc(sizeof(CeedScalar)*(p+1)); 385 // The H1 basis uses Lobatto quadrature points as nodes. 386 CeedLobattoQuadrature(p+1, nodes, NULL); // nodes are in [-1,1] 387 for (CeedInt i = 0; i <= p; i++) { nodes[i] = 0.5+0.5*nodes[i]; } 388 for (CeedInt gsnodes = 0; gsnodes < scalar_size; gsnodes++) { 389 CeedInt rnodes = gsnodes; 390 for (int d = 0; d < dim; d++) { 391 CeedInt d1d = rnodes%nd[d]; 392 coords[gsnodes+scalar_size*d] = ((d1d/p)+nodes[d1d%p]) / nxyz[d]; 393 rnodes /= nd[d]; 394 } 395 } 396 free(nodes); 397 CeedVectorRestoreArray(mesh_coords, &coords); 398 return 0; 399 } 400 401 #ifndef M_PI 402 #define M_PI 3.14159265358979323846 403 #define M_PI_2 1.57079632679489661923 404 #endif 405 406 CeedScalar TransformMeshCoords(int dim, int mesh_size, CeedVector mesh_coords) { 407 CeedScalar exact_volume; 408 CeedScalar *coords; 409 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 410 if (dim == 1) { 411 for (CeedInt i = 0; i < mesh_size; i++) { 412 // map [0,1] to [0,1] varying the mesh density 413 coords[i] = 0.5+1./sqrt(3.)*sin((2./3.)*M_PI*(coords[i]-0.5)); 414 } 415 exact_volume = 1.; 416 } else { 417 CeedInt num_nodes = mesh_size/dim; 418 for (CeedInt i = 0; i < num_nodes; i++) { 419 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar 420 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi 421 CeedScalar u = coords[i], v = coords[i+num_nodes]; 422 u = 1.+u; 423 v = M_PI_2*v; 424 coords[i] = u*cos(v); 425 coords[i+num_nodes] = u*sin(v); 426 } 427 exact_volume = 3./4.*M_PI; 428 } 429 CeedVectorRestoreArray(mesh_coords, &coords); 430 return exact_volume; 431 } 432