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