1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors. 2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details. 3 // 4 // SPDX-License-Identifier: BSD-2-Clause 5 // 6 // This file is part of CEED: http://github.com/ceed 7 8 // libCEED Example 2 9 // 10 // This example illustrates a simple usage of libCEED to compute the surface 11 // area of a 3D body using matrix-free application of a diffusion operator. 12 // Arbitrary mesh and solution degrees in 1D, 2D and 3D are supported from the 13 // same code. 14 // 15 // The example has no dependencies, and is designed to be self-contained. For 16 // additional examples that use external discretization libraries (MFEM, PETSc, 17 // etc.) see the subdirectories in libceed/examples. 18 // 19 // All libCEED objects use a Ceed device object constructed based on a command 20 // line argument (-ceed). 21 // 22 // Build with: 23 // 24 // make ex2-surface [CEED_DIR=</path/to/libceed>] 25 // 26 // Sample runs: 27 // 28 // ./ex2-surface 29 // ./ex2-surface -ceed /cpu/self 30 // ./ex2-surface -ceed /gpu/cuda 31 // 32 // Test in 1D-3D 33 //TESTARGS(name="1D_user_QFunction") -ceed {ceed_resource} -d 1 -t 34 //TESTARGS(name="2D_user_QFunction") -ceed {ceed_resource} -d 2 -t 35 //TESTARGS(name="3D_user_QFunction") -ceed {ceed_resource} -d 3 -t 36 //TESTARGS(name="1D_Gallery_QFunction") -ceed {ceed_resource} -d 1 -t -g 37 //TESTARGS(name="2D_Gallery_QFunction") -ceed {ceed_resource} -d 2 -t -g 38 //TESTARGS(name="3D_Gallery_QFunction") -ceed {ceed_resource} -d 3 -t -g 39 40 /// @file 41 /// libCEED example using diffusion operator to compute surface area 42 43 #include <ceed.h> 44 #include <math.h> 45 #include <stdlib.h> 46 #include <string.h> 47 #include "ex2-surface.h" 48 49 // Auxiliary functions. 50 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, 51 CeedInt num_xyz[3]); 52 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], 53 CeedInt degree, CeedInt num_comp, CeedInt *size, 54 CeedInt num_qpts, CeedElemRestriction *restr, 55 CeedElemRestriction *restr_i); 56 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], CeedInt mesh_degree, 57 CeedVector mesh_coords); 58 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, 59 CeedVector mesh_coords); 60 61 int main(int argc, const char *argv[]) { 62 const char *ceed_spec = "/cpu/self"; 63 CeedInt dim = 3; // dimension of the mesh 64 CeedInt num_comp_x = 3; // number of x components 65 CeedInt mesh_degree = 4; // polynomial degree for the mesh 66 CeedInt sol_degree = 4; // polynomial degree for the solution 67 CeedInt num_qpts = sol_degree + 2; // number of 1D quadrature points 68 CeedInt prob_size = -1; // approximate problem size 69 CeedInt help = 0, test = 0, gallery = 0; 70 71 // Process command line arguments. 72 for (int ia = 1; ia < argc; ia++) { 73 // LCOV_EXCL_START 74 int next_arg = ((ia+1) < argc), parse_error = 0; 75 if (!strcmp(argv[ia],"-h")) { 76 help = 1; 77 } else if (!strcmp(argv[ia],"-c") || !strcmp(argv[ia],"-ceed")) { 78 parse_error = next_arg ? ceed_spec = argv[++ia], 0 : 1; 79 } else if (!strcmp(argv[ia],"-d")) { 80 parse_error = next_arg ? dim = atoi(argv[++ia]), 0 : 1; 81 num_comp_x = dim; 82 } else if (!strcmp(argv[ia],"-m")) { 83 parse_error = next_arg ? mesh_degree = atoi(argv[++ia]), 0 : 1; 84 } else if (!strcmp(argv[ia],"-p")) { 85 parse_error = next_arg ? sol_degree = atoi(argv[++ia]), 0 : 1; 86 } else if (!strcmp(argv[ia],"-q")) { 87 parse_error = next_arg ? num_qpts = atoi(argv[++ia]), 0 : 1; 88 } else if (!strcmp(argv[ia],"-s")) { 89 parse_error = next_arg ? prob_size = atoi(argv[++ia]), 0 : 1; 90 } else if (!strcmp(argv[ia],"-t")) { 91 test = 1; 92 } else if (!strcmp(argv[ia],"-g")) { 93 gallery = 1; 94 } 95 if (parse_error) { 96 printf("Error parsing command line options.\n"); 97 return 1; 98 } 99 // LCOV_EXCL_STOP 100 } 101 if (prob_size < 0) prob_size = test ? 16*16*dim*dim : 256*1024; 102 103 // Set mesh_degree = sol_degree. 104 mesh_degree = fmax(mesh_degree, sol_degree); 105 sol_degree = mesh_degree; 106 107 // Print the values of all options: 108 if (!test || help) { 109 // LCOV_EXCL_START 110 printf("Selected options: [command line option] : <current value>\n"); 111 printf(" Ceed specification [-c] : %s\n", ceed_spec); 112 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim); 113 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree); 114 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree); 115 printf(" Num. 1D quadr. pts [-q] : %" CeedInt_FMT "\n", num_qpts); 116 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size); 117 printf(" QFunction source [-g] : %s\n", gallery?"gallery":"header"); 118 if (help) { 119 printf("Test/quiet mode is %s\n", (test?"ON":"OFF (use -t to enable)")); 120 return 0; 121 } 122 printf("\n"); 123 // LCOV_EXCL_STOP 124 } 125 126 // Select appropriate backend and logical device based on the <ceed-spec> 127 // command line argument. 128 Ceed ceed; 129 CeedInit(ceed_spec, &ceed); 130 131 // Construct the mesh and solution bases. 132 CeedBasis mesh_basis, sol_basis; 133 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, 134 num_qpts, CEED_GAUSS, &mesh_basis); 135 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, 136 CEED_GAUSS, &sol_basis); 137 138 // Determine the mesh size based on the given approximate problem size. 139 CeedInt num_xyz[3]; 140 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 141 142 if (!test) { 143 // LCOV_EXCL_START 144 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 145 if (dim > 1) { printf(", ny = %" CeedInt_FMT, num_xyz[1]); } 146 if (dim > 2) { printf(", nz = %" CeedInt_FMT, num_xyz[2]); } 147 printf("\n"); 148 // LCOV_EXCL_STOP 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, q_data_restr_i; 155 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, 156 &mesh_size, num_qpts, &mesh_restr, NULL); 157 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, dim*(dim+1)/2, 158 &sol_size, num_qpts, NULL, &q_data_restr_i); 159 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, 160 num_qpts, &sol_restr, NULL); 161 if (!test) { 162 // LCOV_EXCL_START 163 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size/dim); 164 printf("Number of solution nodes : %" CeedInt_FMT "\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, num_xyz, mesh_degree, mesh_coords); 172 173 // Apply a transformation to the mesh. 174 CeedScalar exact_sa = TransformMeshCoords(dim, mesh_size, mesh_coords); 175 176 // Context data to be passed to the 'f_build_diff' 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 diffusion operator (i.e. computes its 185 // quadrature data) and set its context data. 186 CeedQFunction qf_build; 187 switch (gallery) { 188 case 0: 189 // This creates the QFunction directly. 190 CeedQFunctionCreateInterior(ceed, 1, f_build_diff, 191 f_build_diff_loc, &qf_build); 192 CeedQFunctionAddInput(qf_build, "dx", num_comp_x*dim, CEED_EVAL_GRAD); 193 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 194 CeedQFunctionAddOutput(qf_build, "qdata", dim*(dim+1)/2, CEED_EVAL_NONE); 195 CeedQFunctionSetContext(qf_build, build_ctx); 196 break; 197 case 1: { 198 // This creates the QFunction via the gallery. 199 char name[16] = ""; 200 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DBuild", dim); 201 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 202 break; 203 } 204 } 205 206 // Create the operator that builds the quadrature data for the diffusion 207 // operator. 208 CeedOperator op_build; 209 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, 210 CEED_QFUNCTION_NONE, &op_build); 211 CeedOperatorSetField(op_build, "dx", mesh_restr, mesh_basis, 212 CEED_VECTOR_ACTIVE); 213 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, 214 mesh_basis, CEED_VECTOR_NONE); 215 CeedOperatorSetField(op_build, "qdata", q_data_restr_i, 216 CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 217 218 // Compute the quadrature data for the diffusion operator. 219 CeedVector q_data; 220 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 221 CeedInt num_elem = 1; 222 for (CeedInt d = 0; d < dim; d++) 223 num_elem *= num_xyz[d]; 224 CeedVectorCreate(ceed, num_elem*elem_qpts*dim*(dim+1)/2, &q_data); 225 CeedOperatorApply(op_build, mesh_coords, q_data, 226 CEED_REQUEST_IMMEDIATE); 227 228 // Create the QFunction that defines the action of the diffusion operator. 229 CeedQFunction qf_apply; 230 switch (gallery) { 231 case 0: 232 // This creates the QFunction directly. 233 CeedQFunctionCreateInterior(ceed, 1, f_apply_diff, 234 f_apply_diff_loc, &qf_apply); 235 CeedQFunctionAddInput(qf_apply, "du", dim, CEED_EVAL_GRAD); 236 CeedQFunctionAddInput(qf_apply, "qdata", dim*(dim+1)/2, CEED_EVAL_NONE); 237 CeedQFunctionAddOutput(qf_apply, "dv", dim, CEED_EVAL_GRAD); 238 CeedQFunctionSetContext(qf_apply, build_ctx); 239 break; 240 case 1: { 241 // This creates the QFunction via the gallery. 242 char name[16] = ""; 243 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DApply", dim); 244 CeedQFunctionCreateInteriorByName(ceed, name, &qf_apply); 245 break; 246 } 247 } 248 249 // Create the diffusion operator. 250 CeedOperator op_apply; 251 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, 252 CEED_QFUNCTION_NONE, &op_apply); 253 CeedOperatorSetField(op_apply, "du", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 254 CeedOperatorSetField(op_apply, "qdata", q_data_restr_i, CEED_BASIS_COLLOCATED, 255 q_data); 256 CeedOperatorSetField(op_apply, "dv", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 257 258 // Create auxiliary solution-size vectors. 259 CeedVector u, v; 260 CeedVectorCreate(ceed, sol_size, &u); 261 CeedVectorCreate(ceed, sol_size, &v); 262 263 // Initialize 'u' with sum of coordinates, x+y+z. 264 CeedScalar *u_array; 265 const CeedScalar *x_array; 266 CeedVectorGetArrayWrite(u, CEED_MEM_HOST, &u_array); 267 CeedVectorGetArrayRead(mesh_coords, CEED_MEM_HOST, &x_array); 268 for (CeedInt i = 0; i < sol_size; i++) { 269 u_array[i] = 0; 270 for (CeedInt d = 0; d < dim; d++) 271 u_array[i] += x_array[i+d*sol_size]; 272 } 273 CeedVectorRestoreArray(u, &u_array); 274 CeedVectorRestoreArrayRead(mesh_coords, &x_array); 275 276 // Compute the mesh surface area using the diff operator: 277 // sa = 1^T \cdot abs( K \cdot x). 278 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 279 280 // Compute and print the sum of the entries of 'v' giving the mesh surface area. 281 const CeedScalar *v_array; 282 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 283 CeedScalar sa = 0.; 284 for (CeedInt i = 0; i < sol_size; i++) { 285 sa += fabs(v_array[i]); 286 } 287 CeedVectorRestoreArrayRead(v, &v_array); 288 if (!test) { 289 // LCOV_EXCL_START 290 printf(" done.\n"); 291 printf("Exact mesh surface area : % .14g\n", exact_sa); 292 printf("Computed mesh surface area : % .14g\n", sa); 293 printf("Surface area error : % .14g\n", sa-exact_sa); 294 // LCOV_EXCL_STOP 295 } else { 296 CeedScalar tol = (dim==1 ? 10000.*CEED_EPSILON : dim==2 ? 1E-1 : 1E-1); 297 if (fabs(sa-exact_sa)>tol) 298 // LCOV_EXCL_START 299 printf("Surface area error : % .14g\n", sa-exact_sa); 300 // LCOV_EXCL_STOP 301 } 302 303 // Free dynamically allocated memory. 304 CeedVectorDestroy(&u); 305 CeedVectorDestroy(&v); 306 CeedVectorDestroy(&q_data); 307 CeedVectorDestroy(&mesh_coords); 308 CeedOperatorDestroy(&op_apply); 309 CeedQFunctionDestroy(&qf_apply); 310 CeedQFunctionContextDestroy(&build_ctx); 311 CeedOperatorDestroy(&op_build); 312 CeedQFunctionDestroy(&qf_build); 313 CeedElemRestrictionDestroy(&sol_restr); 314 CeedElemRestrictionDestroy(&mesh_restr); 315 CeedElemRestrictionDestroy(&q_data_restr_i); 316 CeedBasisDestroy(&sol_basis); 317 CeedBasisDestroy(&mesh_basis); 318 CeedDestroy(&ceed); 319 return 0; 320 } 321 322 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, 323 CeedInt num_xyz[3]) { 324 // Use the approximate formula: 325 // prob_size ~ num_elem * degree^dim 326 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 327 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 328 while (num_elem > 1) { 329 num_elem /= 2; 330 s++; 331 } 332 CeedInt r = s%dim; 333 for (CeedInt d = 0; d < dim; d++) { 334 CeedInt sd = s/dim; 335 if (r > 0) { sd++; r--; } 336 num_xyz[d] = 1 << sd; 337 } 338 return 0; 339 } 340 341 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], 342 CeedInt degree, CeedInt num_comp, CeedInt *size, 343 CeedInt num_qpts, CeedElemRestriction *restr, 344 CeedElemRestriction *restr_i) { 345 CeedInt p = degree + 1; 346 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 347 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 348 CeedInt nd[3], num_elem = 1, scalar_size = 1; 349 for (CeedInt d = 0; d < dim; d++) { 350 num_elem *= num_xyz[d]; 351 nd[d] = num_xyz[d] * (p - 1) + 1; 352 scalar_size *= nd[d]; 353 } 354 *size = scalar_size*num_comp; 355 // elem: 0 1 n-1 356 // |---*-...-*---|---*-...-*---|- ... -|--...--| 357 // num_nodes: 0 1 p-1 p p+1 2*p n*p 358 CeedInt *el_nodes = malloc(sizeof(CeedInt)*num_elem*num_nodes); 359 for (CeedInt e = 0; e < num_elem; e++) { 360 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 361 for (CeedInt d = 0; d < dim; d++) { e_xyz[d] = re%num_xyz[d]; re /= num_xyz[d]; } 362 CeedInt *loc_el_nodes = el_nodes + e*num_nodes; 363 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 364 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 365 for (CeedInt d = 0; d < dim; d++) { 366 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 367 g_nodes_stride *= nd[d]; 368 r_nodes /= p; 369 } 370 loc_el_nodes[l_nodes] = g_nodes; 371 } 372 } 373 if (restr) 374 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, 375 num_comp * scalar_size, CEED_MEM_HOST, 376 CEED_COPY_VALUES, el_nodes, restr); 377 free(el_nodes); 378 379 if (restr_i) { 380 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, 381 num_comp, num_comp * elem_qpts * num_elem, 382 CEED_STRIDES_BACKEND, restr_i); 383 } 384 385 return 0; 386 } 387 388 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], CeedInt mesh_degree, 389 CeedVector mesh_coords) { 390 CeedInt p = mesh_degree + 1; 391 CeedInt nd[3], num_elem = 1, scalar_size = 1; 392 for (CeedInt d = 0; d < dim; d++) { 393 num_elem *= num_xyz[d]; 394 nd[d] = num_xyz[d] * (p - 1) + 1; 395 scalar_size *= nd[d]; 396 } 397 CeedScalar *coords; 398 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 399 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 400 // The H1 basis uses Lobatto quadrature points as nodes. 401 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 402 for (CeedInt i = 0; i < p; i++) { nodes[i] = 0.5 + 0.5 * nodes[i]; } 403 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 404 CeedInt r_nodes = gs_nodes; 405 for (CeedInt d = 0; d < dim; d++) { 406 CeedInt d1d = r_nodes % nd[d]; 407 coords[gs_nodes + scalar_size * d] = ((d1d / (p - 1)) + nodes[d1d % 408 (p - 1)]) / num_xyz[d]; 409 r_nodes /= nd[d]; 410 } 411 } 412 free(nodes); 413 CeedVectorRestoreArray(mesh_coords, &coords); 414 return 0; 415 } 416 417 #ifndef M_PI 418 #define M_PI 3.14159265358979323846 419 #endif 420 421 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, 422 CeedVector mesh_coords) { 423 CeedScalar exact_sa = (dim == 1 ? 2 : dim == 2 ? 4 : 6); 424 CeedScalar *coords; 425 426 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 427 for (CeedInt i = 0; i < mesh_size; i++) { 428 // map [0,1] to [0,1] varying the mesh density 429 coords[i] = 0.5 + 1./sqrt(3.) * sin((2./3.) * M_PI * (coords[i] - 0.5)); 430 } 431 CeedVectorRestoreArray(mesh_coords, &coords); 432 433 return exact_sa; 434 } 435