1 // Copyright (c) 2017-2025, 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 area of a 3D body using matrix-free application of a diffusion operator. 11 // Arbitrary mesh and solution degrees in 1D, 2D and 3D are supported from the same code. 12 // 13 // The example has no dependencies, and is designed to be self-contained. 14 // For additional examples that use external discretization libraries (MFEM, PETSc, etc.) see the subdirectories in libceed/examples. 15 // 16 // All libCEED objects use a Ceed device object constructed based on a command line argument (-ceed). 17 // 18 // Build with: 19 // 20 // make ex2-surface [CEED_DIR=</path/to/libceed>] 21 // 22 // Sample runs: 23 // 24 // ./ex2-surface 25 // ./ex2-surface -ceed /cpu/self 26 // ./ex2-surface -ceed /gpu/cuda 27 // 28 // Test in 1D-3D 29 //TESTARGS(name="1D User QFunction") -ceed {ceed_resource} -d 1 -t 30 //TESTARGS(name="2D User QFunction") -ceed {ceed_resource} -d 2 -t 31 //TESTARGS(name="3D User QFunction") -ceed {ceed_resource} -d 3 -t 32 //TESTARGS(name="1D Gallery QFunction") -ceed {ceed_resource} -d 1 -t -g 33 //TESTARGS(name="2D Gallery QFunction") -ceed {ceed_resource} -d 2 -t -g 34 //TESTARGS(name="3D Gallery QFunction") -ceed {ceed_resource} -d 3 -t -g 35 36 /// @file 37 /// libCEED example using diffusion operator to compute surface area 38 39 #include "ex2-surface.h" 40 41 #include <ceed.h> 42 #include <math.h> 43 #include <stdio.h> 44 #include <stdlib.h> 45 #include <string.h> 46 47 // Auxiliary functions 48 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[3]); 49 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 50 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction); 51 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], CeedInt mesh_degree, CeedVector mesh_coords); 52 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords); 53 54 // Main example 55 int main(int argc, const char *argv[]) { 56 const char *ceed_spec = "/cpu/self"; 57 CeedInt dim = 3; // dimension of the mesh 58 CeedInt num_comp_x = 3; // number of x components 59 CeedInt mesh_degree = 4; // polynomial degree for the mesh 60 CeedInt sol_degree = 4; // polynomial degree for the solution 61 CeedInt num_qpts = sol_degree + 2; // number of 1D quadrature points 62 CeedInt prob_size = -1; // approximate problem size 63 CeedInt help = 0, test = 0, gallery = 0, benchmark = 0; 64 65 // Process command line arguments. 66 for (int ia = 1; ia < argc; ia++) { 67 // LCOV_EXCL_START 68 int next_arg = ((ia + 1) < argc), parse_error = 0; 69 if (!strcmp(argv[ia], "-h")) { 70 help = 1; 71 } else if (!strcmp(argv[ia], "-c") || !strcmp(argv[ia], "-ceed")) { 72 parse_error = next_arg ? ceed_spec = argv[++ia], 0 : 1; 73 } else if (!strcmp(argv[ia], "-d")) { 74 parse_error = next_arg ? dim = atoi(argv[++ia]), 0 : 1; 75 num_comp_x = dim; 76 } else if (!strcmp(argv[ia], "-m")) { 77 parse_error = next_arg ? mesh_degree = atoi(argv[++ia]), 0 : 1; 78 } else if (!strcmp(argv[ia], "-p")) { 79 parse_error = next_arg ? sol_degree = atoi(argv[++ia]), 0 : 1; 80 } else if (!strcmp(argv[ia], "-q")) { 81 parse_error = next_arg ? num_qpts = atoi(argv[++ia]), 0 : 1; 82 } else if (!strcmp(argv[ia], "-s")) { 83 parse_error = next_arg ? prob_size = atoi(argv[++ia]), 0 : 1; 84 } else if (!strcmp(argv[ia], "-b")) { 85 parse_error = next_arg ? benchmark = atoi(argv[++ia]), 0 : 1; 86 } else if (!strcmp(argv[ia], "-t")) { 87 test = 1; 88 } else if (!strcmp(argv[ia], "-g")) { 89 gallery = 1; 90 } 91 if (parse_error) { 92 printf("Error parsing command line options.\n"); 93 return 1; 94 } 95 // LCOV_EXCL_STOP 96 } 97 if (prob_size < 0) prob_size = test ? 16 * 16 * dim * dim : 256 * 1024; 98 99 // Set mesh_degree = sol_degree. 100 mesh_degree = fmax(mesh_degree, sol_degree); 101 sol_degree = mesh_degree; 102 103 // Print the values of all options: 104 if (!test || help) { 105 // LCOV_EXCL_START 106 printf("Selected options: [command line option] : <current value>\n"); 107 printf(" Ceed specification [-c] : %s\n", ceed_spec); 108 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim); 109 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree); 110 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree); 111 printf(" Num. 1D quadrature pts [-q] : %" CeedInt_FMT "\n", num_qpts); 112 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size); 113 printf(" QFunction source [-g] : %s\n", gallery ? "gallery" : "header"); 114 if (help) { 115 printf("Test/quiet mode is %s\n", (test ? "ON" : "OFF (use -t to enable)")); 116 return 0; 117 } 118 printf("\n"); 119 // LCOV_EXCL_STOP 120 } 121 122 // Select appropriate backend and logical device based on the (-ceed) command line argument. 123 Ceed ceed; 124 125 CeedInit(ceed_spec, &ceed); 126 127 // Construct the mesh and solution bases. 128 CeedBasis mesh_basis, sol_basis; 129 130 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, num_qpts, CEED_GAUSS, &mesh_basis); 131 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, CEED_GAUSS, &sol_basis); 132 133 // Determine the mesh size based on the given approximate problem size. 134 CeedInt num_xyz[3]; 135 136 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 137 138 if (!test) { 139 // LCOV_EXCL_START 140 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 141 if (dim > 1) printf(", ny = %" CeedInt_FMT, num_xyz[1]); 142 if (dim > 2) printf(", nz = %" CeedInt_FMT, num_xyz[2]); 143 printf("\n"); 144 // LCOV_EXCL_STOP 145 } 146 147 // Build CeedElemRestriction objects describing the mesh and solution discrete representations. 148 CeedInt mesh_size, sol_size; 149 CeedElemRestriction mesh_restriction, sol_restriction, q_data_restriction; 150 151 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restriction, NULL); 152 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, dim * (dim + 1) / 2, &sol_size, num_qpts, NULL, &q_data_restriction); 153 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restriction, NULL); 154 if (!test) { 155 // LCOV_EXCL_START 156 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size / dim); 157 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size); 158 // LCOV_EXCL_STOP 159 } 160 161 // Create a CeedVector with the mesh coordinates. 162 CeedVector mesh_coords; 163 164 CeedVectorCreate(ceed, mesh_size, &mesh_coords); 165 SetCartesianMeshCoords(dim, num_xyz, mesh_degree, mesh_coords); 166 167 // Apply a transformation to the mesh. 168 CeedScalar exact_surface_area = TransformMeshCoords(dim, mesh_size, mesh_coords); 169 170 // Context data to be passed to the 'build_diff' QFunction. 171 CeedQFunctionContext build_ctx; 172 struct BuildContext build_ctx_data; 173 174 build_ctx_data.dim = build_ctx_data.space_dim = dim; 175 CeedQFunctionContextCreate(ceed, &build_ctx); 176 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(build_ctx_data), &build_ctx_data); 177 178 // Create the QFunction that builds the diffusion operator (i.e. computes its quadrature data) and set its context data. 179 CeedQFunction qf_build; 180 181 if (gallery) { 182 // This creates the QFunction via the gallery. 183 char name[16] = ""; 184 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DBuild", dim); 185 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 186 } else { 187 // This creates the QFunction directly. 188 CeedQFunctionCreateInterior(ceed, 1, build_diff, build_diff_loc, &qf_build); 189 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 190 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 191 CeedQFunctionAddOutput(qf_build, "qdata", dim * (dim + 1) / 2, CEED_EVAL_NONE); 192 CeedQFunctionSetContext(qf_build, build_ctx); 193 } 194 195 // Create the operator that builds the quadrature data for the diffusion operator. 196 CeedOperator op_build; 197 198 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 199 CeedOperatorSetField(op_build, "dx", mesh_restriction, mesh_basis, CEED_VECTOR_ACTIVE); 200 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 201 CeedOperatorSetField(op_build, "qdata", q_data_restriction, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE); 202 203 // Compute the quadrature data for the diffusion operator. 204 CeedVector q_data; 205 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 206 CeedInt num_elem = 1; 207 208 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 209 CeedVectorCreate(ceed, num_elem * elem_qpts * dim * (dim + 1) / 2, &q_data); 210 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 211 212 // Create the QFunction that defines the action of the diffusion operator. 213 CeedQFunction qf_apply; 214 215 if (gallery) { 216 // This creates the QFunction via the gallery. 217 char name[25] = ""; 218 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DApply", dim); 219 CeedQFunctionCreateInteriorByName(ceed, name, &qf_apply); 220 } else { 221 // This creates the QFunction directly. 222 CeedQFunctionCreateInterior(ceed, 1, apply_diff, apply_diff_loc, &qf_apply); 223 CeedQFunctionAddInput(qf_apply, "du", dim, CEED_EVAL_GRAD); 224 CeedQFunctionAddInput(qf_apply, "qdata", dim * (dim + 1) / 2, CEED_EVAL_NONE); 225 CeedQFunctionAddOutput(qf_apply, "dv", dim, CEED_EVAL_GRAD); 226 CeedQFunctionSetContext(qf_apply, build_ctx); 227 } 228 229 // Create the diffusion operator. 230 CeedOperator op_apply; 231 232 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 233 CeedOperatorSetField(op_apply, "du", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 234 CeedOperatorSetField(op_apply, "qdata", q_data_restriction, CEED_BASIS_NONE, q_data); 235 CeedOperatorSetField(op_apply, "dv", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 236 237 // Create auxiliary solution-size vectors. 238 CeedVector u, v; 239 240 CeedVectorCreate(ceed, sol_size, &u); 241 CeedVectorCreate(ceed, sol_size, &v); 242 243 // Initialize 'u' with sum of coordinates, x+y+z. 244 { 245 CeedScalar *u_array; 246 const CeedScalar *x_array; 247 248 CeedVectorGetArrayWrite(u, CEED_MEM_HOST, &u_array); 249 CeedVectorGetArrayRead(mesh_coords, CEED_MEM_HOST, &x_array); 250 for (CeedInt i = 0; i < sol_size; i++) { 251 u_array[i] = 0; 252 for (CeedInt d = 0; d < dim; d++) u_array[i] += x_array[i + d * sol_size]; 253 } 254 CeedVectorRestoreArray(u, &u_array); 255 CeedVectorRestoreArrayRead(mesh_coords, &x_array); 256 } 257 258 // Compute the mesh surface area using the diff operator: surface_area = 1^T \cdot abs( K \cdot x). 259 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 260 261 // Benchmark runs 262 if (!test && benchmark) { 263 // LCOV_EXCL_START 264 printf(" Executing %d benchmarking runs...\n", benchmark); 265 // LCOV_EXCL_STOP 266 } 267 for (CeedInt i = 0; i < benchmark; i++) { 268 // LCOV_EXCL_START 269 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 270 // LCOV_EXCL_STOP 271 } 272 273 // Compute and print the sum of the entries of 'v' giving the mesh surface area. 274 CeedScalar surface_area = 0.; 275 { 276 const CeedScalar *v_array; 277 278 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 279 for (CeedInt i = 0; i < sol_size; i++) surface_area += fabs(v_array[i]); 280 CeedVectorRestoreArrayRead(v, &v_array); 281 } 282 if (!test) { 283 // LCOV_EXCL_START 284 printf(" done.\n"); 285 printf("Exact mesh surface area : % .14g\n", exact_surface_area); 286 printf("Computed mesh surface area : % .14g\n", surface_area); 287 printf("Surface area error : % .14g\n", surface_area - exact_surface_area); 288 // LCOV_EXCL_STOP 289 } else { 290 CeedScalar tol = (dim == 1 ? 10000. * CEED_EPSILON : dim == 2 ? 1E-1 : 1E-1); 291 292 if (fabs(surface_area - exact_surface_area) > tol) printf("Surface area error : % .14g\n", surface_area - exact_surface_area); 293 } 294 295 // Free dynamically allocated memory. 296 CeedVectorDestroy(&u); 297 CeedVectorDestroy(&v); 298 CeedVectorDestroy(&q_data); 299 CeedVectorDestroy(&mesh_coords); 300 CeedOperatorDestroy(&op_apply); 301 CeedQFunctionDestroy(&qf_apply); 302 CeedQFunctionContextDestroy(&build_ctx); 303 CeedOperatorDestroy(&op_build); 304 CeedQFunctionDestroy(&qf_build); 305 CeedElemRestrictionDestroy(&sol_restriction); 306 CeedElemRestrictionDestroy(&mesh_restriction); 307 CeedElemRestrictionDestroy(&q_data_restriction); 308 CeedBasisDestroy(&sol_basis); 309 CeedBasisDestroy(&mesh_basis); 310 CeedDestroy(&ceed); 311 return 0; 312 } 313 314 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[3]) { 315 // Use the approximate formula: 316 // prob_size ~ num_elem * degree^dim 317 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 318 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 319 320 while (num_elem > 1) { 321 num_elem /= 2; 322 s++; 323 } 324 CeedInt r = s % dim; 325 326 for (CeedInt d = 0; d < dim; d++) { 327 CeedInt sd = s / dim; 328 329 if (r > 0) { 330 sd++; 331 r--; 332 } 333 num_xyz[d] = 1 << sd; 334 } 335 return 0; 336 } 337 338 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 339 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction) { 340 CeedInt p = degree + 1; 341 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 342 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 343 CeedInt nd[3], num_elem = 1, scalar_size = 1; 344 345 for (CeedInt d = 0; d < dim; d++) { 346 num_elem *= num_xyz[d]; 347 nd[d] = num_xyz[d] * (p - 1) + 1; 348 scalar_size *= nd[d]; 349 } 350 *size = scalar_size * num_comp; 351 // elem: 0 1 n-1 352 // |---*-...-*---|---*-...-*---|- ... -|--...--| 353 // num_nodes: 0 1 p-1 p p+1 2*p n*p 354 CeedInt *el_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 355 356 for (CeedInt e = 0; e < num_elem; e++) { 357 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 358 359 for (CeedInt d = 0; d < dim; d++) { 360 e_xyz[d] = re % num_xyz[d]; 361 re /= num_xyz[d]; 362 } 363 CeedInt *local_elem_nodes = el_nodes + e * num_nodes; 364 365 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 366 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 367 368 for (CeedInt d = 0; d < dim; d++) { 369 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 370 g_nodes_stride *= nd[d]; 371 r_nodes /= p; 372 } 373 local_elem_nodes[l_nodes] = g_nodes; 374 } 375 } 376 if (restriction) { 377 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, el_nodes, 378 restriction); 379 } 380 free(el_nodes); 381 382 if (q_data_restriction) { 383 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, q_data_restriction); 384 } 385 386 return 0; 387 } 388 389 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], CeedInt mesh_degree, CeedVector mesh_coords) { 390 CeedInt p = mesh_degree + 1; 391 CeedInt nd[3], scalar_size = 1; 392 393 for (CeedInt d = 0; d < dim; d++) { 394 nd[d] = num_xyz[d] * (p - 1) + 1; 395 scalar_size *= nd[d]; 396 } 397 CeedScalar *coords; 398 399 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 400 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 401 402 // The H1 basis uses Lobatto quadrature points as nodes. 403 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 404 for (CeedInt i = 0; i < p; i++) nodes[i] = 0.5 + 0.5 * nodes[i]; 405 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 406 CeedInt r_nodes = gs_nodes; 407 408 for (CeedInt d = 0; d < dim; d++) { 409 CeedInt d1d = r_nodes % nd[d]; 410 411 coords[gs_nodes + scalar_size * d] = ((d1d / (p - 1)) + nodes[d1d % (p - 1)]) / num_xyz[d]; 412 r_nodes /= nd[d]; 413 } 414 } 415 free(nodes); 416 CeedVectorRestoreArray(mesh_coords, &coords); 417 return 0; 418 } 419 420 #ifndef M_PI 421 #define M_PI 3.14159265358979323846 422 #endif 423 424 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 425 CeedScalar exact_surface_area = (dim == 1 ? 2 : dim == 2 ? 4 : 6); 426 CeedScalar *coords; 427 428 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 429 for (CeedInt i = 0; i < mesh_size; i++) { 430 // map [0,1] to [0,1] varying the mesh density 431 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 432 } 433 CeedVectorRestoreArray(mesh_coords, &coords); 434 return exact_surface_area; 435 } 436