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 1 9 // 10 // This example illustrates a simple usage of libCEED to compute the volume of a 3D body using matrix-free application of a mass operator. 11 // This example also uses a diffusion operator, which provides zero contribution to the computed volume but demonstrates libCEED's ability 12 // to handle multiple basis evaluation modes for the same input and output vectors. 13 // Arbitrary mesh and solution degrees in 1D, 2D and 3D are supported from the same code. 14 // 15 // The example has no dependencies, and is designed to be self-contained. 16 // For additional examples that use external discretization libraries (MFEM, PETSc, etc.) see the subdirectories in libceed/examples. 17 // 18 // All libCEED objects use a Ceed device object constructed based on a command line argument (-ceed). 19 // 20 // Build with: 21 // 22 // make ex3-volume [CEED_DIR=</path/to/libceed>] 23 // 24 // Sample runs: 25 // 26 // ./ex3-volume 27 // ./ex3-volume -ceed /cpu/self 28 // ./ex3-volume -ceed /gpu/cuda 29 // 30 // Test in 1D-3D 31 //TESTARGS(name="1D User QFunction") -ceed {ceed_resource} -d 1 -t 32 //TESTARGS(name="2D User QFunction") -ceed {ceed_resource} -d 2 -t 33 //TESTARGS(name="3D User QFunction") -ceed {ceed_resource} -d 3 -t 34 35 /// @file 36 /// libCEED example using mass operator to compute volume 37 38 #include "ex3-volume.h" 39 40 #include <ceed.h> 41 #include <math.h> 42 #include <stdio.h> 43 #include <stdlib.h> 44 #include <string.h> 45 46 // Auxiliary functions 47 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]); 48 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 49 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction); 50 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords); 51 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords); 52 53 // Main example 54 int main(int argc, const char *argv[]) { 55 const char *ceed_spec = "/cpu/self"; 56 CeedInt dim = 3; // dimension of the mesh 57 CeedInt num_comp_x = 3; // number of x components 58 CeedInt mesh_degree = 4; // polynomial degree for the mesh 59 CeedInt sol_degree = 4; // polynomial degree for the solution 60 CeedInt num_qpts = sol_degree + 2; // number of 1D quadrature points 61 CeedInt prob_size = -1; // approximate problem size 62 CeedInt help = 0, test = 0, benchmark = 0; 63 64 // Process command line arguments. 65 for (int ia = 1; ia < argc; ia++) { 66 // LCOV_EXCL_START 67 int next_arg = ((ia + 1) < argc), parse_error = 0; 68 if (!strcmp(argv[ia], "-h")) { 69 help = 1; 70 } else if (!strcmp(argv[ia], "-c") || !strcmp(argv[ia], "-ceed")) { 71 parse_error = next_arg ? ceed_spec = argv[++ia], 0 : 1; 72 } else if (!strcmp(argv[ia], "-d")) { 73 parse_error = next_arg ? dim = atoi(argv[++ia]), 0 : 1; 74 num_comp_x = dim; 75 } else if (!strcmp(argv[ia], "-m")) { 76 parse_error = next_arg ? mesh_degree = atoi(argv[++ia]), 0 : 1; 77 } else if (!strcmp(argv[ia], "-p")) { 78 parse_error = next_arg ? sol_degree = atoi(argv[++ia]), 0 : 1; 79 } else if (!strcmp(argv[ia], "-q")) { 80 parse_error = next_arg ? num_qpts = atoi(argv[++ia]), 0 : 1; 81 } else if (!strcmp(argv[ia], "-s")) { 82 parse_error = next_arg ? prob_size = atoi(argv[++ia]), 0 : 1; 83 } else if (!strcmp(argv[ia], "-b")) { 84 parse_error = next_arg ? benchmark = atoi(argv[++ia]), 0 : 1; 85 } else if (!strcmp(argv[ia], "-t")) { 86 test = 1; 87 } 88 if (parse_error) { 89 printf("Error parsing command line options.\n"); 90 return 1; 91 } 92 // LCOV_EXCL_STOP 93 } 94 if (prob_size < 0) prob_size = test ? 8 * 16 : 256 * 1024; 95 96 // Print the values of all options: 97 if (!test || help) { 98 // LCOV_EXCL_START 99 printf("Selected options: [command line option] : <current value>\n"); 100 printf(" Ceed specification [-c] : %s\n", ceed_spec); 101 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim); 102 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree); 103 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree); 104 printf(" Num. 1D quadrature pts [-q] : %" CeedInt_FMT "\n", num_qpts); 105 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size); 106 printf(" QFunction source : header"); 107 if (help) { 108 printf("Test/quiet mode is %s\n", (test ? "ON" : "OFF (use -t to enable)")); 109 return 0; 110 } 111 printf("\n"); 112 // LCOV_EXCL_STOP 113 } 114 115 // Select appropriate backend and logical device based on the (-ceed) command line argument. 116 Ceed ceed; 117 118 CeedInit(ceed_spec, &ceed); 119 120 // Construct the mesh and solution bases. 121 CeedBasis mesh_basis, sol_basis; 122 123 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, num_qpts, CEED_GAUSS, &mesh_basis); 124 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, CEED_GAUSS, &sol_basis); 125 126 // Determine the mesh size based on the given approximate problem size. 127 CeedInt num_xyz[dim]; 128 129 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 130 if (!test) { 131 // LCOV_EXCL_START 132 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 133 if (dim > 1) printf(", ny = %" CeedInt_FMT, num_xyz[1]); 134 if (dim > 2) printf(", nz = %" CeedInt_FMT, num_xyz[2]); 135 printf("\n"); 136 // LCOV_EXCL_STOP 137 } 138 139 // Build CeedElemRestriction objects describing the mesh and solution discrete representations. 140 CeedInt mesh_size, sol_size; 141 CeedElemRestriction mesh_restriction, sol_restriction, q_data_restriction; 142 143 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restriction, NULL); 144 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1 + dim * (dim + 1) / 2, &sol_size, num_qpts, NULL, &q_data_restriction); 145 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restriction, NULL); 146 if (!test) { 147 // LCOV_EXCL_START 148 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size / dim); 149 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size); 150 // LCOV_EXCL_STOP 151 } 152 153 // Create a CeedVector with the mesh coordinates. 154 CeedVector mesh_coords; 155 156 CeedVectorCreate(ceed, mesh_size, &mesh_coords); 157 SetCartesianMeshCoords(dim, num_xyz, mesh_degree, mesh_coords); 158 159 // Apply a transformation to the mesh. 160 CeedScalar exact_volume = TransformMeshCoords(dim, mesh_size, mesh_coords); 161 162 // Context data to be passed to the 'build_mass_diff' QFunction. 163 CeedQFunctionContext build_ctx; 164 struct BuildContext build_ctx_data; 165 166 build_ctx_data.dim = build_ctx_data.space_dim = dim; 167 CeedQFunctionContextCreate(ceed, &build_ctx); 168 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(build_ctx_data), &build_ctx_data); 169 170 // Create the QFunction that builds the mass + diffusion operator (i.e. computes its quadrature data) and set its context data. 171 CeedQFunction qf_build; 172 173 CeedQFunctionCreateInterior(ceed, 1, build_mass_diff, build_mass_diff_loc, &qf_build); 174 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 175 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 176 CeedQFunctionAddOutput(qf_build, "qdata", 1 + dim * (dim + 1) / 2, CEED_EVAL_NONE); 177 CeedQFunctionSetContext(qf_build, build_ctx); 178 179 // Create the operator that builds the quadrature data for the mass + diffusion operator. 180 CeedOperator op_build; 181 182 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 183 CeedOperatorSetField(op_build, "dx", mesh_restriction, mesh_basis, CEED_VECTOR_ACTIVE); 184 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 185 CeedOperatorSetField(op_build, "qdata", q_data_restriction, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE); 186 187 // Compute the quadrature data for the mass + diffusion operator. 188 CeedVector q_data; 189 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 190 CeedInt num_elem = 1; 191 192 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 193 CeedVectorCreate(ceed, num_elem * elem_qpts * (1 + dim * (dim + 1) / 2), &q_data); 194 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 195 196 // Create the QFunction that defines the action of the mass + diffusion operator. 197 CeedQFunction qf_apply; 198 199 CeedQFunctionCreateInterior(ceed, 1, apply_mass_diff, apply_mass_diff_loc, &qf_apply); 200 CeedQFunctionAddInput(qf_apply, "u", 1, CEED_EVAL_INTERP); 201 CeedQFunctionAddInput(qf_apply, "du", dim, CEED_EVAL_GRAD); 202 CeedQFunctionAddInput(qf_apply, "qdata", 1 + dim * (dim + 1) / 2, CEED_EVAL_NONE); 203 CeedQFunctionAddOutput(qf_apply, "v", 1, CEED_EVAL_INTERP); 204 CeedQFunctionAddOutput(qf_apply, "dv", dim, CEED_EVAL_GRAD); 205 CeedQFunctionSetContext(qf_apply, build_ctx); 206 207 // Create the mass + diffusion operator. 208 CeedOperator op_apply; 209 210 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 211 CeedOperatorSetField(op_apply, "u", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 212 CeedOperatorSetField(op_apply, "du", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 213 CeedOperatorSetField(op_apply, "qdata", q_data_restriction, CEED_BASIS_NONE, q_data); 214 CeedOperatorSetField(op_apply, "v", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 215 CeedOperatorSetField(op_apply, "dv", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 216 217 // Create auxiliary solution-size vectors. 218 CeedVector u, v; 219 220 CeedVectorCreate(ceed, sol_size, &u); 221 CeedVectorCreate(ceed, sol_size, &v); 222 223 // Initialize 'u' with ones. 224 CeedVectorSetValue(u, 1.0); 225 226 // Compute the mesh volume using the mass + diffusion operator: volume = 1^T \cdot M \cdot 1 227 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 228 229 // Benchmark runs 230 if (!test && benchmark) { 231 // LCOV_EXCL_START 232 printf(" Executing %d benchmarking runs...\n", benchmark); 233 // LCOV_EXCL_STOP 234 } 235 for (CeedInt i = 0; i < benchmark; i++) { 236 // LCOV_EXCL_START 237 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 238 // LCOV_EXCL_STOP 239 } 240 241 // Compute and print the sum of the entries of 'v' giving the mesh volume. 242 CeedScalar volume = 0.; 243 244 { 245 const CeedScalar *v_array; 246 247 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 248 for (CeedInt i = 0; i < sol_size; i++) volume += v_array[i]; 249 CeedVectorRestoreArrayRead(v, &v_array); 250 } 251 if (!test) { 252 // LCOV_EXCL_START 253 printf(" done.\n"); 254 printf("Exact mesh volume : % .14g\n", exact_volume); 255 printf("Computed mesh volume : % .14g\n", volume); 256 printf("Volume error : % .14g\n", volume - exact_volume); 257 // LCOV_EXCL_STOP 258 } else { 259 CeedScalar tol = (dim == 1 ? 200. * CEED_EPSILON : dim == 2 ? 1E-5 : 1E-5); 260 261 if (fabs(volume - exact_volume) > tol) printf("Volume error : % .1e\n", volume - exact_volume); 262 } 263 264 // Free dynamically allocated memory. 265 CeedVectorDestroy(&u); 266 CeedVectorDestroy(&v); 267 CeedVectorDestroy(&q_data); 268 CeedVectorDestroy(&mesh_coords); 269 CeedOperatorDestroy(&op_apply); 270 CeedQFunctionDestroy(&qf_apply); 271 CeedQFunctionContextDestroy(&build_ctx); 272 CeedOperatorDestroy(&op_build); 273 CeedQFunctionDestroy(&qf_build); 274 CeedElemRestrictionDestroy(&sol_restriction); 275 CeedElemRestrictionDestroy(&mesh_restriction); 276 CeedElemRestrictionDestroy(&q_data_restriction); 277 CeedBasisDestroy(&sol_basis); 278 CeedBasisDestroy(&mesh_basis); 279 CeedDestroy(&ceed); 280 return 0; 281 } 282 283 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]) { 284 // Use the approximate formula: 285 // prob_size ~ num_elem * degree^dim 286 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 287 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 288 289 while (num_elem > 1) { 290 num_elem /= 2; 291 s++; 292 } 293 CeedInt r = s % dim; 294 295 for (CeedInt d = 0; d < dim; d++) { 296 CeedInt sd = s / dim; 297 298 if (r > 0) { 299 sd++; 300 r--; 301 } 302 num_xyz[d] = 1 << sd; 303 } 304 return 0; 305 } 306 307 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 308 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction) { 309 CeedInt p = degree + 1; 310 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 311 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 312 CeedInt nd[3], num_elem = 1, scalar_size = 1; 313 314 for (CeedInt d = 0; d < dim; d++) { 315 num_elem *= num_xyz[d]; 316 nd[d] = num_xyz[d] * (p - 1) + 1; 317 scalar_size *= nd[d]; 318 } 319 *size = scalar_size * num_comp; 320 // elem: 0 1 n-1 321 // |---*-...-*---|---*-...-*---|- ... -|--...--| 322 // num_nodes: 0 1 p-1 p p+1 2*p n*p 323 CeedInt *elem_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 324 325 for (CeedInt e = 0; e < num_elem; e++) { 326 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 327 328 for (CeedInt d = 0; d < dim; d++) { 329 e_xyz[d] = re % num_xyz[d]; 330 re /= num_xyz[d]; 331 } 332 CeedInt *local_elem_nodes = elem_nodes + e * num_nodes; 333 334 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 335 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 336 337 for (CeedInt d = 0; d < dim; d++) { 338 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 339 g_nodes_stride *= nd[d]; 340 r_nodes /= p; 341 } 342 local_elem_nodes[l_nodes] = g_nodes; 343 } 344 } 345 if (restriction) { 346 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, elem_nodes, 347 restriction); 348 } 349 if (q_data_restriction) { 350 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, q_data_restriction); 351 } 352 free(elem_nodes); 353 return 0; 354 } 355 356 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords) { 357 CeedInt p = mesh_degree + 1; 358 CeedInt nd[3], scalar_size = 1; 359 360 for (CeedInt d = 0; d < dim; d++) { 361 nd[d] = num_xyz[d] * (p - 1) + 1; 362 scalar_size *= nd[d]; 363 } 364 CeedScalar *coords; 365 366 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 367 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 368 369 // The H1 basis uses Lobatto quadrature points as nodes. 370 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 371 for (CeedInt i = 0; i < p; i++) nodes[i] = 0.5 + 0.5 * nodes[i]; 372 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 373 CeedInt r_nodes = gs_nodes; 374 375 for (CeedInt d = 0; d < dim; d++) { 376 CeedInt d_1d = r_nodes % nd[d]; 377 coords[gs_nodes + scalar_size * d] = ((d_1d / (p - 1)) + nodes[d_1d % (p - 1)]) / num_xyz[d]; 378 r_nodes /= nd[d]; 379 } 380 } 381 free(nodes); 382 CeedVectorRestoreArray(mesh_coords, &coords); 383 return 0; 384 } 385 386 #ifndef M_PI 387 #define M_PI 3.14159265358979323846 388 #define M_PI_2 1.57079632679489661923 389 #endif 390 391 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 392 CeedScalar exact_volume; 393 CeedScalar *coords; 394 395 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 396 if (dim == 1) { 397 for (CeedInt i = 0; i < mesh_size; i++) { 398 // map [0,1] to [0,1] varying the mesh density 399 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 400 } 401 exact_volume = 1.; 402 } else { 403 CeedInt num_nodes = mesh_size / dim; 404 for (CeedInt i = 0; i < num_nodes; i++) { 405 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar 406 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi 407 CeedScalar u = coords[i], v = coords[i + num_nodes]; 408 409 u = 1. + u; 410 v = M_PI_2 * v; 411 coords[i] = u * cos(v); 412 coords[i + num_nodes] = u * sin(v); 413 } 414 exact_volume = 3. / 4. * M_PI; 415 } 416 CeedVectorRestoreArray(mesh_coords, &coords); 417 return exact_volume; 418 } 419