1 // Copyright (c) 2017-2024, 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 // 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 ex1-volume [CEED_DIR=</path/to/libceed>] 21 // 22 // Sample runs: 23 // 24 // ./ex1-volume 25 // ./ex1-volume -ceed /cpu/self 26 // ./ex1-volume -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 mass operator to compute volume 38 39 #include "ex1-volume.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[dim]); 49 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], 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[dim], 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 ? 8 * 16 : 256 * 1024; 98 99 // Print the values of all options: 100 if (!test || help) { 101 // LCOV_EXCL_START 102 printf("Selected options: [command line option] : <current value>\n"); 103 printf(" Ceed specification [-c] : %s\n", ceed_spec); 104 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim); 105 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree); 106 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree); 107 printf(" Num. 1D quadrature pts [-q] : %" CeedInt_FMT "\n", num_qpts); 108 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size); 109 printf(" QFunction source [-g] : %s\n", gallery ? "gallery" : "header"); 110 if (help) { 111 printf("Test/quiet mode is %s\n", (test ? "ON" : "OFF (use -t to enable)")); 112 return 0; 113 } 114 printf("\n"); 115 // LCOV_EXCL_STOP 116 } 117 118 // Select appropriate backend and logical device based on the (-ceed) command line argument. 119 Ceed ceed; 120 121 CeedInit(ceed_spec, &ceed); 122 123 // Construct the mesh and solution bases. 124 CeedBasis mesh_basis, sol_basis; 125 126 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, num_qpts, CEED_GAUSS, &mesh_basis); 127 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, CEED_GAUSS, &sol_basis); 128 129 // Determine the mesh size based on the given approximate problem size. 130 CeedInt num_xyz[dim]; 131 132 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 133 if (!test) { 134 // LCOV_EXCL_START 135 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 136 if (dim > 1) printf(", ny = %" CeedInt_FMT, num_xyz[1]); 137 if (dim > 2) printf(", nz = %" CeedInt_FMT, num_xyz[2]); 138 printf("\n"); 139 // LCOV_EXCL_STOP 140 } 141 142 // Build CeedElemRestriction objects describing the mesh and solution discrete representations. 143 CeedInt mesh_size, sol_size; 144 CeedElemRestriction mesh_restriction, sol_restriction, q_data_restriction; 145 146 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restriction, NULL); 147 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restriction, &q_data_restriction); 148 if (!test) { 149 // LCOV_EXCL_START 150 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size / dim); 151 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size); 152 // LCOV_EXCL_STOP 153 } 154 155 // Create a CeedVector with the mesh coordinates. 156 CeedVector mesh_coords; 157 158 CeedVectorCreate(ceed, mesh_size, &mesh_coords); 159 SetCartesianMeshCoords(dim, num_xyz, mesh_degree, mesh_coords); 160 161 // Apply a transformation to the mesh. 162 CeedScalar exact_volume = TransformMeshCoords(dim, mesh_size, mesh_coords); 163 164 // Context data to be passed to the 'build_mass' QFunction. 165 CeedQFunctionContext build_ctx; 166 struct BuildContext build_ctx_data; 167 168 build_ctx_data.dim = build_ctx_data.space_dim = dim; 169 CeedQFunctionContextCreate(ceed, &build_ctx); 170 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(build_ctx_data), &build_ctx_data); 171 172 // Create the QFunction that builds the mass operator (i.e. computes its quadrature data) and set its context data. 173 CeedQFunction qf_build; 174 175 if (gallery) { 176 // This creates the QFunction via the gallery. 177 char name[13] = ""; 178 snprintf(name, sizeof name, "Mass%" CeedInt_FMT "DBuild", dim); 179 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 180 } else { 181 // This creates the QFunction directly. 182 CeedQFunctionCreateInterior(ceed, 1, build_mass, build_mass_loc, &qf_build); 183 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 184 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 185 CeedQFunctionAddOutput(qf_build, "qdata", 1, CEED_EVAL_NONE); 186 CeedQFunctionSetContext(qf_build, build_ctx); 187 } 188 189 // Create the operator that builds the quadrature data for the mass operator. 190 CeedOperator op_build; 191 192 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 193 CeedOperatorSetField(op_build, "dx", mesh_restriction, mesh_basis, CEED_VECTOR_ACTIVE); 194 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 195 CeedOperatorSetField(op_build, "qdata", q_data_restriction, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE); 196 197 // Compute the quadrature data for the mass operator. 198 CeedVector q_data; 199 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 200 CeedInt num_elem = 1; 201 202 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 203 CeedVectorCreate(ceed, num_elem * elem_qpts, &q_data); 204 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 205 206 // Create the QFunction that defines the action of the mass operator. 207 CeedQFunction qf_apply; 208 209 if (gallery) { 210 // This creates the QFunction via the gallery. 211 CeedQFunctionCreateInteriorByName(ceed, "MassApply", &qf_apply); 212 } else { 213 // This creates the QFunction directly. 214 CeedQFunctionCreateInterior(ceed, 1, apply_mass, apply_mass_loc, &qf_apply); 215 CeedQFunctionAddInput(qf_apply, "u", 1, CEED_EVAL_INTERP); 216 CeedQFunctionAddInput(qf_apply, "qdata", 1, CEED_EVAL_NONE); 217 CeedQFunctionAddOutput(qf_apply, "v", 1, CEED_EVAL_INTERP); 218 } 219 220 // Create the mass operator. 221 CeedOperator op_apply; 222 223 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 224 CeedOperatorSetField(op_apply, "u", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 225 CeedOperatorSetField(op_apply, "qdata", q_data_restriction, CEED_BASIS_NONE, q_data); 226 CeedOperatorSetField(op_apply, "v", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 227 228 // Create auxiliary solution-size vectors. 229 CeedVector u, v; 230 231 CeedVectorCreate(ceed, sol_size, &u); 232 CeedVectorCreate(ceed, sol_size, &v); 233 234 // Initialize 'u' with ones. 235 CeedVectorSetValue(u, 1.0); 236 237 // Compute the mesh volume using the mass operator: volume = 1^T \cdot M \cdot 1 238 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 239 240 // Benchmark runs 241 if (!test && benchmark) { 242 // LCOV_EXCL_START 243 printf(" Executing %d benchmarking runs...\n", benchmark); 244 // LCOV_EXCL_STOP 245 } 246 for (CeedInt i = 0; i < benchmark; i++) { 247 // LCOV_EXCL_START 248 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 249 // LCOV_EXCL_STOP 250 } 251 252 // Compute and print the sum of the entries of 'v' giving the mesh volume. 253 CeedScalar volume = 0.; 254 255 { 256 const CeedScalar *v_array; 257 258 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 259 for (CeedInt i = 0; i < sol_size; i++) volume += v_array[i]; 260 CeedVectorRestoreArrayRead(v, &v_array); 261 } 262 if (!test) { 263 // LCOV_EXCL_START 264 printf(" done.\n"); 265 printf("Exact mesh volume : % .14g\n", exact_volume); 266 printf("Computed mesh volume : % .14g\n", volume); 267 printf("Volume error : % .14g\n", volume - exact_volume); 268 // LCOV_EXCL_STOP 269 } else { 270 CeedScalar tol = (dim == 1 ? 200. * CEED_EPSILON : dim == 2 ? 1E-5 : 1E-5); 271 272 if (fabs(volume - exact_volume) > tol) printf("Volume error : % .1e\n", volume - exact_volume); 273 } 274 275 // Free dynamically allocated memory. 276 CeedVectorDestroy(&u); 277 CeedVectorDestroy(&v); 278 CeedVectorDestroy(&q_data); 279 CeedVectorDestroy(&mesh_coords); 280 CeedOperatorDestroy(&op_apply); 281 CeedQFunctionDestroy(&qf_apply); 282 CeedQFunctionContextDestroy(&build_ctx); 283 CeedOperatorDestroy(&op_build); 284 CeedQFunctionDestroy(&qf_build); 285 CeedElemRestrictionDestroy(&sol_restriction); 286 CeedElemRestrictionDestroy(&mesh_restriction); 287 CeedElemRestrictionDestroy(&q_data_restriction); 288 CeedBasisDestroy(&sol_basis); 289 CeedBasisDestroy(&mesh_basis); 290 CeedDestroy(&ceed); 291 return 0; 292 } 293 294 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]) { 295 // Use the approximate formula: 296 // prob_size ~ num_elem * degree^dim 297 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 298 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 299 300 while (num_elem > 1) { 301 num_elem /= 2; 302 s++; 303 } 304 CeedInt r = s % dim; 305 306 for (CeedInt d = 0; d < dim; d++) { 307 CeedInt sd = s / dim; 308 309 if (r > 0) { 310 sd++; 311 r--; 312 } 313 num_xyz[d] = 1 << sd; 314 } 315 return 0; 316 } 317 318 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 319 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction) { 320 CeedInt p = degree + 1; 321 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 322 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 323 CeedInt nd[3], num_elem = 1, scalar_size = 1; 324 325 for (CeedInt d = 0; d < dim; d++) { 326 num_elem *= num_xyz[d]; 327 nd[d] = num_xyz[d] * (p - 1) + 1; 328 scalar_size *= nd[d]; 329 } 330 *size = scalar_size * num_comp; 331 // elem: 0 1 n-1 332 // |---*-...-*---|---*-...-*---|- ... -|--...--| 333 // num_nodes: 0 1 p-1 p p+1 2*p n*p 334 CeedInt *elem_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 335 336 for (CeedInt e = 0; e < num_elem; e++) { 337 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 338 339 for (CeedInt d = 0; d < dim; d++) { 340 e_xyz[d] = re % num_xyz[d]; 341 re /= num_xyz[d]; 342 } 343 CeedInt *local_elem_nodes = elem_nodes + e * num_nodes; 344 345 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 346 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 347 348 for (CeedInt d = 0; d < dim; d++) { 349 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 350 g_nodes_stride *= nd[d]; 351 r_nodes /= p; 352 } 353 local_elem_nodes[l_nodes] = g_nodes; 354 } 355 } 356 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, elem_nodes, 357 restriction); 358 if (q_data_restriction) { 359 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, q_data_restriction); 360 } 361 free(elem_nodes); 362 return 0; 363 } 364 365 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords) { 366 CeedInt p = mesh_degree + 1; 367 CeedInt nd[3], scalar_size = 1; 368 369 for (CeedInt d = 0; d < dim; d++) { 370 nd[d] = num_xyz[d] * (p - 1) + 1; 371 scalar_size *= nd[d]; 372 } 373 CeedScalar *coords; 374 375 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 376 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 377 378 // The H1 basis uses Lobatto quadrature points as nodes. 379 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 380 for (CeedInt i = 0; i < p; i++) nodes[i] = 0.5 + 0.5 * nodes[i]; 381 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 382 CeedInt r_nodes = gs_nodes; 383 384 for (CeedInt d = 0; d < dim; d++) { 385 CeedInt d_1d = r_nodes % nd[d]; 386 387 coords[gs_nodes + scalar_size * d] = ((d_1d / (p - 1)) + nodes[d_1d % (p - 1)]) / num_xyz[d]; 388 r_nodes /= 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(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 402 CeedScalar exact_volume; 403 CeedScalar *coords; 404 405 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 406 if (dim == 1) { 407 for (CeedInt i = 0; i < mesh_size; i++) { 408 // map [0,1] to [0,1] varying the mesh density 409 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 410 } 411 exact_volume = 1.; 412 } else { 413 CeedInt num_nodes = mesh_size / dim; 414 415 for (CeedInt i = 0; i < num_nodes; i++) { 416 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar 417 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi 418 CeedScalar u = coords[i], v = coords[i + num_nodes]; 419 420 u = 1. + u; 421 v = M_PI_2 * v; 422 coords[i] = u * cos(v); 423 coords[i + num_nodes] = u * sin(v); 424 } 425 exact_volume = 3. / 4. * M_PI; 426 } 427 CeedVectorRestoreArray(mesh_coords, &coords); 428 return exact_volume; 429 } 430