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 1 9 // 10 // This example illustrates a simple usage of libCEED to compute the volume of a 11 // 3D body using matrix-free application of a mass operator. Arbitrary mesh and 12 // solution degrees in 1D, 2D and 3D are supported from the same code. 13 // 14 // The example has no dependencies, and is designed to be self-contained. For 15 // additional examples that use external discretization libraries (MFEM, PETSc, 16 // etc.) see the subdirectories in libceed/examples. 17 // 18 // All libCEED objects use a Ceed device object constructed based on a command 19 // line argument (-ceed). 20 // 21 // Build with: 22 // 23 // make ex1-volume [CEED_DIR=</path/to/libceed>] 24 // 25 // Sample runs: 26 // 27 // ./ex1-volume 28 // ./ex1-volume -ceed /cpu/self 29 // ./ex1-volume -ceed /gpu/cuda 30 // 31 // Test in 1D-3D 32 //TESTARGS(name="1D_User_QFunction") -ceed {ceed_resource} -d 1 -t 33 //TESTARGS(name="2D_User_QFunction") -ceed {ceed_resource} -d 2 -t 34 //TESTARGS(name="3D_User_QFunction") -ceed {ceed_resource} -d 3 -t 35 //TESTARGS(name="1D_Gallery_QFunction") -ceed {ceed_resource} -d 1 -t -g 36 //TESTARGS(name="2D_Gallery_QFunction") -ceed {ceed_resource} -d 2 -t -g 37 //TESTARGS(name="3D_Gallery_QFunction") -ceed {ceed_resource} -d 3 -t -g 38 39 /// @file 40 /// libCEED example using mass operator to compute volume 41 42 #include <ceed.h> 43 #include <math.h> 44 #include <stdlib.h> 45 #include <string.h> 46 #include "ex1-volume.h" 47 48 // Auxiliary functions. 49 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, 50 CeedInt num_xyz[dim]); 51 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], 52 CeedInt degree, CeedInt num_comp, CeedInt *size, 53 CeedInt num_qpts, CeedElemRestriction *restr, 54 CeedElemRestriction *restr_i); 55 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], 56 CeedInt mesh_degree, CeedVector mesh_coords); 57 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, 58 CeedVector mesh_coords); 59 60 int main(int argc, const char *argv[]) { 61 const char *ceed_spec = "/cpu/self"; 62 CeedInt dim = 3; // dimension of the mesh 63 CeedInt num_comp_x = 3; // number of x components 64 CeedInt mesh_degree = 4; // polynomial degree for the mesh 65 CeedInt sol_degree = 4; // polynomial degree for the solution 66 CeedInt num_qpts = sol_degree + 2; // number of 1D quadrature points 67 CeedInt prob_size = -1; // approximate problem size 68 CeedInt help = 0, test = 0, gallery = 0; 69 70 // Process command line arguments. 71 for (int ia = 1; ia < argc; ia++) { 72 // LCOV_EXCL_START 73 int next_arg = ((ia+1) < argc), parse_error = 0; 74 if (!strcmp(argv[ia],"-h")) { 75 help = 1; 76 } else if (!strcmp(argv[ia],"-c") || !strcmp(argv[ia],"-ceed")) { 77 parse_error = next_arg ? ceed_spec = argv[++ia], 0 : 1; 78 } else if (!strcmp(argv[ia],"-d")) { 79 parse_error = next_arg ? dim = atoi(argv[++ia]), 0 : 1; 80 num_comp_x = dim; 81 } else if (!strcmp(argv[ia],"-m")) { 82 parse_error = next_arg ? mesh_degree = atoi(argv[++ia]), 0 : 1; 83 } else if (!strcmp(argv[ia],"-p")) { 84 parse_error = next_arg ? sol_degree= atoi(argv[++ia]), 0 : 1; 85 } else if (!strcmp(argv[ia],"-q")) { 86 parse_error = next_arg ? num_qpts = atoi(argv[++ia]), 0 : 1; 87 } else if (!strcmp(argv[ia],"-s")) { 88 parse_error = next_arg ? prob_size = atoi(argv[++ia]), 0 : 1; 89 } else if (!strcmp(argv[ia],"-t")) { 90 test = 1; 91 } else if (!strcmp(argv[ia],"-g")) { 92 gallery = 1; 93 } 94 if (parse_error) { 95 printf("Error parsing command line options.\n"); 96 return 1; 97 } 98 // LCOV_EXCL_STOP 99 } 100 if (prob_size < 0) prob_size = test ? 8*16 : 256*1024; 101 102 // Print the values of all options: 103 if (!test || help) { 104 // LCOV_EXCL_START 105 printf("Selected options: [command line option] : <current value>\n"); 106 printf(" Ceed specification [-c] : %s\n", ceed_spec); 107 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim); 108 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree); 109 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree); 110 printf(" Num. 1D quadr. pts [-q] : %" CeedInt_FMT "\n", num_qpts); 111 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size); 112 printf(" QFunction source [-g] : %s\n", gallery?"gallery":"header"); 113 if (help) { 114 printf("Test/quiet mode is %s\n", (test?"ON":"OFF (use -t to enable)")); 115 return 0; 116 } 117 printf("\n"); 118 // LCOV_EXCL_STOP 119 } 120 121 // Select appropriate backend and logical device based on the <ceed-spec> 122 // command line argument. 123 Ceed ceed; 124 CeedInit(ceed_spec, &ceed); 125 126 // Construct the mesh and solution bases. 127 CeedBasis mesh_basis, sol_basis; 128 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, 129 num_qpts, CEED_GAUSS, &mesh_basis); 130 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, 131 CEED_GAUSS, &sol_basis); 132 133 // Determine the mesh size based on the given approximate problem size. 134 CeedInt num_xyz[dim]; 135 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 136 if (!test) { 137 // LCOV_EXCL_START 138 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 139 if (dim > 1) { printf(", ny = %" CeedInt_FMT, num_xyz[1]); } 140 if (dim > 2) { printf(", nz = %" CeedInt_FMT, num_xyz[2]); } 141 printf("\n"); 142 // LCOV_EXCL_STOP 143 } 144 145 // Build CeedElemRestriction objects describing the mesh and solution discrete 146 // representations. 147 CeedInt mesh_size, sol_size; 148 CeedElemRestriction mesh_restr, sol_restr, sol_restr_i; 149 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, 150 &mesh_size, num_qpts, &mesh_restr, NULL); 151 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, 152 num_qpts, &sol_restr, &sol_restr_i); 153 if (!test) { 154 // LCOV_EXCL_START 155 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size/dim); 156 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size); 157 // LCOV_EXCL_STOP 158 } 159 160 // Create a CeedVector with the mesh coordinates. 161 CeedVector mesh_coords; 162 CeedVectorCreate(ceed, mesh_size, &mesh_coords); 163 SetCartesianMeshCoords(dim, num_xyz, mesh_degree, mesh_coords); 164 165 // Apply a transformation to the mesh. 166 CeedScalar exact_vol = TransformMeshCoords(dim, mesh_size, mesh_coords); 167 168 // Context data to be passed to the 'f_build_mass' QFunction. 169 CeedQFunctionContext build_ctx; 170 struct BuildContext build_ctx_data; 171 build_ctx_data.dim = build_ctx_data.space_dim = dim; 172 CeedQFunctionContextCreate(ceed, &build_ctx); 173 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, 174 sizeof(build_ctx_data), &build_ctx_data); 175 176 // Create the QFunction that builds the mass operator (i.e. computes its 177 // quadrature data) and set its context data. 178 CeedQFunction qf_build; 179 switch (gallery) { 180 case 0: 181 // This creates the QFunction directly. 182 CeedQFunctionCreateInterior(ceed, 1, f_build_mass, 183 f_build_mass_loc, &qf_build); 184 CeedQFunctionAddInput(qf_build, "dx", num_comp_x*dim, CEED_EVAL_GRAD); 185 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 186 CeedQFunctionAddOutput(qf_build, "qdata", 1, CEED_EVAL_NONE); 187 CeedQFunctionSetContext(qf_build, build_ctx); 188 break; 189 case 1: { 190 // This creates the QFunction via the gallery. 191 char name[13] = ""; 192 snprintf(name, sizeof name, "Mass%" CeedInt_FMT "DBuild", dim); 193 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 194 break; 195 } 196 } 197 198 // Create the operator that builds the quadrature data for the mass operator. 199 CeedOperator op_build; 200 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, 201 CEED_QFUNCTION_NONE, &op_build); 202 CeedOperatorSetField(op_build, "dx", mesh_restr, mesh_basis, 203 CEED_VECTOR_ACTIVE); 204 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, 205 mesh_basis, CEED_VECTOR_NONE); 206 CeedOperatorSetField(op_build, "qdata", sol_restr_i, CEED_BASIS_COLLOCATED, 207 CEED_VECTOR_ACTIVE); 208 209 // Compute the quadrature data for the mass operator. 210 CeedVector q_data; 211 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 212 CeedInt num_elem = 1; 213 for (CeedInt d = 0; d < dim; d++) 214 num_elem *= num_xyz[d]; 215 CeedVectorCreate(ceed, num_elem*elem_qpts, &q_data); 216 CeedOperatorApply(op_build, mesh_coords, q_data, 217 CEED_REQUEST_IMMEDIATE); 218 219 // Create the QFunction that defines the action of the mass operator. 220 CeedQFunction qf_apply; 221 switch (gallery) { 222 case 0: 223 // This creates the QFunction directly. 224 CeedQFunctionCreateInterior(ceed, 1, f_apply_mass, 225 f_apply_mass_loc, &qf_apply); 226 CeedQFunctionAddInput(qf_apply, "u", 1, CEED_EVAL_INTERP); 227 CeedQFunctionAddInput(qf_apply, "qdata", 1, CEED_EVAL_NONE); 228 CeedQFunctionAddOutput(qf_apply, "v", 1, CEED_EVAL_INTERP); 229 break; 230 case 1: 231 // This creates the QFunction via the gallery. 232 CeedQFunctionCreateInteriorByName(ceed, "MassApply", &qf_apply); 233 break; 234 } 235 236 // Create the mass operator. 237 CeedOperator op_apply; 238 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, 239 CEED_QFUNCTION_NONE, &op_apply); 240 CeedOperatorSetField(op_apply, "u", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 241 CeedOperatorSetField(op_apply, "qdata", sol_restr_i, CEED_BASIS_COLLOCATED, 242 q_data); 243 CeedOperatorSetField(op_apply, "v", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 244 245 // Create auxiliary solution-size vectors. 246 CeedVector u, v; 247 CeedVectorCreate(ceed, sol_size, &u); 248 CeedVectorCreate(ceed, sol_size, &v); 249 250 // Initialize 'u' and 'v' with ones. 251 CeedVectorSetValue(u, 1.0); 252 253 // Compute the mesh volume using the mass operator: vol = 1^T \cdot M \cdot 1 254 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 255 256 // Compute and print the sum of the entries of 'v' giving the mesh volume. 257 const CeedScalar *v_array; 258 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 259 CeedScalar vol = 0.; 260 for (CeedInt i = 0; i < sol_size; i++) { 261 vol += v_array[i]; 262 } 263 CeedVectorRestoreArrayRead(v, &v_array); 264 if (!test) { 265 // LCOV_EXCL_START 266 printf(" done.\n"); 267 printf("Exact mesh volume : % .14g\n", exact_vol); 268 printf("Computed mesh volume : % .14g\n", vol); 269 printf("Volume error : % .14g\n", vol-exact_vol); 270 // LCOV_EXCL_STOP 271 } else { 272 CeedScalar tol = (dim==1 ? 100.*CEED_EPSILON : dim==2 ? 1E-5 : 1E-5); 273 if (fabs(vol-exact_vol)>tol) 274 // LCOV_EXCL_START 275 printf("Volume error : % .1e\n", vol-exact_vol); 276 // LCOV_EXCL_STOP 277 } 278 279 // Free dynamically allocated memory. 280 CeedVectorDestroy(&u); 281 CeedVectorDestroy(&v); 282 CeedVectorDestroy(&q_data); 283 CeedVectorDestroy(&mesh_coords); 284 CeedOperatorDestroy(&op_apply); 285 CeedQFunctionDestroy(&qf_apply); 286 CeedQFunctionContextDestroy(&build_ctx); 287 CeedOperatorDestroy(&op_build); 288 CeedQFunctionDestroy(&qf_build); 289 CeedElemRestrictionDestroy(&sol_restr); 290 CeedElemRestrictionDestroy(&mesh_restr); 291 CeedElemRestrictionDestroy(&sol_restr_i); 292 CeedBasisDestroy(&sol_basis); 293 CeedBasisDestroy(&mesh_basis); 294 CeedDestroy(&ceed); 295 return 0; 296 } 297 298 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, 299 CeedInt num_xyz[dim]) { 300 // Use the approximate formula: 301 // prob_size ~ num_elem * degree^dim 302 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 303 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 304 while (num_elem > 1) { 305 num_elem /= 2; 306 s++; 307 } 308 CeedInt r = s%dim; 309 for (CeedInt d = 0; d < dim; d++) { 310 CeedInt sd = s/dim; 311 if (r > 0) { sd++; r--; } 312 num_xyz[d] = 1 << sd; 313 } 314 return 0; 315 } 316 317 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], 318 CeedInt degree, CeedInt num_comp, CeedInt *size, 319 CeedInt num_qpts, CeedElemRestriction *restr, 320 CeedElemRestriction *restr_i) { 321 CeedInt p = degree + 1; 322 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 323 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 324 CeedInt nd[3], num_elem = 1, scalar_size = 1; 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 for (CeedInt e = 0; e < num_elem; e++) { 336 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 337 for (CeedInt d = 0; d < dim; d++) { e_xyz[d] = re % num_xyz[d]; re /= num_xyz[d]; } 338 CeedInt *loc_el_nodes = elem_nodes + e*num_nodes; 339 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 340 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 341 for (CeedInt d = 0; d < dim; d++) { 342 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 343 g_nodes_stride *= nd[d]; 344 r_nodes /= p; 345 } 346 loc_el_nodes[l_nodes] = g_nodes; 347 } 348 } 349 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, 350 num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, 351 elem_nodes, restr); 352 if (restr_i) 353 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, 354 num_comp, num_comp * elem_qpts * num_elem, 355 CEED_STRIDES_BACKEND, restr_i); 356 free(elem_nodes); 357 return 0; 358 } 359 360 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], 361 CeedInt mesh_degree, CeedVector mesh_coords) { 362 CeedInt p = mesh_degree + 1; 363 CeedInt nd[3], num_elem = 1, scalar_size = 1; 364 for (CeedInt d = 0; d < dim; d++) { 365 num_elem *= num_xyz[d]; 366 nd[d] = num_xyz[d] * (p - 1) + 1; 367 scalar_size *= nd[d]; 368 } 369 CeedScalar *coords; 370 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 371 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 372 // The H1 basis uses Lobatto quadrature points as nodes. 373 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 374 for (CeedInt i = 0; i < p; i++) { nodes[i] = 0.5 + 0.5 * nodes[i]; } 375 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 376 CeedInt r_nodes = gs_nodes; 377 for (CeedInt d = 0; d < dim; d++) { 378 CeedInt d_1d = r_nodes % nd[d]; 379 coords[gs_nodes + scalar_size * d] = ((d_1d / (p - 1)) + nodes[d_1d % 380 (p - 1)]) / num_xyz[d]; 381 r_nodes /= nd[d]; 382 } 383 } 384 free(nodes); 385 CeedVectorRestoreArray(mesh_coords, &coords); 386 return 0; 387 } 388 389 #ifndef M_PI 390 #define M_PI 3.14159265358979323846 391 #define M_PI_2 1.57079632679489661923 392 #endif 393 394 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, 395 CeedVector mesh_coords) { 396 CeedScalar exact_volume; 397 CeedScalar *coords; 398 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 399 if (dim == 1) { 400 for (CeedInt i = 0; i < mesh_size; i++) { 401 // map [0,1] to [0,1] varying the mesh density 402 coords[i] = 0.5 + 1./sqrt(3.) * sin((2./3.) * M_PI*(coords[i] - 0.5)); 403 } 404 exact_volume = 1.; 405 } else { 406 CeedInt num_nodes = mesh_size/dim; 407 for (CeedInt i = 0; i < num_nodes; i++) { 408 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar 409 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi 410 CeedScalar u = coords[i], v = coords[i+num_nodes]; 411 u = 1. + u; 412 v = M_PI_2 * v; 413 coords[i] = u * cos(v); 414 coords[i+num_nodes] = u * sin(v); 415 } 416 exact_volume = 3./4. * M_PI; 417 } 418 CeedVectorRestoreArray(mesh_coords, &coords); 419 return exact_volume; 420 } 421