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 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 <stdlib.h> 44 #include <string.h> 45 46 // Auxiliary functions 47 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[3]); 48 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 49 CeedElemRestriction *restr, CeedElemRestriction *restr_i); 50 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], 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, gallery = 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], "-t")) { 84 test = 1; 85 } else if (!strcmp(argv[ia], "-g")) { 86 gallery = 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 ? 16 * 16 * dim * dim : 256 * 1024; 95 96 // Set mesh_degree = sol_degree. 97 mesh_degree = fmax(mesh_degree, sol_degree); 98 sol_degree = mesh_degree; 99 100 // Print the values of all options: 101 if (!test || help) { 102 // LCOV_EXCL_START 103 printf("Selected options: [command line option] : <current value>\n"); 104 printf(" Ceed specification [-c] : %s\n", ceed_spec); 105 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim); 106 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree); 107 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree); 108 printf(" Num. 1D quadr. pts [-q] : %" CeedInt_FMT "\n", num_qpts); 109 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size); 110 printf(" QFunction source [-g] : %s\n", gallery ? "gallery" : "header"); 111 if (help) { 112 printf("Test/quiet mode is %s\n", (test ? "ON" : "OFF (use -t to enable)")); 113 return 0; 114 } 115 printf("\n"); 116 // LCOV_EXCL_STOP 117 } 118 119 // Select appropriate backend and logical device based on the (-ceed) command line argument. 120 Ceed ceed; 121 CeedInit(ceed_spec, &ceed); 122 123 // Construct the mesh and solution bases. 124 CeedBasis mesh_basis, sol_basis; 125 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, num_qpts, CEED_GAUSS, &mesh_basis); 126 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, CEED_GAUSS, &sol_basis); 127 128 // Determine the mesh size based on the given approximate problem size. 129 CeedInt num_xyz[3]; 130 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 131 132 if (!test) { 133 // LCOV_EXCL_START 134 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 135 if (dim > 1) printf(", ny = %" CeedInt_FMT, num_xyz[1]); 136 if (dim > 2) printf(", nz = %" CeedInt_FMT, num_xyz[2]); 137 printf("\n"); 138 // LCOV_EXCL_STOP 139 } 140 141 // Build CeedElemRestriction objects describing the mesh and solution discrete representations. 142 CeedInt mesh_size, sol_size; 143 CeedElemRestriction mesh_restr, sol_restr, q_data_restr_i; 144 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restr, NULL); 145 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, dim * (dim + 1) / 2, &sol_size, num_qpts, NULL, &q_data_restr_i); 146 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restr, NULL); 147 if (!test) { 148 // LCOV_EXCL_START 149 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size / dim); 150 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size); 151 // LCOV_EXCL_STOP 152 } 153 154 // Create a CeedVector with the mesh coordinates. 155 CeedVector mesh_coords; 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_sa = TransformMeshCoords(dim, mesh_size, mesh_coords); 161 162 // Context data to be passed to the 'f_build_diff' QFunction. 163 CeedQFunctionContext build_ctx; 164 struct BuildContext build_ctx_data; 165 build_ctx_data.dim = build_ctx_data.space_dim = dim; 166 CeedQFunctionContextCreate(ceed, &build_ctx); 167 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(build_ctx_data), &build_ctx_data); 168 169 // Create the QFunction that builds the diffusion operator (i.e. computes its quadrature data) and set its context data. 170 CeedQFunction qf_build; 171 switch (gallery) { 172 case 0: 173 // This creates the QFunction directly. 174 CeedQFunctionCreateInterior(ceed, 1, f_build_diff, f_build_diff_loc, &qf_build); 175 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 176 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 177 CeedQFunctionAddOutput(qf_build, "qdata", dim * (dim + 1) / 2, CEED_EVAL_NONE); 178 CeedQFunctionSetContext(qf_build, build_ctx); 179 break; 180 case 1: { 181 // This creates the QFunction via the gallery. 182 char name[16] = ""; 183 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DBuild", dim); 184 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 185 break; 186 } 187 } 188 189 // Create the operator that builds the quadrature data for the diffusion operator. 190 CeedOperator op_build; 191 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 192 CeedOperatorSetField(op_build, "dx", mesh_restr, mesh_basis, CEED_VECTOR_ACTIVE); 193 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 194 CeedOperatorSetField(op_build, "qdata", q_data_restr_i, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 195 196 // Compute the quadrature data for the diffusion operator. 197 CeedVector q_data; 198 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 199 CeedInt num_elem = 1; 200 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 201 CeedVectorCreate(ceed, num_elem * elem_qpts * dim * (dim + 1) / 2, &q_data); 202 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 203 204 // Create the QFunction that defines the action of the diffusion operator. 205 CeedQFunction qf_apply; 206 switch (gallery) { 207 case 0: 208 // This creates the QFunction directly. 209 CeedQFunctionCreateInterior(ceed, 1, f_apply_diff, f_apply_diff_loc, &qf_apply); 210 CeedQFunctionAddInput(qf_apply, "du", dim, CEED_EVAL_GRAD); 211 CeedQFunctionAddInput(qf_apply, "qdata", dim * (dim + 1) / 2, CEED_EVAL_NONE); 212 CeedQFunctionAddOutput(qf_apply, "dv", dim, CEED_EVAL_GRAD); 213 CeedQFunctionSetContext(qf_apply, build_ctx); 214 break; 215 case 1: { 216 // This creates the QFunction via the gallery. 217 char name[16] = ""; 218 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DApply", dim); 219 CeedQFunctionCreateInteriorByName(ceed, name, &qf_apply); 220 break; 221 } 222 } 223 224 // Create the diffusion operator. 225 CeedOperator op_apply; 226 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 227 CeedOperatorSetField(op_apply, "du", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 228 CeedOperatorSetField(op_apply, "qdata", q_data_restr_i, CEED_BASIS_COLLOCATED, q_data); 229 CeedOperatorSetField(op_apply, "dv", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 230 231 // Create auxiliary solution-size vectors. 232 CeedVector u, v; 233 CeedVectorCreate(ceed, sol_size, &u); 234 CeedVectorCreate(ceed, sol_size, &v); 235 236 // Initialize 'u' with sum of coordinates, x+y+z. 237 CeedScalar *u_array; 238 const CeedScalar *x_array; 239 CeedVectorGetArrayWrite(u, CEED_MEM_HOST, &u_array); 240 CeedVectorGetArrayRead(mesh_coords, CEED_MEM_HOST, &x_array); 241 for (CeedInt i = 0; i < sol_size; i++) { 242 u_array[i] = 0; 243 for (CeedInt d = 0; d < dim; d++) u_array[i] += x_array[i + d * sol_size]; 244 } 245 CeedVectorRestoreArray(u, &u_array); 246 CeedVectorRestoreArrayRead(mesh_coords, &x_array); 247 248 // Compute the mesh surface area using the diff operator: 249 // sa = 1^T \cdot abs( K \cdot x). 250 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 251 252 // Compute and print the sum of the entries of 'v' giving the mesh surface area. 253 const CeedScalar *v_array; 254 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 255 CeedScalar sa = 0.; 256 for (CeedInt i = 0; i < sol_size; i++) sa += fabs(v_array[i]); 257 CeedVectorRestoreArrayRead(v, &v_array); 258 if (!test) { 259 // LCOV_EXCL_START 260 printf(" done.\n"); 261 printf("Exact mesh surface area : % .14g\n", exact_sa); 262 printf("Computed mesh surface area : % .14g\n", sa); 263 printf("Surface area error : % .14g\n", sa - exact_sa); 264 // LCOV_EXCL_STOP 265 } else { 266 CeedScalar tol = (dim == 1 ? 10000. * CEED_EPSILON : dim == 2 ? 1E-1 : 1E-1); 267 if (fabs(sa - exact_sa) > tol) printf("Surface area error : % .14g\n", sa - exact_sa); 268 } 269 270 // Free dynamically allocated memory. 271 CeedVectorDestroy(&u); 272 CeedVectorDestroy(&v); 273 CeedVectorDestroy(&q_data); 274 CeedVectorDestroy(&mesh_coords); 275 CeedOperatorDestroy(&op_apply); 276 CeedQFunctionDestroy(&qf_apply); 277 CeedQFunctionContextDestroy(&build_ctx); 278 CeedOperatorDestroy(&op_build); 279 CeedQFunctionDestroy(&qf_build); 280 CeedElemRestrictionDestroy(&sol_restr); 281 CeedElemRestrictionDestroy(&mesh_restr); 282 CeedElemRestrictionDestroy(&q_data_restr_i); 283 CeedBasisDestroy(&sol_basis); 284 CeedBasisDestroy(&mesh_basis); 285 CeedDestroy(&ceed); 286 return 0; 287 } 288 289 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[3]) { 290 // Use the approximate formula: 291 // prob_size ~ num_elem * degree^dim 292 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 293 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 294 while (num_elem > 1) { 295 num_elem /= 2; 296 s++; 297 } 298 CeedInt r = s % dim; 299 for (CeedInt d = 0; d < dim; d++) { 300 CeedInt sd = s / dim; 301 if (r > 0) { 302 sd++; 303 r--; 304 } 305 num_xyz[d] = 1 << sd; 306 } 307 return 0; 308 } 309 310 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 311 CeedElemRestriction *restr, CeedElemRestriction *restr_i) { 312 CeedInt p = degree + 1; 313 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 314 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 315 CeedInt nd[3], num_elem = 1, scalar_size = 1; 316 for (CeedInt d = 0; d < dim; d++) { 317 num_elem *= num_xyz[d]; 318 nd[d] = num_xyz[d] * (p - 1) + 1; 319 scalar_size *= nd[d]; 320 } 321 *size = scalar_size * num_comp; 322 // elem: 0 1 n-1 323 // |---*-...-*---|---*-...-*---|- ... -|--...--| 324 // num_nodes: 0 1 p-1 p p+1 2*p n*p 325 CeedInt *el_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 326 for (CeedInt e = 0; e < num_elem; e++) { 327 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 328 for (CeedInt d = 0; d < dim; d++) { 329 e_xyz[d] = re % num_xyz[d]; 330 re /= num_xyz[d]; 331 } 332 CeedInt *loc_el_nodes = el_nodes + e * num_nodes; 333 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 334 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 335 for (CeedInt d = 0; d < dim; d++) { 336 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 337 g_nodes_stride *= nd[d]; 338 r_nodes /= p; 339 } 340 loc_el_nodes[l_nodes] = g_nodes; 341 } 342 } 343 if (restr) 344 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, el_nodes, 345 restr); 346 free(el_nodes); 347 348 if (restr_i) { 349 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, restr_i); 350 } 351 352 return 0; 353 } 354 355 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], CeedInt mesh_degree, CeedVector mesh_coords) { 356 CeedInt p = mesh_degree + 1; 357 CeedInt nd[3], num_elem = 1, scalar_size = 1; 358 for (CeedInt d = 0; d < dim; d++) { 359 num_elem *= num_xyz[d]; 360 nd[d] = num_xyz[d] * (p - 1) + 1; 361 scalar_size *= nd[d]; 362 } 363 CeedScalar *coords; 364 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 365 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 366 // The H1 basis uses Lobatto quadrature points as nodes. 367 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 368 for (CeedInt i = 0; i < p; i++) { 369 nodes[i] = 0.5 + 0.5 * nodes[i]; 370 } 371 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 372 CeedInt r_nodes = gs_nodes; 373 for (CeedInt d = 0; d < dim; d++) { 374 CeedInt d1d = r_nodes % nd[d]; 375 coords[gs_nodes + scalar_size * d] = ((d1d / (p - 1)) + nodes[d1d % (p - 1)]) / num_xyz[d]; 376 r_nodes /= nd[d]; 377 } 378 } 379 free(nodes); 380 CeedVectorRestoreArray(mesh_coords, &coords); 381 return 0; 382 } 383 384 #ifndef M_PI 385 #define M_PI 3.14159265358979323846 386 #endif 387 388 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 389 CeedScalar exact_sa = (dim == 1 ? 2 : dim == 2 ? 4 : 6); 390 CeedScalar *coords; 391 392 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 393 for (CeedInt i = 0; i < mesh_size; i++) { 394 // map [0,1] to [0,1] varying the mesh density 395 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 396 } 397 CeedVectorRestoreArray(mesh_coords, &coords); 398 399 return exact_sa; 400 } 401