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 *restriction, CeedElemRestriction *q_data_restriction); 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 quadrature 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_restriction, sol_restriction, q_data_restriction; 144 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restriction, NULL); 145 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, dim * (dim + 1) / 2, &sol_size, num_qpts, NULL, &q_data_restriction); 146 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restriction, 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_surface_area = TransformMeshCoords(dim, mesh_size, mesh_coords); 161 162 // Context data to be passed to the '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 if (gallery) { 172 // This creates the QFunction via the gallery. 173 char name[16] = ""; 174 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DBuild", dim); 175 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 176 } else { 177 // This creates the QFunction directly. 178 CeedQFunctionCreateInterior(ceed, 1, build_diff, build_diff_loc, &qf_build); 179 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 180 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 181 CeedQFunctionAddOutput(qf_build, "qdata", dim * (dim + 1) / 2, CEED_EVAL_NONE); 182 CeedQFunctionSetContext(qf_build, build_ctx); 183 } 184 185 // Create the operator that builds the quadrature data for the diffusion operator. 186 CeedOperator op_build; 187 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 188 CeedOperatorSetField(op_build, "dx", mesh_restriction, mesh_basis, CEED_VECTOR_ACTIVE); 189 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 190 CeedOperatorSetField(op_build, "qdata", q_data_restriction, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 191 192 // Compute the quadrature data for the diffusion operator. 193 CeedVector q_data; 194 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 195 CeedInt num_elem = 1; 196 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 197 CeedVectorCreate(ceed, num_elem * elem_qpts * dim * (dim + 1) / 2, &q_data); 198 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 199 200 // Create the QFunction that defines the action of the diffusion operator. 201 CeedQFunction qf_apply; 202 if (gallery) { 203 // This creates the QFunction via the gallery. 204 char name[16] = ""; 205 snprintf(name, sizeof name, "Poisson%" CeedInt_FMT "DApply", dim); 206 CeedQFunctionCreateInteriorByName(ceed, name, &qf_apply); 207 } else { 208 // This creates the QFunction directly. 209 CeedQFunctionCreateInterior(ceed, 1, apply_diff, 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 } 215 216 // Create the diffusion operator. 217 CeedOperator op_apply; 218 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 219 CeedOperatorSetField(op_apply, "du", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 220 CeedOperatorSetField(op_apply, "qdata", q_data_restriction, CEED_BASIS_COLLOCATED, q_data); 221 CeedOperatorSetField(op_apply, "dv", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 222 223 // Create auxiliary solution-size vectors. 224 CeedVector u, v; 225 CeedVectorCreate(ceed, sol_size, &u); 226 CeedVectorCreate(ceed, sol_size, &v); 227 228 // Initialize 'u' with sum of coordinates, x+y+z. 229 { 230 CeedScalar *u_array; 231 const CeedScalar *x_array; 232 CeedVectorGetArrayWrite(u, CEED_MEM_HOST, &u_array); 233 CeedVectorGetArrayRead(mesh_coords, CEED_MEM_HOST, &x_array); 234 for (CeedInt i = 0; i < sol_size; i++) { 235 u_array[i] = 0; 236 for (CeedInt d = 0; d < dim; d++) u_array[i] += x_array[i + d * sol_size]; 237 } 238 CeedVectorRestoreArray(u, &u_array); 239 CeedVectorRestoreArrayRead(mesh_coords, &x_array); 240 } 241 242 // Compute the mesh surface area using the diff operator: surface_area = 1^T \cdot abs( K \cdot x). 243 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 244 245 // Compute and print the sum of the entries of 'v' giving the mesh surface area. 246 CeedScalar surface_area = 0.; 247 { 248 const CeedScalar *v_array; 249 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 250 for (CeedInt i = 0; i < sol_size; i++) surface_area += fabs(v_array[i]); 251 CeedVectorRestoreArrayRead(v, &v_array); 252 } 253 if (!test) { 254 // LCOV_EXCL_START 255 printf(" done.\n"); 256 printf("Exact mesh surface area : % .14g\n", exact_surface_area); 257 printf("Computed mesh surface area : % .14g\n", surface_area); 258 printf("Surface area error : % .14g\n", surface_area - exact_surface_area); 259 // LCOV_EXCL_STOP 260 } else { 261 CeedScalar tol = (dim == 1 ? 10000. * CEED_EPSILON : dim == 2 ? 1E-1 : 1E-1); 262 if (fabs(surface_area - exact_surface_area) > tol) printf("Surface area error : % .14g\n", surface_area - exact_surface_area); 263 } 264 265 // Free dynamically allocated memory. 266 CeedVectorDestroy(&u); 267 CeedVectorDestroy(&v); 268 CeedVectorDestroy(&q_data); 269 CeedVectorDestroy(&mesh_coords); 270 CeedOperatorDestroy(&op_apply); 271 CeedQFunctionDestroy(&qf_apply); 272 CeedQFunctionContextDestroy(&build_ctx); 273 CeedOperatorDestroy(&op_build); 274 CeedQFunctionDestroy(&qf_build); 275 CeedElemRestrictionDestroy(&sol_restriction); 276 CeedElemRestrictionDestroy(&mesh_restriction); 277 CeedElemRestrictionDestroy(&q_data_restriction); 278 CeedBasisDestroy(&sol_basis); 279 CeedBasisDestroy(&mesh_basis); 280 CeedDestroy(&ceed); 281 return 0; 282 } 283 284 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[3]) { 285 // Use the approximate formula: 286 // prob_size ~ num_elem * degree^dim 287 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 288 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 289 while (num_elem > 1) { 290 num_elem /= 2; 291 s++; 292 } 293 CeedInt r = s % dim; 294 for (CeedInt d = 0; d < dim; d++) { 295 CeedInt sd = s / dim; 296 if (r > 0) { 297 sd++; 298 r--; 299 } 300 num_xyz[d] = 1 << sd; 301 } 302 return 0; 303 } 304 305 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[3], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 306 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction) { 307 CeedInt p = degree + 1; 308 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 309 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 310 CeedInt nd[3], num_elem = 1, scalar_size = 1; 311 for (CeedInt d = 0; d < dim; d++) { 312 num_elem *= num_xyz[d]; 313 nd[d] = num_xyz[d] * (p - 1) + 1; 314 scalar_size *= nd[d]; 315 } 316 *size = scalar_size * num_comp; 317 // elem: 0 1 n-1 318 // |---*-...-*---|---*-...-*---|- ... -|--...--| 319 // num_nodes: 0 1 p-1 p p+1 2*p n*p 320 CeedInt *el_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 321 for (CeedInt e = 0; e < num_elem; e++) { 322 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 323 for (CeedInt d = 0; d < dim; d++) { 324 e_xyz[d] = re % num_xyz[d]; 325 re /= num_xyz[d]; 326 } 327 CeedInt *local_elem_nodes = el_nodes + e * num_nodes; 328 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 329 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 330 for (CeedInt d = 0; d < dim; d++) { 331 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 332 g_nodes_stride *= nd[d]; 333 r_nodes /= p; 334 } 335 local_elem_nodes[l_nodes] = g_nodes; 336 } 337 } 338 if (restriction) 339 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, el_nodes, 340 restriction); 341 free(el_nodes); 342 343 if (q_data_restriction) { 344 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, q_data_restriction); 345 } 346 347 return 0; 348 } 349 350 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[3], CeedInt mesh_degree, CeedVector mesh_coords) { 351 CeedInt p = mesh_degree + 1; 352 CeedInt nd[3], num_elem = 1, scalar_size = 1; 353 for (CeedInt d = 0; d < dim; d++) { 354 num_elem *= num_xyz[d]; 355 nd[d] = num_xyz[d] * (p - 1) + 1; 356 scalar_size *= nd[d]; 357 } 358 CeedScalar *coords; 359 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 360 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 361 // The H1 basis uses Lobatto quadrature points as nodes. 362 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 363 for (CeedInt i = 0; i < p; i++) nodes[i] = 0.5 + 0.5 * nodes[i]; 364 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 365 CeedInt r_nodes = gs_nodes; 366 for (CeedInt d = 0; d < dim; d++) { 367 CeedInt d1d = r_nodes % nd[d]; 368 coords[gs_nodes + scalar_size * d] = ((d1d / (p - 1)) + nodes[d1d % (p - 1)]) / num_xyz[d]; 369 r_nodes /= nd[d]; 370 } 371 } 372 free(nodes); 373 CeedVectorRestoreArray(mesh_coords, &coords); 374 return 0; 375 } 376 377 #ifndef M_PI 378 #define M_PI 3.14159265358979323846 379 #endif 380 381 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 382 CeedScalar exact_surface_area = (dim == 1 ? 2 : dim == 2 ? 4 : 6); 383 CeedScalar *coords; 384 385 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 386 for (CeedInt i = 0; i < mesh_size; i++) { 387 // map [0,1] to [0,1] varying the mesh density 388 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 389 } 390 CeedVectorRestoreArray(mesh_coords, &coords); 391 392 return exact_surface_area; 393 } 394