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 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 <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, 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 ? 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 [-g] : %s\n", gallery ? "gallery" : "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 CeedInit(ceed_spec, &ceed); 118 119 // Construct the mesh and solution bases. 120 CeedBasis mesh_basis, sol_basis; 121 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, num_qpts, CEED_GAUSS, &mesh_basis); 122 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, CEED_GAUSS, &sol_basis); 123 124 // Determine the mesh size based on the given approximate problem size. 125 CeedInt num_xyz[dim]; 126 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz); 127 if (!test) { 128 // LCOV_EXCL_START 129 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]); 130 if (dim > 1) printf(", ny = %" CeedInt_FMT, num_xyz[1]); 131 if (dim > 2) printf(", nz = %" CeedInt_FMT, num_xyz[2]); 132 printf("\n"); 133 // LCOV_EXCL_STOP 134 } 135 136 // Build CeedElemRestriction objects describing the mesh and solution discrete representations. 137 CeedInt mesh_size, sol_size; 138 CeedElemRestriction mesh_restriction, sol_restriction, q_data_restriction; 139 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restriction, NULL); 140 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restriction, &q_data_restriction); 141 if (!test) { 142 // LCOV_EXCL_START 143 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size / dim); 144 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size); 145 // LCOV_EXCL_STOP 146 } 147 148 // Create a CeedVector with the mesh coordinates. 149 CeedVector mesh_coords; 150 CeedVectorCreate(ceed, mesh_size, &mesh_coords); 151 SetCartesianMeshCoords(dim, num_xyz, mesh_degree, mesh_coords); 152 153 // Apply a transformation to the mesh. 154 CeedScalar exact_volume = TransformMeshCoords(dim, mesh_size, mesh_coords); 155 156 // Context data to be passed to the 'build_mass' QFunction. 157 CeedQFunctionContext build_ctx; 158 struct BuildContext build_ctx_data; 159 build_ctx_data.dim = build_ctx_data.space_dim = dim; 160 CeedQFunctionContextCreate(ceed, &build_ctx); 161 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(build_ctx_data), &build_ctx_data); 162 163 // Create the QFunction that builds the mass operator (i.e. computes its quadrature data) and set its context data. 164 CeedQFunction qf_build; 165 if (gallery) { 166 // This creates the QFunction via the gallery. 167 char name[13] = ""; 168 snprintf(name, sizeof name, "Mass%" CeedInt_FMT "DBuild", dim); 169 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 170 } else { 171 // This creates the QFunction directly. 172 CeedQFunctionCreateInterior(ceed, 1, build_mass, build_mass_loc, &qf_build); 173 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 174 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 175 CeedQFunctionAddOutput(qf_build, "qdata", 1, CEED_EVAL_NONE); 176 CeedQFunctionSetContext(qf_build, build_ctx); 177 } 178 179 // Create the operator that builds the quadrature data for the mass operator. 180 CeedOperator op_build; 181 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 182 CeedOperatorSetField(op_build, "dx", mesh_restriction, mesh_basis, CEED_VECTOR_ACTIVE); 183 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 184 CeedOperatorSetField(op_build, "qdata", q_data_restriction, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 185 186 // Compute the quadrature data for the mass operator. 187 CeedVector q_data; 188 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 189 CeedInt num_elem = 1; 190 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 191 CeedVectorCreate(ceed, num_elem * elem_qpts, &q_data); 192 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 193 194 // Create the QFunction that defines the action of the mass operator. 195 CeedQFunction qf_apply; 196 if (gallery) { 197 // This creates the QFunction via the gallery. 198 CeedQFunctionCreateInteriorByName(ceed, "MassApply", &qf_apply); 199 } else { 200 // This creates the QFunction directly. 201 CeedQFunctionCreateInterior(ceed, 1, apply_mass, apply_mass_loc, &qf_apply); 202 CeedQFunctionAddInput(qf_apply, "u", 1, CEED_EVAL_INTERP); 203 CeedQFunctionAddInput(qf_apply, "qdata", 1, CEED_EVAL_NONE); 204 CeedQFunctionAddOutput(qf_apply, "v", 1, CEED_EVAL_INTERP); 205 } 206 207 // Create the mass operator. 208 CeedOperator op_apply; 209 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 210 CeedOperatorSetField(op_apply, "u", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 211 CeedOperatorSetField(op_apply, "qdata", q_data_restriction, CEED_BASIS_COLLOCATED, q_data); 212 CeedOperatorSetField(op_apply, "v", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE); 213 214 // Create auxiliary solution-size vectors. 215 CeedVector u, v; 216 CeedVectorCreate(ceed, sol_size, &u); 217 CeedVectorCreate(ceed, sol_size, &v); 218 219 // Initialize 'u' and 'v' with ones. 220 CeedVectorSetValue(u, 1.0); 221 222 // Compute the mesh volume using the mass operator: volume = 1^T \cdot M \cdot 1 223 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 224 225 // Compute and print the sum of the entries of 'v' giving the mesh volume. 226 CeedScalar volume = 0.; 227 { 228 const CeedScalar *v_array; 229 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 230 for (CeedInt i = 0; i < sol_size; i++) volume += v_array[i]; 231 CeedVectorRestoreArrayRead(v, &v_array); 232 } 233 if (!test) { 234 // LCOV_EXCL_START 235 printf(" done.\n"); 236 printf("Exact mesh volume : % .14g\n", exact_volume); 237 printf("Computed mesh volume : % .14g\n", volume); 238 printf("Volume error : % .14g\n", volume - exact_volume); 239 // LCOV_EXCL_STOP 240 } else { 241 CeedScalar tol = (dim == 1 ? 100. * CEED_EPSILON : dim == 2 ? 1E-5 : 1E-5); 242 if (fabs(volume - exact_volume) > tol) printf("Volume error : % .1e\n", volume - exact_volume); 243 } 244 245 // Free dynamically allocated memory. 246 CeedVectorDestroy(&u); 247 CeedVectorDestroy(&v); 248 CeedVectorDestroy(&q_data); 249 CeedVectorDestroy(&mesh_coords); 250 CeedOperatorDestroy(&op_apply); 251 CeedQFunctionDestroy(&qf_apply); 252 CeedQFunctionContextDestroy(&build_ctx); 253 CeedOperatorDestroy(&op_build); 254 CeedQFunctionDestroy(&qf_build); 255 CeedElemRestrictionDestroy(&sol_restriction); 256 CeedElemRestrictionDestroy(&mesh_restriction); 257 CeedElemRestrictionDestroy(&q_data_restriction); 258 CeedBasisDestroy(&sol_basis); 259 CeedBasisDestroy(&mesh_basis); 260 CeedDestroy(&ceed); 261 return 0; 262 } 263 264 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]) { 265 // Use the approximate formula: 266 // prob_size ~ num_elem * degree^dim 267 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 268 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 269 while (num_elem > 1) { 270 num_elem /= 2; 271 s++; 272 } 273 CeedInt r = s % dim; 274 for (CeedInt d = 0; d < dim; d++) { 275 CeedInt sd = s / dim; 276 if (r > 0) { 277 sd++; 278 r--; 279 } 280 num_xyz[d] = 1 << sd; 281 } 282 return 0; 283 } 284 285 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 286 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction) { 287 CeedInt p = degree + 1; 288 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 289 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 290 CeedInt nd[3], num_elem = 1, scalar_size = 1; 291 for (CeedInt d = 0; d < dim; d++) { 292 num_elem *= num_xyz[d]; 293 nd[d] = num_xyz[d] * (p - 1) + 1; 294 scalar_size *= nd[d]; 295 } 296 *size = scalar_size * num_comp; 297 // elem: 0 1 n-1 298 // |---*-...-*---|---*-...-*---|- ... -|--...--| 299 // num_nodes: 0 1 p-1 p p+1 2*p n*p 300 CeedInt *elem_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 301 for (CeedInt e = 0; e < num_elem; e++) { 302 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 303 for (CeedInt d = 0; d < dim; d++) { 304 e_xyz[d] = re % num_xyz[d]; 305 re /= num_xyz[d]; 306 } 307 CeedInt *local_elem_nodes = elem_nodes + e * num_nodes; 308 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 309 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 310 for (CeedInt d = 0; d < dim; d++) { 311 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 312 g_nodes_stride *= nd[d]; 313 r_nodes /= p; 314 } 315 local_elem_nodes[l_nodes] = g_nodes; 316 } 317 } 318 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, elem_nodes, 319 restriction); 320 if (q_data_restriction) 321 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, q_data_restriction); 322 free(elem_nodes); 323 return 0; 324 } 325 326 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords) { 327 CeedInt p = mesh_degree + 1; 328 CeedInt nd[3], num_elem = 1, scalar_size = 1; 329 for (CeedInt d = 0; d < dim; d++) { 330 num_elem *= num_xyz[d]; 331 nd[d] = num_xyz[d] * (p - 1) + 1; 332 scalar_size *= nd[d]; 333 } 334 CeedScalar *coords; 335 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 336 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 337 // The H1 basis uses Lobatto quadrature points as nodes. 338 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 339 for (CeedInt i = 0; i < p; i++) nodes[i] = 0.5 + 0.5 * nodes[i]; 340 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 341 CeedInt r_nodes = gs_nodes; 342 for (CeedInt d = 0; d < dim; d++) { 343 CeedInt d_1d = r_nodes % nd[d]; 344 coords[gs_nodes + scalar_size * d] = ((d_1d / (p - 1)) + nodes[d_1d % (p - 1)]) / num_xyz[d]; 345 r_nodes /= nd[d]; 346 } 347 } 348 free(nodes); 349 CeedVectorRestoreArray(mesh_coords, &coords); 350 return 0; 351 } 352 353 #ifndef M_PI 354 #define M_PI 3.14159265358979323846 355 #define M_PI_2 1.57079632679489661923 356 #endif 357 358 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 359 CeedScalar exact_volume; 360 CeedScalar *coords; 361 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 362 if (dim == 1) { 363 for (CeedInt i = 0; i < mesh_size; i++) { 364 // map [0,1] to [0,1] varying the mesh density 365 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 366 } 367 exact_volume = 1.; 368 } else { 369 CeedInt num_nodes = mesh_size / dim; 370 for (CeedInt i = 0; i < num_nodes; i++) { 371 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar 372 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi 373 CeedScalar u = coords[i], v = coords[i + num_nodes]; 374 u = 1. + u; 375 v = M_PI_2 * v; 376 coords[i] = u * cos(v); 377 coords[i + num_nodes] = u * sin(v); 378 } 379 exact_volume = 3. / 4. * M_PI; 380 } 381 CeedVectorRestoreArray(mesh_coords, &coords); 382 return exact_volume; 383 } 384