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 *restr, CeedElemRestriction *restr_i); 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 quadr. 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_restr, sol_restr, sol_restr_i; 139 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restr, NULL); 140 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restr, &sol_restr_i); 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_vol = TransformMeshCoords(dim, mesh_size, mesh_coords); 155 156 // Context data to be passed to the 'f_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 switch (gallery) { 166 case 0: 167 // This creates the QFunction directly. 168 CeedQFunctionCreateInterior(ceed, 1, f_build_mass, f_build_mass_loc, &qf_build); 169 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD); 170 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT); 171 CeedQFunctionAddOutput(qf_build, "qdata", 1, CEED_EVAL_NONE); 172 CeedQFunctionSetContext(qf_build, build_ctx); 173 break; 174 case 1: { 175 // This creates the QFunction via the gallery. 176 char name[13] = ""; 177 snprintf(name, sizeof name, "Mass%" CeedInt_FMT "DBuild", dim); 178 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build); 179 break; 180 } 181 } 182 183 // Create the operator that builds the quadrature data for the mass operator. 184 CeedOperator op_build; 185 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build); 186 CeedOperatorSetField(op_build, "dx", mesh_restr, mesh_basis, CEED_VECTOR_ACTIVE); 187 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE); 188 CeedOperatorSetField(op_build, "qdata", sol_restr_i, CEED_BASIS_COLLOCATED, CEED_VECTOR_ACTIVE); 189 190 // Compute the quadrature data for the mass operator. 191 CeedVector q_data; 192 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); 193 CeedInt num_elem = 1; 194 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d]; 195 CeedVectorCreate(ceed, num_elem * elem_qpts, &q_data); 196 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE); 197 198 // Create the QFunction that defines the action of the mass operator. 199 CeedQFunction qf_apply; 200 switch (gallery) { 201 case 0: 202 // This creates the QFunction directly. 203 CeedQFunctionCreateInterior(ceed, 1, f_apply_mass, f_apply_mass_loc, &qf_apply); 204 CeedQFunctionAddInput(qf_apply, "u", 1, CEED_EVAL_INTERP); 205 CeedQFunctionAddInput(qf_apply, "qdata", 1, CEED_EVAL_NONE); 206 CeedQFunctionAddOutput(qf_apply, "v", 1, CEED_EVAL_INTERP); 207 break; 208 case 1: 209 // This creates the QFunction via the gallery. 210 CeedQFunctionCreateInteriorByName(ceed, "MassApply", &qf_apply); 211 break; 212 } 213 214 // Create the mass operator. 215 CeedOperator op_apply; 216 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply); 217 CeedOperatorSetField(op_apply, "u", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 218 CeedOperatorSetField(op_apply, "qdata", sol_restr_i, CEED_BASIS_COLLOCATED, q_data); 219 CeedOperatorSetField(op_apply, "v", sol_restr, sol_basis, CEED_VECTOR_ACTIVE); 220 221 // Create auxiliary solution-size vectors. 222 CeedVector u, v; 223 CeedVectorCreate(ceed, sol_size, &u); 224 CeedVectorCreate(ceed, sol_size, &v); 225 226 // Initialize 'u' and 'v' with ones. 227 CeedVectorSetValue(u, 1.0); 228 229 // Compute the mesh volume using the mass operator: vol = 1^T \cdot M \cdot 1 230 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE); 231 232 // Compute and print the sum of the entries of 'v' giving the mesh volume. 233 const CeedScalar *v_array; 234 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array); 235 CeedScalar vol = 0.; 236 for (CeedInt i = 0; i < sol_size; i++) vol += v_array[i]; 237 CeedVectorRestoreArrayRead(v, &v_array); 238 if (!test) { 239 // LCOV_EXCL_START 240 printf(" done.\n"); 241 printf("Exact mesh volume : % .14g\n", exact_vol); 242 printf("Computed mesh volume : % .14g\n", vol); 243 printf("Volume error : % .14g\n", vol - exact_vol); 244 // LCOV_EXCL_STOP 245 } else { 246 CeedScalar tol = (dim == 1 ? 100. * CEED_EPSILON : dim == 2 ? 1E-5 : 1E-5); 247 if (fabs(vol - exact_vol) > tol) printf("Volume error : % .1e\n", vol - exact_vol); 248 } 249 250 // Free dynamically allocated memory. 251 CeedVectorDestroy(&u); 252 CeedVectorDestroy(&v); 253 CeedVectorDestroy(&q_data); 254 CeedVectorDestroy(&mesh_coords); 255 CeedOperatorDestroy(&op_apply); 256 CeedQFunctionDestroy(&qf_apply); 257 CeedQFunctionContextDestroy(&build_ctx); 258 CeedOperatorDestroy(&op_build); 259 CeedQFunctionDestroy(&qf_build); 260 CeedElemRestrictionDestroy(&sol_restr); 261 CeedElemRestrictionDestroy(&mesh_restr); 262 CeedElemRestrictionDestroy(&sol_restr_i); 263 CeedBasisDestroy(&sol_basis); 264 CeedBasisDestroy(&mesh_basis); 265 CeedDestroy(&ceed); 266 return 0; 267 } 268 269 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]) { 270 // Use the approximate formula: 271 // prob_size ~ num_elem * degree^dim 272 CeedInt num_elem = prob_size / CeedIntPow(degree, dim); 273 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem 274 while (num_elem > 1) { 275 num_elem /= 2; 276 s++; 277 } 278 CeedInt r = s % dim; 279 for (CeedInt d = 0; d < dim; d++) { 280 CeedInt sd = s / dim; 281 if (r > 0) { 282 sd++; 283 r--; 284 } 285 num_xyz[d] = 1 << sd; 286 } 287 return 0; 288 } 289 290 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts, 291 CeedElemRestriction *restr, CeedElemRestriction *restr_i) { 292 CeedInt p = degree + 1; 293 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element 294 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element 295 CeedInt nd[3], num_elem = 1, scalar_size = 1; 296 for (CeedInt d = 0; d < dim; d++) { 297 num_elem *= num_xyz[d]; 298 nd[d] = num_xyz[d] * (p - 1) + 1; 299 scalar_size *= nd[d]; 300 } 301 *size = scalar_size * num_comp; 302 // elem: 0 1 n-1 303 // |---*-...-*---|---*-...-*---|- ... -|--...--| 304 // num_nodes: 0 1 p-1 p p+1 2*p n*p 305 CeedInt *elem_nodes = malloc(sizeof(CeedInt) * num_elem * num_nodes); 306 for (CeedInt e = 0; e < num_elem; e++) { 307 CeedInt e_xyz[3] = {1, 1, 1}, re = e; 308 for (CeedInt d = 0; d < dim; d++) { 309 e_xyz[d] = re % num_xyz[d]; 310 re /= num_xyz[d]; 311 } 312 CeedInt *loc_el_nodes = elem_nodes + e * num_nodes; 313 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) { 314 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes; 315 for (CeedInt d = 0; d < dim; d++) { 316 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride; 317 g_nodes_stride *= nd[d]; 318 r_nodes /= p; 319 } 320 loc_el_nodes[l_nodes] = g_nodes; 321 } 322 } 323 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, elem_nodes, 324 restr); 325 if (restr_i) CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, restr_i); 326 free(elem_nodes); 327 return 0; 328 } 329 330 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords) { 331 CeedInt p = mesh_degree + 1; 332 CeedInt nd[3], num_elem = 1, scalar_size = 1; 333 for (CeedInt d = 0; d < dim; d++) { 334 num_elem *= num_xyz[d]; 335 nd[d] = num_xyz[d] * (p - 1) + 1; 336 scalar_size *= nd[d]; 337 } 338 CeedScalar *coords; 339 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords); 340 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p); 341 // The H1 basis uses Lobatto quadrature points as nodes. 342 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1] 343 for (CeedInt i = 0; i < p; i++) { 344 nodes[i] = 0.5 + 0.5 * nodes[i]; 345 } 346 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) { 347 CeedInt r_nodes = gs_nodes; 348 for (CeedInt d = 0; d < dim; d++) { 349 CeedInt d_1d = r_nodes % nd[d]; 350 coords[gs_nodes + scalar_size * d] = ((d_1d / (p - 1)) + nodes[d_1d % (p - 1)]) / num_xyz[d]; 351 r_nodes /= nd[d]; 352 } 353 } 354 free(nodes); 355 CeedVectorRestoreArray(mesh_coords, &coords); 356 return 0; 357 } 358 359 #ifndef M_PI 360 #define M_PI 3.14159265358979323846 361 #define M_PI_2 1.57079632679489661923 362 #endif 363 364 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) { 365 CeedScalar exact_volume; 366 CeedScalar *coords; 367 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords); 368 if (dim == 1) { 369 for (CeedInt i = 0; i < mesh_size; i++) { 370 // map [0,1] to [0,1] varying the mesh density 371 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5)); 372 } 373 exact_volume = 1.; 374 } else { 375 CeedInt num_nodes = mesh_size / dim; 376 for (CeedInt i = 0; i < num_nodes; i++) { 377 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar 378 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi 379 CeedScalar u = coords[i], v = coords[i + num_nodes]; 380 u = 1. + u; 381 v = M_PI_2 * v; 382 coords[i] = u * cos(v); 383 coords[i + num_nodes] = u * sin(v); 384 } 385 exact_volume = 3. / 4. * M_PI; 386 } 387 CeedVectorRestoreArray(mesh_coords, &coords); 388 return exact_volume; 389 } 390