1 // Copyright (c) 2017-2026, 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 <stdio.h>
44 #include <stdlib.h>
45 #include <string.h>
46
47 // Auxiliary functions
48 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]);
49 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts,
50 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction);
51 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords);
52 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords);
53
54 // Main example
main(int argc,const char * argv[])55 int main(int argc, const char *argv[]) {
56 const char *ceed_spec = "/cpu/self";
57 CeedInt dim = 3; // dimension of the mesh
58 CeedInt num_comp_x = 3; // number of x components
59 CeedInt mesh_degree = 4; // polynomial degree for the mesh
60 CeedInt sol_degree = 4; // polynomial degree for the solution
61 CeedInt num_qpts = sol_degree + 2; // number of 1D quadrature points
62 CeedInt prob_size = -1; // approximate problem size
63 CeedInt help = 0, test = 0, gallery = 0, benchmark = 0;
64
65 // Process command line arguments.
66 for (int ia = 1; ia < argc; ia++) {
67 // LCOV_EXCL_START
68 int next_arg = ((ia + 1) < argc), parse_error = 0;
69 if (!strcmp(argv[ia], "-h")) {
70 help = 1;
71 } else if (!strcmp(argv[ia], "-c") || !strcmp(argv[ia], "-ceed")) {
72 parse_error = next_arg ? ceed_spec = argv[++ia], 0 : 1;
73 } else if (!strcmp(argv[ia], "-d")) {
74 parse_error = next_arg ? dim = atoi(argv[++ia]), 0 : 1;
75 num_comp_x = dim;
76 } else if (!strcmp(argv[ia], "-m")) {
77 parse_error = next_arg ? mesh_degree = atoi(argv[++ia]), 0 : 1;
78 } else if (!strcmp(argv[ia], "-p")) {
79 parse_error = next_arg ? sol_degree = atoi(argv[++ia]), 0 : 1;
80 } else if (!strcmp(argv[ia], "-q")) {
81 parse_error = next_arg ? num_qpts = atoi(argv[++ia]), 0 : 1;
82 } else if (!strcmp(argv[ia], "-s")) {
83 parse_error = next_arg ? prob_size = atoi(argv[++ia]), 0 : 1;
84 } else if (!strcmp(argv[ia], "-b")) {
85 parse_error = next_arg ? benchmark = atoi(argv[++ia]), 0 : 1;
86 } else if (!strcmp(argv[ia], "-t")) {
87 test = 1;
88 } else if (!strcmp(argv[ia], "-g")) {
89 gallery = 1;
90 }
91 if (parse_error) {
92 printf("Error parsing command line options.\n");
93 return 1;
94 }
95 // LCOV_EXCL_STOP
96 }
97 if (prob_size < 0) prob_size = test ? 8 * 16 : 256 * 1024;
98
99 // Print the values of all options:
100 if (!test || help) {
101 // LCOV_EXCL_START
102 printf("Selected options: [command line option] : <current value>\n");
103 printf(" Ceed specification [-c] : %s\n", ceed_spec);
104 printf(" Mesh dimension [-d] : %" CeedInt_FMT "\n", dim);
105 printf(" Mesh degree [-m] : %" CeedInt_FMT "\n", mesh_degree);
106 printf(" Solution degree [-p] : %" CeedInt_FMT "\n", sol_degree);
107 printf(" Num. 1D quadrature pts [-q] : %" CeedInt_FMT "\n", num_qpts);
108 printf(" Approx. # unknowns [-s] : %" CeedInt_FMT "\n", prob_size);
109 printf(" QFunction source [-g] : %s\n", gallery ? "gallery" : "header");
110 if (help) {
111 printf("Test/quiet mode is %s\n", (test ? "ON" : "OFF (use -t to enable)"));
112 return 0;
113 }
114 printf("\n");
115 // LCOV_EXCL_STOP
116 }
117
118 // Select appropriate backend and logical device based on the (-ceed) command line argument.
119 Ceed ceed;
120
121 CeedInit(ceed_spec, &ceed);
122
123 // Construct the mesh and solution bases.
124 CeedBasis mesh_basis, sol_basis;
125
126 CeedBasisCreateTensorH1Lagrange(ceed, dim, num_comp_x, mesh_degree + 1, num_qpts, CEED_GAUSS, &mesh_basis);
127 CeedBasisCreateTensorH1Lagrange(ceed, dim, 1, sol_degree + 1, num_qpts, CEED_GAUSS, &sol_basis);
128
129 // Determine the mesh size based on the given approximate problem size.
130 CeedInt num_xyz[dim];
131
132 GetCartesianMeshSize(dim, sol_degree, prob_size, num_xyz);
133 if (!test) {
134 // LCOV_EXCL_START
135 printf("Mesh size: nx = %" CeedInt_FMT, num_xyz[0]);
136 if (dim > 1) printf(", ny = %" CeedInt_FMT, num_xyz[1]);
137 if (dim > 2) printf(", nz = %" CeedInt_FMT, num_xyz[2]);
138 printf("\n");
139 // LCOV_EXCL_STOP
140 }
141
142 // Build CeedElemRestriction objects describing the mesh and solution discrete representations.
143 CeedInt mesh_size, sol_size;
144 CeedElemRestriction mesh_restriction, sol_restriction, q_data_restriction;
145
146 BuildCartesianRestriction(ceed, dim, num_xyz, mesh_degree, num_comp_x, &mesh_size, num_qpts, &mesh_restriction, NULL);
147 BuildCartesianRestriction(ceed, dim, num_xyz, sol_degree, 1, &sol_size, num_qpts, &sol_restriction, &q_data_restriction);
148 if (!test) {
149 // LCOV_EXCL_START
150 printf("Number of mesh nodes : %" CeedInt_FMT "\n", mesh_size / dim);
151 printf("Number of solution nodes : %" CeedInt_FMT "\n", sol_size);
152 // LCOV_EXCL_STOP
153 }
154
155 // Create a CeedVector with the mesh coordinates.
156 CeedVector mesh_coords;
157
158 CeedVectorCreate(ceed, mesh_size, &mesh_coords);
159 SetCartesianMeshCoords(dim, num_xyz, mesh_degree, mesh_coords);
160
161 // Apply a transformation to the mesh.
162 CeedScalar exact_volume = TransformMeshCoords(dim, mesh_size, mesh_coords);
163
164 // Context data to be passed to the 'build_mass' QFunction.
165 CeedQFunctionContext build_ctx;
166 struct BuildContext build_ctx_data;
167
168 build_ctx_data.dim = build_ctx_data.space_dim = dim;
169 CeedQFunctionContextCreate(ceed, &build_ctx);
170 CeedQFunctionContextSetData(build_ctx, CEED_MEM_HOST, CEED_USE_POINTER, sizeof(build_ctx_data), &build_ctx_data);
171
172 // Create the QFunction that builds the mass operator (i.e. computes its quadrature data) and set its context data.
173 CeedQFunction qf_build;
174
175 if (gallery) {
176 // This creates the QFunction via the gallery.
177 char name[13] = "";
178 snprintf(name, sizeof name, "Mass%" CeedInt_FMT "DBuild", dim);
179 CeedQFunctionCreateInteriorByName(ceed, name, &qf_build);
180 } else {
181 // This creates the QFunction directly.
182 CeedQFunctionCreateInterior(ceed, 1, build_mass, build_mass_loc, &qf_build);
183 CeedQFunctionAddInput(qf_build, "dx", num_comp_x * dim, CEED_EVAL_GRAD);
184 CeedQFunctionAddInput(qf_build, "weights", 1, CEED_EVAL_WEIGHT);
185 CeedQFunctionAddOutput(qf_build, "qdata", 1, CEED_EVAL_NONE);
186 CeedQFunctionSetContext(qf_build, build_ctx);
187 }
188
189 // Create the operator that builds the quadrature data for the mass operator.
190 CeedOperator op_build;
191
192 CeedOperatorCreate(ceed, qf_build, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_build);
193 CeedOperatorSetField(op_build, "dx", mesh_restriction, mesh_basis, CEED_VECTOR_ACTIVE);
194 CeedOperatorSetField(op_build, "weights", CEED_ELEMRESTRICTION_NONE, mesh_basis, CEED_VECTOR_NONE);
195 CeedOperatorSetField(op_build, "qdata", q_data_restriction, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE);
196
197 // Compute the quadrature data for the mass operator.
198 CeedVector q_data;
199 CeedInt elem_qpts = CeedIntPow(num_qpts, dim);
200 CeedInt num_elem = 1;
201
202 for (CeedInt d = 0; d < dim; d++) num_elem *= num_xyz[d];
203 CeedVectorCreate(ceed, num_elem * elem_qpts, &q_data);
204 CeedOperatorApply(op_build, mesh_coords, q_data, CEED_REQUEST_IMMEDIATE);
205
206 // Create the QFunction that defines the action of the mass operator.
207 CeedQFunction qf_apply;
208
209 if (gallery) {
210 // This creates the QFunction via the gallery.
211 CeedQFunctionCreateInteriorByName(ceed, "MassApply", &qf_apply);
212 } else {
213 // This creates the QFunction directly.
214 CeedQFunctionCreateInterior(ceed, 1, apply_mass, apply_mass_loc, &qf_apply);
215 CeedQFunctionAddInput(qf_apply, "u", 1, CEED_EVAL_INTERP);
216 CeedQFunctionAddInput(qf_apply, "qdata", 1, CEED_EVAL_NONE);
217 CeedQFunctionAddOutput(qf_apply, "v", 1, CEED_EVAL_INTERP);
218 }
219
220 // Create the mass operator.
221 CeedOperator op_apply;
222
223 CeedOperatorCreate(ceed, qf_apply, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, &op_apply);
224 CeedOperatorSetField(op_apply, "u", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE);
225 CeedOperatorSetField(op_apply, "qdata", q_data_restriction, CEED_BASIS_NONE, q_data);
226 CeedOperatorSetField(op_apply, "v", sol_restriction, sol_basis, CEED_VECTOR_ACTIVE);
227
228 // Create auxiliary solution-size vectors.
229 CeedVector u, v;
230
231 CeedVectorCreate(ceed, sol_size, &u);
232 CeedVectorCreate(ceed, sol_size, &v);
233
234 // Initialize 'u' with ones.
235 CeedVectorSetValue(u, 1.0);
236
237 // Compute the mesh volume using the mass operator: volume = 1^T \cdot M \cdot 1
238 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE);
239
240 // Benchmark runs
241 if (!test && benchmark) {
242 // LCOV_EXCL_START
243 printf(" Executing %d benchmarking runs...\n", benchmark);
244 // LCOV_EXCL_STOP
245 }
246 for (CeedInt i = 0; i < benchmark; i++) {
247 // LCOV_EXCL_START
248 CeedOperatorApply(op_apply, u, v, CEED_REQUEST_IMMEDIATE);
249 // LCOV_EXCL_STOP
250 }
251
252 // Compute and print the sum of the entries of 'v' giving the mesh volume.
253 CeedScalar volume = 0.;
254
255 {
256 const CeedScalar *v_array;
257
258 CeedVectorGetArrayRead(v, CEED_MEM_HOST, &v_array);
259 for (CeedInt i = 0; i < sol_size; i++) volume += v_array[i];
260 CeedVectorRestoreArrayRead(v, &v_array);
261 }
262 if (!test) {
263 // LCOV_EXCL_START
264 printf(" done.\n");
265 printf("Exact mesh volume : % .14g\n", exact_volume);
266 printf("Computed mesh volume : % .14g\n", volume);
267 printf("Volume error : % .14g\n", volume - exact_volume);
268 // LCOV_EXCL_STOP
269 } else {
270 CeedScalar tol = (dim == 1 ? 200. * CEED_EPSILON : dim == 2 ? 1E-5 : 1E-5);
271
272 if (fabs(volume - exact_volume) > tol) printf("Volume error : % .1e\n", volume - exact_volume);
273 }
274
275 // Free dynamically allocated memory.
276 CeedVectorDestroy(&u);
277 CeedVectorDestroy(&v);
278 CeedVectorDestroy(&q_data);
279 CeedVectorDestroy(&mesh_coords);
280 CeedOperatorDestroy(&op_apply);
281 CeedQFunctionDestroy(&qf_apply);
282 CeedQFunctionContextDestroy(&build_ctx);
283 CeedOperatorDestroy(&op_build);
284 CeedQFunctionDestroy(&qf_build);
285 CeedElemRestrictionDestroy(&sol_restriction);
286 CeedElemRestrictionDestroy(&mesh_restriction);
287 CeedElemRestrictionDestroy(&q_data_restriction);
288 CeedBasisDestroy(&sol_basis);
289 CeedBasisDestroy(&mesh_basis);
290 CeedDestroy(&ceed);
291 return 0;
292 }
293
GetCartesianMeshSize(CeedInt dim,CeedInt degree,CeedInt prob_size,CeedInt num_xyz[dim])294 int GetCartesianMeshSize(CeedInt dim, CeedInt degree, CeedInt prob_size, CeedInt num_xyz[dim]) {
295 // Use the approximate formula:
296 // prob_size ~ num_elem * degree^dim
297 CeedInt num_elem = prob_size / CeedIntPow(degree, dim);
298 CeedInt s = 0; // find s: num_elem/2 < 2^s <= num_elem
299
300 while (num_elem > 1) {
301 num_elem /= 2;
302 s++;
303 }
304 CeedInt r = s % dim;
305
306 for (CeedInt d = 0; d < dim; d++) {
307 CeedInt sd = s / dim;
308
309 if (r > 0) {
310 sd++;
311 r--;
312 }
313 num_xyz[d] = 1 << sd;
314 }
315 return 0;
316 }
317
BuildCartesianRestriction(Ceed ceed,CeedInt dim,CeedInt num_xyz[dim],CeedInt degree,CeedInt num_comp,CeedInt * size,CeedInt num_qpts,CeedElemRestriction * restriction,CeedElemRestriction * q_data_restriction)318 int BuildCartesianRestriction(Ceed ceed, CeedInt dim, CeedInt num_xyz[dim], CeedInt degree, CeedInt num_comp, CeedInt *size, CeedInt num_qpts,
319 CeedElemRestriction *restriction, CeedElemRestriction *q_data_restriction) {
320 CeedInt p = degree + 1;
321 CeedInt num_nodes = CeedIntPow(p, dim); // number of scalar nodes per element
322 CeedInt elem_qpts = CeedIntPow(num_qpts, dim); // number of qpts per element
323 CeedInt nd[3], num_elem = 1, scalar_size = 1;
324
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
336 for (CeedInt e = 0; e < num_elem; e++) {
337 CeedInt e_xyz[3] = {1, 1, 1}, re = e;
338
339 for (CeedInt d = 0; d < dim; d++) {
340 e_xyz[d] = re % num_xyz[d];
341 re /= num_xyz[d];
342 }
343 CeedInt *local_elem_nodes = elem_nodes + e * num_nodes;
344
345 for (CeedInt l_nodes = 0; l_nodes < num_nodes; l_nodes++) {
346 CeedInt g_nodes = 0, g_nodes_stride = 1, r_nodes = l_nodes;
347
348 for (CeedInt d = 0; d < dim; d++) {
349 g_nodes += (e_xyz[d] * (p - 1) + r_nodes % p) * g_nodes_stride;
350 g_nodes_stride *= nd[d];
351 r_nodes /= p;
352 }
353 local_elem_nodes[l_nodes] = g_nodes;
354 }
355 }
356 CeedElemRestrictionCreate(ceed, num_elem, num_nodes, num_comp, scalar_size, num_comp * scalar_size, CEED_MEM_HOST, CEED_COPY_VALUES, elem_nodes,
357 restriction);
358 if (q_data_restriction) {
359 CeedElemRestrictionCreateStrided(ceed, num_elem, elem_qpts, num_comp, num_comp * elem_qpts * num_elem, CEED_STRIDES_BACKEND, q_data_restriction);
360 }
361 free(elem_nodes);
362 return 0;
363 }
364
SetCartesianMeshCoords(CeedInt dim,CeedInt num_xyz[dim],CeedInt mesh_degree,CeedVector mesh_coords)365 int SetCartesianMeshCoords(CeedInt dim, CeedInt num_xyz[dim], CeedInt mesh_degree, CeedVector mesh_coords) {
366 CeedInt p = mesh_degree + 1;
367 CeedInt nd[3], scalar_size = 1;
368
369 for (CeedInt d = 0; d < dim; d++) {
370 nd[d] = num_xyz[d] * (p - 1) + 1;
371 scalar_size *= nd[d];
372 }
373 CeedScalar *coords;
374
375 CeedVectorGetArrayWrite(mesh_coords, CEED_MEM_HOST, &coords);
376 CeedScalar *nodes = malloc(sizeof(CeedScalar) * p);
377
378 // The H1 basis uses Lobatto quadrature points as nodes.
379 CeedLobattoQuadrature(p, nodes, NULL); // nodes are in [-1,1]
380 for (CeedInt i = 0; i < p; i++) nodes[i] = 0.5 + 0.5 * nodes[i];
381 for (CeedInt gs_nodes = 0; gs_nodes < scalar_size; gs_nodes++) {
382 CeedInt r_nodes = gs_nodes;
383
384 for (CeedInt d = 0; d < dim; d++) {
385 CeedInt d_1d = r_nodes % nd[d];
386
387 coords[gs_nodes + scalar_size * d] = ((d_1d / (p - 1)) + nodes[d_1d % (p - 1)]) / num_xyz[d];
388 r_nodes /= nd[d];
389 }
390 }
391 free(nodes);
392 CeedVectorRestoreArray(mesh_coords, &coords);
393 return 0;
394 }
395
396 #ifndef M_PI
397 #define M_PI 3.14159265358979323846
398 #define M_PI_2 1.57079632679489661923
399 #endif
400
TransformMeshCoords(CeedInt dim,CeedInt mesh_size,CeedVector mesh_coords)401 CeedScalar TransformMeshCoords(CeedInt dim, CeedInt mesh_size, CeedVector mesh_coords) {
402 CeedScalar exact_volume;
403 CeedScalar *coords;
404
405 CeedVectorGetArray(mesh_coords, CEED_MEM_HOST, &coords);
406 if (dim == 1) {
407 for (CeedInt i = 0; i < mesh_size; i++) {
408 // map [0,1] to [0,1] varying the mesh density
409 coords[i] = 0.5 + 1. / sqrt(3.) * sin((2. / 3.) * M_PI * (coords[i] - 0.5));
410 }
411 exact_volume = 1.;
412 } else {
413 CeedInt num_nodes = mesh_size / dim;
414
415 for (CeedInt i = 0; i < num_nodes; i++) {
416 // map (x,y) from [0,1]x[0,1] to the quarter annulus with polar
417 // coordinates, (r,phi) in [1,2]x[0,pi/2] with area = 3/4*pi
418 CeedScalar u = coords[i], v = coords[i + num_nodes];
419
420 u = 1. + u;
421 v = M_PI_2 * v;
422 coords[i] = u * cos(v);
423 coords[i + num_nodes] = u * sin(v);
424 }
425 exact_volume = 3. / 4. * M_PI;
426 }
427 CeedVectorRestoreArray(mesh_coords, &coords);
428 return exact_volume;
429 }
430