Actual source code: ex10.c

  1: static char help[] = "Tests implementation of PetscSpace_Sum by solving the Poisson equations using a PetscSpace_Poly and a PetscSpace_Sum and checking that \
  2:   solutions agree up to machine precision.\n\n";

  4: #include <petscdmplex.h>
  5: #include <petscds.h>
  6: #include <petscfe.h>
  7: #include <petscsnes.h>
  8: /* We are solving the system of equations:
  9:  * \vec{u} = -\grad{p}
 10:  * \div{u} = f
 11:  */

 13: /* Exact solutions for linear velocity
 14:    \vec{u} = \vec{x};
 15:    p = -0.5*(\vec{x} \cdot \vec{x});
 16:    */
 17: static PetscErrorCode linear_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 18: {
 19:   PetscInt c;

 21:   for (c = 0; c < Nc; ++c) u[c] = x[c];
 22:   return PETSC_SUCCESS;
 23: }

 25: static PetscErrorCode linear_p(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 26: {
 27:   PetscInt d;

 29:   u[0] = 0.;
 30:   for (d = 0; d < dim; ++d) u[0] += -0.5 * x[d] * x[d];
 31:   return PETSC_SUCCESS;
 32: }

 34: static PetscErrorCode linear_divu(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, void *ctx)
 35: {
 36:   u[0] = dim;
 37:   return PETSC_SUCCESS;
 38: }

 40: /* fx_v are the residual functions for the equation \vec{u} = \grad{p}. f0_v is the term <v,u>.*/
 41: static void f0_v(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 42: {
 43:   PetscInt i;

 45:   for (i = 0; i < dim; ++i) f0[i] = u[uOff[0] + i];
 46: }

 48: /* f1_v is the term <v,-\grad{p}> but we integrate by parts to get <\grad{v}, -p*I> */
 49: static void f1_v(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 50: {
 51:   PetscInt c;

 53:   for (c = 0; c < dim; ++c) {
 54:     PetscInt d;

 56:     for (d = 0; d < dim; ++d) f1[c * dim + d] = (c == d) ? -u[uOff[1]] : 0;
 57:   }
 58: }

 60: /* Residual function for enforcing \div{u} = f. */
 61: static void f0_q_linear(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 62: {
 63:   PetscScalar rhs, divu = 0;
 64:   PetscInt    i;

 66:   (void)linear_divu(dim, t, x, dim, &rhs, NULL);
 67:   for (i = 0; i < dim; ++i) divu += u_x[uOff_x[0] + i * dim + i];
 68:   f0[0] = divu - rhs;
 69: }

 71: /* Boundary residual. Dirichlet boundary for u means u_bdy=p*n */
 72: static void f0_bd_u_linear(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 73: {
 74:   PetscScalar pressure;
 75:   PetscInt    d;

 77:   (void)linear_p(dim, t, x, dim, &pressure, NULL);
 78:   for (d = 0; d < dim; ++d) f0[d] = pressure * n[d];
 79: }

 81: /* gx_yz are the jacobian functions obtained by taking the derivative of the y residual w.r.t z*/
 82: static void g0_vu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
 83: {
 84:   PetscInt c;

 86:   for (c = 0; c < dim; ++c) g0[c * dim + c] = 1.0;
 87: }

 89: static void g1_qu(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
 90: {
 91:   PetscInt c;

 93:   for (c = 0; c < dim; ++c) g1[c * dim + c] = 1.0;
 94: }

 96: static void g2_vp(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
 97: {
 98:   PetscInt c;

100:   for (c = 0; c < dim; ++c) g2[c * dim + c] = -1.0;
101: }

103: typedef struct {
104:   PetscInt dummy;
105: } UserCtx;

107: static PetscErrorCode CreateMesh(MPI_Comm comm, UserCtx *user, DM *mesh)
108: {
109:   PetscFunctionBegin;
110:   PetscCall(DMCreate(comm, mesh));
111:   PetscCall(DMSetType(*mesh, DMPLEX));
112:   PetscCall(DMSetFromOptions(*mesh));
113:   PetscCall(DMSetApplicationContext(*mesh, user));
114:   PetscCall(DMViewFromOptions(*mesh, NULL, "-dm_view"));
115:   PetscFunctionReturn(PETSC_SUCCESS);
116: }

118: /* Setup the system of equations that we wish to solve */
119: static PetscErrorCode SetupProblem(DM dm, UserCtx *user)
120: {
121:   PetscDS        ds;
122:   DMLabel        label;
123:   PetscWeakForm  wf;
124:   const PetscInt id = 1;
125:   PetscInt       bd;

127:   PetscFunctionBegin;
128:   PetscCall(DMGetDS(dm, &ds));
129:   /* All of these are independent of the user's choice of solution */
130:   PetscCall(PetscDSSetResidual(ds, 0, f0_v, f1_v));
131:   PetscCall(PetscDSSetResidual(ds, 1, f0_q_linear, NULL));
132:   PetscCall(PetscDSSetJacobian(ds, 0, 0, g0_vu, NULL, NULL, NULL));
133:   PetscCall(PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_vp, NULL));
134:   PetscCall(PetscDSSetJacobian(ds, 1, 0, NULL, g1_qu, NULL, NULL));

136:   PetscCall(DMGetLabel(dm, "marker", &label));
137:   PetscCall(PetscDSAddBoundary(ds, DM_BC_NATURAL, "Boundary Integral", label, 1, &id, 0, 0, NULL, (void (*)(void))NULL, NULL, user, &bd));
138:   PetscCall(PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
139:   PetscCall(PetscWeakFormSetIndexBdResidual(wf, label, 1, 0, 0, 0, f0_bd_u_linear, 0, NULL));

141:   PetscCall(PetscDSSetExactSolution(ds, 0, linear_u, NULL));
142:   PetscCall(PetscDSSetExactSolution(ds, 1, linear_p, NULL));
143:   PetscFunctionReturn(PETSC_SUCCESS);
144: }

146: /* Create the finite element spaces we will use for this system */
147: static PetscErrorCode SetupDiscretization(DM mesh, DM mesh_sum, PetscErrorCode (*setup)(DM, UserCtx *), UserCtx *user)
148: {
149:   DM        cdm = mesh, cdm_sum = mesh_sum;
150:   PetscDS   ds;
151:   PetscFE   u, divu, u_sum, divu_sum;
152:   PetscInt  dim;
153:   PetscBool simplex;

155:   PetscFunctionBegin;
156:   PetscCall(DMGetDimension(mesh, &dim));
157:   PetscCall(DMPlexIsSimplex(mesh, &simplex));

159:   {
160:     PetscBool force;
161:     // Turn off automatic quadrature selection as a test
162:     PetscCall(DMGetDS(mesh_sum, &ds));
163:     PetscCall(PetscDSGetForceQuad(ds, &force));
164:     if (force) PetscCall(PetscDSSetForceQuad(ds, PETSC_FALSE));
165:   }

167:   /* Create FE objects and give them names so that options can be set from
168:    * command line. Each field gets 2 instances (i.e. velocity and velocity_sum)created twice so that we can compare between approaches. */
169:   PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh), dim, dim, simplex, "velocity_", -1, &u));
170:   PetscCall(PetscObjectSetName((PetscObject)u, "velocity"));
171:   PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh_sum), dim, dim, simplex, "velocity_sum_", -1, &u_sum));
172:   PetscCall(PetscObjectSetName((PetscObject)u_sum, "velocity_sum"));
173:   PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh), dim, 1, simplex, "divu_", -1, &divu));
174:   PetscCall(PetscObjectSetName((PetscObject)divu, "divu"));
175:   PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh_sum), dim, 1, simplex, "divu_sum_", -1, &divu_sum));
176:   PetscCall(PetscObjectSetName((PetscObject)divu_sum, "divu_sum"));

178:   PetscCall(PetscFECopyQuadrature(u, divu));
179:   PetscCall(PetscFECopyQuadrature(u_sum, divu_sum));

181:   /* Associate the FE objects with the mesh and setup the system */
182:   PetscCall(DMSetField(mesh, 0, NULL, (PetscObject)u));
183:   PetscCall(DMSetField(mesh, 1, NULL, (PetscObject)divu));
184:   PetscCall(DMCreateDS(mesh));
185:   PetscCall((*setup)(mesh, user));

187:   PetscCall(DMSetField(mesh_sum, 0, NULL, (PetscObject)u_sum));
188:   PetscCall(DMSetField(mesh_sum, 1, NULL, (PetscObject)divu_sum));
189:   PetscCall(DMCreateDS(mesh_sum));
190:   PetscCall((*setup)(mesh_sum, user));

192:   while (cdm) {
193:     PetscCall(DMCopyDisc(mesh, cdm));
194:     PetscCall(DMGetCoarseDM(cdm, &cdm));
195:   }

197:   while (cdm_sum) {
198:     PetscCall(DMCopyDisc(mesh_sum, cdm_sum));
199:     PetscCall(DMGetCoarseDM(cdm_sum, &cdm_sum));
200:   }

202:   /* The Mesh now owns the fields, so we can destroy the FEs created in this
203:    * function */
204:   PetscCall(PetscFEDestroy(&u));
205:   PetscCall(PetscFEDestroy(&divu));
206:   PetscCall(PetscFEDestroy(&u_sum));
207:   PetscCall(PetscFEDestroy(&divu_sum));
208:   PetscCall(DMDestroy(&cdm));
209:   PetscCall(DMDestroy(&cdm_sum));
210:   PetscFunctionReturn(PETSC_SUCCESS);
211: }

213: int main(int argc, char **argv)
214: {
215:   UserCtx         user;
216:   DM              dm, dm_sum;
217:   SNES            snes, snes_sum;
218:   Vec             u, u_sum;
219:   PetscReal       errNorm;
220:   const PetscReal errTol = PETSC_SMALL;

222:   PetscFunctionBeginUser;
223:   PetscCall(PetscInitialize(&argc, &argv, NULL, help));

225:   /* Set up a snes for the standard approach, one space with 2 components */
226:   PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
227:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
228:   PetscCall(SNESSetDM(snes, dm));

230:   /* Set up a snes for the sum space approach, where each subspace of the sum space represents one component */
231:   PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes_sum));
232:   PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm_sum));
233:   PetscCall(SNESSetDM(snes_sum, dm_sum));
234:   PetscCall(SetupDiscretization(dm, dm_sum, SetupProblem, &user));

236:   /* Set up and solve the system using standard approach. */
237:   PetscCall(DMCreateGlobalVector(dm, &u));
238:   PetscCall(VecSet(u, 0.0));
239:   PetscCall(PetscObjectSetName((PetscObject)u, "solution"));
240:   PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
241:   PetscCall(SNESSetFromOptions(snes));
242:   PetscCall(DMSNESCheckFromOptions(snes, u));
243:   PetscCall(SNESSolve(snes, NULL, u));
244:   PetscCall(SNESGetSolution(snes, &u));
245:   PetscCall(VecViewFromOptions(u, NULL, "-solution_view"));

247:   /* Set up and solve the sum space system */
248:   PetscCall(DMCreateGlobalVector(dm_sum, &u_sum));
249:   PetscCall(VecSet(u_sum, 0.0));
250:   PetscCall(PetscObjectSetName((PetscObject)u_sum, "solution_sum"));
251:   PetscCall(DMPlexSetSNESLocalFEM(dm_sum, PETSC_FALSE, &user));
252:   PetscCall(SNESSetFromOptions(snes_sum));
253:   PetscCall(DMSNESCheckFromOptions(snes_sum, u_sum));
254:   PetscCall(SNESSolve(snes_sum, NULL, u_sum));
255:   PetscCall(SNESGetSolution(snes_sum, &u_sum));
256:   PetscCall(VecViewFromOptions(u_sum, NULL, "-solution_sum_view"));

258:   /* Check if standard solution and sum space solution match to machine precision */
259:   PetscCall(VecAXPY(u_sum, -1, u));
260:   PetscCall(VecNorm(u_sum, NORM_2, &errNorm));
261:   PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Sum space provides the same solution as a regular space: %s", (errNorm < errTol) ? "true" : "false"));

263:   /* Cleanup */
264:   PetscCall(VecDestroy(&u_sum));
265:   PetscCall(VecDestroy(&u));
266:   PetscCall(SNESDestroy(&snes_sum));
267:   PetscCall(SNESDestroy(&snes));
268:   PetscCall(DMDestroy(&dm_sum));
269:   PetscCall(DMDestroy(&dm));
270:   PetscCall(PetscFinalize());
271:   return 0;
272: }

274: /*TEST
275:   test:
276:     suffix: 2d_lagrange
277:     requires: triangle
278:     args: -velocity_petscspace_degree 1 \
279:       -velocity_petscspace_type poly \
280:       -velocity_petscspace_components 2\
281:       -velocity_petscdualspace_type lagrange \
282:       -divu_petscspace_degree 0 \
283:       -divu_petscspace_type poly \
284:       -divu_petscdualspace_lagrange_continuity false \
285:       -velocity_sum_petscfe_default_quadrature_order 1 \
286:       -velocity_sum_petscspace_degree 1 \
287:       -velocity_sum_petscspace_type sum \
288:       -velocity_sum_petscspace_variables 2 \
289:       -velocity_sum_petscspace_components 2 \
290:       -velocity_sum_petscspace_sum_spaces 2 \
291:       -velocity_sum_petscspace_sum_concatenate true \
292:       -velocity_sum_petscdualspace_type lagrange \
293:       -velocity_sum_sumcomp_0_petscspace_type poly \
294:       -velocity_sum_sumcomp_0_petscspace_degree 1 \
295:       -velocity_sum_sumcomp_0_petscspace_variables 2 \
296:       -velocity_sum_sumcomp_0_petscspace_components 1 \
297:       -velocity_sum_sumcomp_1_petscspace_type poly \
298:       -velocity_sum_sumcomp_1_petscspace_degree 1 \
299:       -velocity_sum_sumcomp_1_petscspace_variables 2 \
300:       -velocity_sum_sumcomp_1_petscspace_components 1 \
301:       -divu_sum_petscspace_degree 0 \
302:       -divu_sum_petscspace_type sum \
303:       -divu_sum_petscspace_variables 2 \
304:       -divu_sum_petscspace_components 1 \
305:       -divu_sum_petscspace_sum_spaces 1 \
306:       -divu_sum_petscspace_sum_concatenate true \
307:       -divu_sum_petscdualspace_lagrange_continuity false \
308:       -divu_sum_sumcomp_0_petscspace_type poly \
309:       -divu_sum_sumcomp_0_petscspace_degree 0 \
310:       -divu_sum_sumcomp_0_petscspace_variables 2 \
311:       -divu_sum_sumcomp_0_petscspace_components 1 \
312:       -dm_refine 0 \
313:       -snes_error_if_not_converged \
314:       -ksp_rtol 1e-10 \
315:       -ksp_error_if_not_converged \
316:       -pc_type fieldsplit\
317:       -pc_fieldsplit_type schur\
318:       -divu_sum_petscdualspace_lagrange_continuity false \
319:       -pc_fieldsplit_schur_precondition full
320: TEST*/