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, PetscCtx 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, PetscCtx ctx)
26: {
27: u[0] = 0.;
28: for (PetscInt d = 0; d < dim; ++d) u[0] += -0.5 * x[d] * x[d];
29: return PETSC_SUCCESS;
30: }
32: static PetscErrorCode linear_divu(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
33: {
34: u[0] = dim;
35: return PETSC_SUCCESS;
36: }
38: /* fx_v are the residual functions for the equation \vec{u} = \grad{p}. f0_v is the term <v,u>.*/
39: 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[])
40: {
41: for (PetscInt i = 0; i < dim; ++i) f0[i] = u[uOff[0] + i];
42: }
44: /* f1_v is the term <v,-\grad{p}> but we integrate by parts to get <\grad{v}, -p*I> */
45: 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[])
46: {
47: PetscInt c;
49: for (c = 0; c < dim; ++c) {
50: for (PetscInt d = 0; d < dim; ++d) f1[c * dim + d] = (c == d) ? -u[uOff[1]] : 0;
51: }
52: }
54: /* Residual function for enforcing \div{u} = f. */
55: 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[])
56: {
57: PetscScalar rhs, divu = 0;
59: (void)linear_divu(dim, t, x, dim, &rhs, NULL);
60: for (PetscInt i = 0; i < dim; ++i) divu += u_x[uOff_x[0] + i * dim + i];
61: f0[0] = divu - rhs;
62: }
64: /* Boundary residual. Dirichlet boundary for u means u_bdy=p*n */
65: 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[])
66: {
67: PetscScalar pressure;
69: (void)linear_p(dim, t, x, dim, &pressure, NULL);
70: for (PetscInt d = 0; d < dim; ++d) f0[d] = pressure * n[d];
71: }
73: /* gx_yz are the jacobian functions obtained by taking the derivative of the y residual w.r.t z*/
74: 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[])
75: {
76: for (PetscInt c = 0; c < dim; ++c) g0[c * dim + c] = 1.0;
77: }
79: 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[])
80: {
81: for (PetscInt c = 0; c < dim; ++c) g1[c * dim + c] = 1.0;
82: }
84: 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[])
85: {
86: for (PetscInt c = 0; c < dim; ++c) g2[c * dim + c] = -1.0;
87: }
89: typedef struct {
90: PetscInt dummy;
91: } AppCtx;
93: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *ctx, DM *mesh)
94: {
95: PetscFunctionBegin;
96: PetscCall(DMCreate(comm, mesh));
97: PetscCall(DMSetType(*mesh, DMPLEX));
98: PetscCall(DMSetFromOptions(*mesh));
99: PetscCall(DMSetApplicationContext(*mesh, ctx));
100: PetscCall(DMViewFromOptions(*mesh, NULL, "-dm_view"));
101: PetscFunctionReturn(PETSC_SUCCESS);
102: }
104: /* Setup the system of equations that we wish to solve */
105: static PetscErrorCode SetupProblem(DM dm, AppCtx *ctx)
106: {
107: PetscDS ds;
108: DMLabel label;
109: PetscWeakForm wf;
110: const PetscInt id = 1;
111: PetscInt bd;
113: PetscFunctionBegin;
114: PetscCall(DMGetDS(dm, &ds));
115: /* All of these are independent of the user's choice of solution */
116: PetscCall(PetscDSSetResidual(ds, 0, f0_v, f1_v));
117: PetscCall(PetscDSSetResidual(ds, 1, f0_q_linear, NULL));
118: PetscCall(PetscDSSetJacobian(ds, 0, 0, g0_vu, NULL, NULL, NULL));
119: PetscCall(PetscDSSetJacobian(ds, 0, 1, NULL, NULL, g2_vp, NULL));
120: PetscCall(PetscDSSetJacobian(ds, 1, 0, NULL, g1_qu, NULL, NULL));
122: PetscCall(DMGetLabel(dm, "marker", &label));
123: PetscCall(PetscDSAddBoundary(ds, DM_BC_NATURAL, "Boundary Integral", label, 1, &id, 0, 0, NULL, (PetscFortranCallbackFn *)NULL, NULL, ctx, &bd));
124: PetscCall(PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
125: PetscCall(PetscWeakFormSetIndexBdResidual(wf, label, 1, 0, 0, 0, f0_bd_u_linear, 0, NULL));
127: PetscCall(PetscDSSetExactSolution(ds, 0, linear_u, NULL));
128: PetscCall(PetscDSSetExactSolution(ds, 1, linear_p, NULL));
129: PetscFunctionReturn(PETSC_SUCCESS);
130: }
132: /* Create the finite element spaces we will use for this system */
133: static PetscErrorCode SetupDiscretization(DM mesh, DM mesh_sum, PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *ctx)
134: {
135: DM cdm = mesh, cdm_sum = mesh_sum;
136: PetscDS ds;
137: PetscFE u, divu, u_sum, divu_sum;
138: PetscInt dim;
139: PetscBool simplex;
141: PetscFunctionBegin;
142: PetscCall(DMGetDimension(mesh, &dim));
143: PetscCall(DMPlexIsSimplex(mesh, &simplex));
145: {
146: PetscBool force;
147: // Turn off automatic quadrature selection as a test
148: PetscCall(DMGetDS(mesh_sum, &ds));
149: PetscCall(PetscDSGetForceQuad(ds, &force));
150: if (force) PetscCall(PetscDSSetForceQuad(ds, PETSC_FALSE));
151: }
153: /* Create FE objects and give them names so that options can be set from
154: * command line. Each field gets 2 instances (i.e. velocity and velocity_sum)created twice so that we can compare between approaches. */
155: PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh), dim, dim, simplex, "velocity_", -1, &u));
156: PetscCall(PetscObjectSetName((PetscObject)u, "velocity"));
157: PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh_sum), dim, dim, simplex, "velocity_sum_", -1, &u_sum));
158: PetscCall(PetscObjectSetName((PetscObject)u_sum, "velocity_sum"));
159: PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh), dim, 1, simplex, "divu_", -1, &divu));
160: PetscCall(PetscObjectSetName((PetscObject)divu, "divu"));
161: PetscCall(PetscFECreateDefault(PetscObjectComm((PetscObject)mesh_sum), dim, 1, simplex, "divu_sum_", -1, &divu_sum));
162: PetscCall(PetscObjectSetName((PetscObject)divu_sum, "divu_sum"));
164: PetscCall(PetscFECopyQuadrature(u, divu));
165: PetscCall(PetscFECopyQuadrature(u_sum, divu_sum));
167: /* Associate the FE objects with the mesh and setup the system */
168: PetscCall(DMSetField(mesh, 0, NULL, (PetscObject)u));
169: PetscCall(DMSetField(mesh, 1, NULL, (PetscObject)divu));
170: PetscCall(DMCreateDS(mesh));
171: PetscCall((*setup)(mesh, ctx));
173: PetscCall(DMSetField(mesh_sum, 0, NULL, (PetscObject)u_sum));
174: PetscCall(DMSetField(mesh_sum, 1, NULL, (PetscObject)divu_sum));
175: PetscCall(DMCreateDS(mesh_sum));
176: PetscCall((*setup)(mesh_sum, ctx));
178: while (cdm) {
179: PetscCall(DMCopyDisc(mesh, cdm));
180: PetscCall(DMGetCoarseDM(cdm, &cdm));
181: }
183: while (cdm_sum) {
184: PetscCall(DMCopyDisc(mesh_sum, cdm_sum));
185: PetscCall(DMGetCoarseDM(cdm_sum, &cdm_sum));
186: }
188: /* The Mesh now owns the fields, so we can destroy the FEs created in this
189: * function */
190: PetscCall(PetscFEDestroy(&u));
191: PetscCall(PetscFEDestroy(&divu));
192: PetscCall(PetscFEDestroy(&u_sum));
193: PetscCall(PetscFEDestroy(&divu_sum));
194: PetscCall(DMDestroy(&cdm));
195: PetscCall(DMDestroy(&cdm_sum));
196: PetscFunctionReturn(PETSC_SUCCESS);
197: }
199: int main(int argc, char **argv)
200: {
201: AppCtx ctx;
202: DM dm, dm_sum;
203: SNES snes, snes_sum;
204: Vec u, u_sum;
205: PetscReal errNorm;
206: const PetscReal errTol = PETSC_SMALL;
208: PetscFunctionBeginUser;
209: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
211: /* Set up a snes for the standard approach, one space with 2 components */
212: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
213: PetscCall(CreateMesh(PETSC_COMM_WORLD, &ctx, &dm));
214: PetscCall(SNESSetDM(snes, dm));
216: /* Set up a snes for the sum space approach, where each subspace of the sum space represents one component */
217: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes_sum));
218: PetscCall(CreateMesh(PETSC_COMM_WORLD, &ctx, &dm_sum));
219: PetscCall(SNESSetDM(snes_sum, dm_sum));
220: PetscCall(SetupDiscretization(dm, dm_sum, SetupProblem, &ctx));
222: /* Set up and solve the system using standard approach. */
223: PetscCall(DMCreateGlobalVector(dm, &u));
224: PetscCall(PetscObjectSetName((PetscObject)u, "solution"));
225: PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &ctx));
226: PetscCall(SNESSetFromOptions(snes));
227: PetscCall(DMSNESCheckFromOptions(snes, u));
228: PetscCall(SNESSolve(snes, NULL, u));
229: PetscCall(SNESGetSolution(snes, &u));
230: PetscCall(VecViewFromOptions(u, NULL, "-solution_view"));
232: /* Set up and solve the sum space system */
233: PetscCall(DMCreateGlobalVector(dm_sum, &u_sum));
234: PetscCall(PetscObjectSetName((PetscObject)u_sum, "solution_sum"));
235: PetscCall(DMPlexSetSNESLocalFEM(dm_sum, PETSC_FALSE, &ctx));
236: PetscCall(SNESSetFromOptions(snes_sum));
237: PetscCall(DMSNESCheckFromOptions(snes_sum, u_sum));
238: PetscCall(SNESSolve(snes_sum, NULL, u_sum));
239: PetscCall(SNESGetSolution(snes_sum, &u_sum));
240: PetscCall(VecViewFromOptions(u_sum, NULL, "-solution_sum_view"));
242: /* Check if standard solution and sum space solution match to machine precision */
243: PetscCall(VecAXPY(u_sum, -1, u));
244: PetscCall(VecNorm(u_sum, NORM_2, &errNorm));
245: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Sum space provides the same solution as a regular space: %s", (errNorm < errTol) ? "true" : "false"));
247: /* Cleanup */
248: PetscCall(VecDestroy(&u_sum));
249: PetscCall(VecDestroy(&u));
250: PetscCall(SNESDestroy(&snes_sum));
251: PetscCall(SNESDestroy(&snes));
252: PetscCall(DMDestroy(&dm_sum));
253: PetscCall(DMDestroy(&dm));
254: PetscCall(PetscFinalize());
255: return 0;
256: }
258: /*TEST
259: test:
260: suffix: 2d_lagrange
261: requires: triangle
262: args: -velocity_petscspace_degree 1 \
263: -velocity_petscspace_type poly \
264: -velocity_petscspace_components 2\
265: -velocity_petscdualspace_type lagrange \
266: -divu_petscspace_degree 0 \
267: -divu_petscspace_type poly \
268: -divu_petscdualspace_lagrange_continuity false \
269: -velocity_sum_petscfe_default_quadrature_order 1 \
270: -velocity_sum_petscspace_degree 1 \
271: -velocity_sum_petscspace_type sum \
272: -velocity_sum_petscspace_variables 2 \
273: -velocity_sum_petscspace_components 2 \
274: -velocity_sum_petscspace_sum_spaces 2 \
275: -velocity_sum_petscspace_sum_concatenate true \
276: -velocity_sum_petscdualspace_type lagrange \
277: -velocity_sum_sumcomp_0_petscspace_type poly \
278: -velocity_sum_sumcomp_0_petscspace_degree 1 \
279: -velocity_sum_sumcomp_0_petscspace_variables 2 \
280: -velocity_sum_sumcomp_0_petscspace_components 1 \
281: -velocity_sum_sumcomp_1_petscspace_type poly \
282: -velocity_sum_sumcomp_1_petscspace_degree 1 \
283: -velocity_sum_sumcomp_1_petscspace_variables 2 \
284: -velocity_sum_sumcomp_1_petscspace_components 1 \
285: -divu_sum_petscspace_degree 0 \
286: -divu_sum_petscspace_type sum \
287: -divu_sum_petscspace_variables 2 \
288: -divu_sum_petscspace_components 1 \
289: -divu_sum_petscspace_sum_spaces 1 \
290: -divu_sum_petscspace_sum_concatenate true \
291: -divu_sum_petscdualspace_lagrange_continuity false \
292: -divu_sum_sumcomp_0_petscspace_type poly \
293: -divu_sum_sumcomp_0_petscspace_degree 0 \
294: -divu_sum_sumcomp_0_petscspace_variables 2 \
295: -divu_sum_sumcomp_0_petscspace_components 1 \
296: -dm_refine 0 \
297: -snes_error_if_not_converged \
298: -ksp_rtol 1e-10 \
299: -ksp_error_if_not_converged \
300: -pc_type fieldsplit\
301: -pc_fieldsplit_type schur\
302: -divu_sum_petscdualspace_lagrange_continuity false \
303: -pc_fieldsplit_schur_precondition full
304: TEST*/