Actual source code: ex13.c
1: static char help[] = "Poisson Problem in 2d and 3d with finite elements.\n\
2: We solve the Poisson problem in a rectangular\n\
3: domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\
4: This example supports automatic convergence estimation\n\
5: and eventually adaptivity.\n\n\n";
7: #include <petscdmplex.h>
8: #include <petscdmceed.h>
9: #include <petscsnes.h>
10: #include <petscds.h>
11: #include <petscconvest.h>
13: typedef struct {
14: /* Domain and mesh definition */
15: PetscBool spectral; /* Look at the spectrum along planes in the solution */
16: PetscBool shear; /* Shear the domain */
17: PetscBool adjoint; /* Solve the adjoint problem */
18: PetscBool homogeneous; /* Use homogeneous boundary conditions */
19: PetscBool viewError; /* Output the solution error */
20: } AppCtx;
22: static PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
23: {
24: *u = 0.0;
25: return PETSC_SUCCESS;
26: }
28: static PetscErrorCode trig_inhomogeneous_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
29: {
30: PetscInt d;
31: *u = 0.0;
32: for (d = 0; d < dim; ++d) *u += PetscSinReal(2.0 * PETSC_PI * x[d]);
33: return PETSC_SUCCESS;
34: }
36: static PetscErrorCode trig_homogeneous_u(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nc, PetscScalar *u, PetscCtx ctx)
37: {
38: PetscInt d;
39: *u = 1.0;
40: for (d = 0; d < dim; ++d) *u *= PetscSinReal(2.0 * PETSC_PI * x[d]);
41: return PETSC_SUCCESS;
42: }
44: /* Compute integral of (residual of solution)*(adjoint solution - projection of adjoint solution) */
45: static void obj_error_u(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 obj[])
46: {
47: obj[0] = a[aOff[0]] * (u[0] - a[aOff[1]]);
48: }
50: static void f0_trig_inhomogeneous_u(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[])
51: {
52: PetscInt d;
53: for (d = 0; d < dim; ++d) f0[0] += -4.0 * PetscSqr(PETSC_PI) * PetscSinReal(2.0 * PETSC_PI * x[d]);
54: }
56: static void f0_trig_homogeneous_u(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[])
57: {
58: for (PetscInt d = 0; d < dim; ++d) {
59: PetscScalar v = 1.;
60: for (PetscInt e = 0; e < dim; e++) {
61: if (e == d) {
62: v *= -4.0 * PetscSqr(PETSC_PI) * PetscSinReal(2.0 * PETSC_PI * x[d]);
63: } else {
64: v *= PetscSinReal(2.0 * PETSC_PI * x[d]);
65: }
66: }
67: f0[0] += v;
68: }
69: }
71: static void f0_unity_u(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[])
72: {
73: f0[0] = 1.0;
74: }
76: static void f0_identityaux_u(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[])
77: {
78: f0[0] = a[0];
79: }
81: static void f1_u(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[])
82: {
83: for (PetscInt d = 0; d < dim; ++d) f1[d] = u_x[d];
84: }
86: static void g3_uu(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 g3[])
87: {
88: for (PetscInt d = 0; d < dim; ++d) g3[d * dim + d] = 1.0;
89: }
91: PLEXFE_QFUNCTION(Laplace, f0_trig_inhomogeneous_u, f1_u)
93: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
94: {
95: PetscFunctionBeginUser;
96: options->shear = PETSC_FALSE;
97: options->spectral = PETSC_FALSE;
98: options->adjoint = PETSC_FALSE;
99: options->homogeneous = PETSC_FALSE;
100: options->viewError = PETSC_FALSE;
102: PetscOptionsBegin(comm, "", "Poisson Problem Options", "DMPLEX");
103: PetscCall(PetscOptionsBool("-shear", "Shear the domain", "ex13.c", options->shear, &options->shear, NULL));
104: PetscCall(PetscOptionsBool("-spectral", "Look at the spectrum along planes of the solution", "ex13.c", options->spectral, &options->spectral, NULL));
105: PetscCall(PetscOptionsBool("-adjoint", "Solve the adjoint problem", "ex13.c", options->adjoint, &options->adjoint, NULL));
106: PetscCall(PetscOptionsBool("-homogeneous", "Use homogeneous boundary conditions", "ex13.c", options->homogeneous, &options->homogeneous, NULL));
107: PetscCall(PetscOptionsBool("-error_view", "Output the solution error", "ex13.c", options->viewError, &options->viewError, NULL));
108: PetscOptionsEnd();
109: PetscFunctionReturn(PETSC_SUCCESS);
110: }
112: static PetscErrorCode CreateSpectralPlanes(DM dm, PetscInt numPlanes, const PetscInt planeDir[], const PetscReal planeCoord[], AppCtx *user)
113: {
114: PetscSection coordSection;
115: Vec coordinates;
116: const PetscScalar *coords;
117: PetscInt dim, p, vStart, vEnd, v;
119: PetscFunctionBeginUser;
120: PetscCall(DMGetCoordinateDim(dm, &dim));
121: PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
122: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
123: PetscCall(DMGetCoordinateSection(dm, &coordSection));
124: PetscCall(VecGetArrayRead(coordinates, &coords));
125: for (p = 0; p < numPlanes; ++p) {
126: DMLabel label;
127: char name[PETSC_MAX_PATH_LEN];
129: PetscCall(PetscSNPrintf(name, PETSC_MAX_PATH_LEN, "spectral_plane_%" PetscInt_FMT, p));
130: PetscCall(DMCreateLabel(dm, name));
131: PetscCall(DMGetLabel(dm, name, &label));
132: PetscCall(DMLabelAddStratum(label, 1));
133: for (v = vStart; v < vEnd; ++v) {
134: PetscInt off;
136: PetscCall(PetscSectionGetOffset(coordSection, v, &off));
137: if (PetscAbsReal(planeCoord[p] - PetscRealPart(coords[off + planeDir[p]])) < PETSC_SMALL) PetscCall(DMLabelSetValue(label, v, 1));
138: }
139: }
140: PetscCall(VecRestoreArrayRead(coordinates, &coords));
141: PetscFunctionReturn(PETSC_SUCCESS);
142: }
144: static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
145: {
146: PetscFunctionBeginUser;
147: PetscCall(DMCreate(comm, dm));
148: PetscCall(DMSetType(*dm, DMPLEX));
149: PetscCall(DMSetFromOptions(*dm));
150: if (user->shear) PetscCall(DMPlexShearGeometry(*dm, DM_X, NULL));
151: PetscCall(DMSetApplicationContext(*dm, user));
152: PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
153: if (user->spectral) {
154: PetscInt planeDir[2] = {0, 1};
155: PetscReal planeCoord[2] = {0., 1.};
157: PetscCall(CreateSpectralPlanes(*dm, 2, planeDir, planeCoord, user));
158: }
159: PetscFunctionReturn(PETSC_SUCCESS);
160: }
162: static PetscErrorCode SetupPrimalProblem(DM dm, AppCtx *user)
163: {
164: PetscDS ds;
165: DMLabel label;
166: const PetscInt id = 1;
167: PetscPointFn *f0 = user->homogeneous ? f0_trig_homogeneous_u : f0_trig_inhomogeneous_u;
168: PetscErrorCode (*ex)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = user->homogeneous ? trig_homogeneous_u : trig_inhomogeneous_u;
170: PetscFunctionBeginUser;
171: PetscCall(DMGetDS(dm, &ds));
172: PetscCall(PetscDSSetResidual(ds, 0, f0, f1_u));
173: PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu));
174: PetscCall(PetscDSSetExactSolution(ds, 0, ex, user));
175: PetscCall(DMGetLabel(dm, "marker", &label));
176: if (label) PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (PetscVoidFn *)ex, NULL, user, NULL));
177: PetscFunctionReturn(PETSC_SUCCESS);
178: }
180: static PetscErrorCode SetupAdjointProblem(DM dm, AppCtx *user)
181: {
182: PetscDS ds;
183: DMLabel label;
184: const PetscInt id = 1;
186: PetscFunctionBeginUser;
187: PetscCall(DMGetDS(dm, &ds));
188: PetscCall(PetscDSSetResidual(ds, 0, f0_unity_u, f1_u));
189: PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, g3_uu));
190: PetscCall(PetscDSSetObjective(ds, 0, obj_error_u));
191: PetscCall(DMGetLabel(dm, "marker", &label));
192: PetscCall(DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (PetscVoidFn *)zero, NULL, user, NULL));
193: PetscFunctionReturn(PETSC_SUCCESS);
194: }
196: static PetscErrorCode SetupErrorProblem(DM dm, AppCtx *user)
197: {
198: PetscDS prob;
200: PetscFunctionBeginUser;
201: PetscCall(DMGetDS(dm, &prob));
202: PetscFunctionReturn(PETSC_SUCCESS);
203: }
205: static PetscErrorCode SetupDiscretization(DM dm, const char name[], PetscErrorCode (*setup)(DM, AppCtx *), AppCtx *user)
206: {
207: DM cdm = dm;
208: PetscFE fe;
209: DMPolytopeType ct;
210: PetscBool simplex;
211: PetscInt dim, cStart;
212: char prefix[PETSC_MAX_PATH_LEN];
214: PetscFunctionBeginUser;
215: PetscCall(DMGetDimension(dm, &dim));
216: PetscCall(DMPlexGetHeightStratum(dm, 0, &cStart, NULL));
217: PetscCall(DMPlexGetCellType(dm, cStart, &ct));
218: simplex = DMPolytopeTypeGetNumVertices(ct) == DMPolytopeTypeGetDim(ct) + 1 ? PETSC_TRUE : PETSC_FALSE;
219: /* Create finite element */
220: PetscCall(PetscSNPrintf(prefix, PETSC_MAX_PATH_LEN, "%s_", name));
221: PetscCall(PetscFECreateDefault(PETSC_COMM_SELF, dim, 1, simplex, name ? prefix : NULL, -1, &fe));
222: PetscCall(PetscObjectSetName((PetscObject)fe, name));
223: /* Set discretization and boundary conditions for each mesh */
224: PetscCall(DMSetField(dm, 0, NULL, (PetscObject)fe));
225: PetscCall(DMCreateDS(dm));
226: PetscCall((*setup)(dm, user));
227: while (cdm) {
228: PetscCall(DMCopyDisc(dm, cdm));
229: /* TODO: Check whether the boundary of coarse meshes is marked */
230: PetscCall(DMGetCoarseDM(cdm, &cdm));
231: }
232: PetscCall(PetscFEDestroy(&fe));
233: #ifdef PETSC_HAVE_LIBCEED
234: PetscBool useCeed;
235: PetscCall(DMPlexGetUseCeed(dm, &useCeed));
236: if (useCeed) PetscCall(DMCeedCreate(dm, PETSC_TRUE, PlexQFunctionLaplace, PlexQFunctionLaplace_loc));
237: #endif
238: PetscFunctionReturn(PETSC_SUCCESS);
239: }
241: static PetscErrorCode ComputeSpectral(Vec u, PetscInt numPlanes, const PetscInt planeDir[], const PetscReal planeCoord[], AppCtx *user)
242: {
243: MPI_Comm comm;
244: DM dm;
245: PetscSection coordSection, section;
246: Vec coordinates, uloc;
247: const PetscScalar *coords, *array;
248: PetscMPIInt size, rank;
250: PetscFunctionBeginUser;
251: if (!user->spectral) PetscFunctionReturn(PETSC_SUCCESS);
252: PetscCall(VecGetDM(u, &dm));
253: PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
254: PetscCallMPI(MPI_Comm_size(comm, &size));
255: PetscCallMPI(MPI_Comm_rank(comm, &rank));
256: PetscCall(DMGetLocalVector(dm, &uloc));
257: PetscCall(DMGlobalToLocalBegin(dm, u, INSERT_VALUES, uloc));
258: PetscCall(DMGlobalToLocalEnd(dm, u, INSERT_VALUES, uloc));
259: PetscCall(DMPlexInsertBoundaryValues(dm, PETSC_TRUE, uloc, 0.0, NULL, NULL, NULL));
260: PetscCall(VecViewFromOptions(uloc, NULL, "-sol_view"));
261: PetscCall(DMGetLocalSection(dm, §ion));
262: PetscCall(VecGetArrayRead(uloc, &array));
263: PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
264: PetscCall(DMGetCoordinateSection(dm, &coordSection));
265: PetscCall(VecGetArrayRead(coordinates, &coords));
266: for (PetscInt p = 0; p < numPlanes; ++p) {
267: DMLabel label;
268: char name[PETSC_MAX_PATH_LEN];
269: Mat F;
270: Vec x, y;
271: IS stratum;
272: PetscReal *ray, *gray;
273: PetscScalar *rvals, *svals, *gsvals;
274: PetscInt *perm, *nperm;
275: PetscInt n, N, i, j, off, offu;
276: PetscMPIInt in;
277: const PetscInt *points;
279: PetscCall(PetscSNPrintf(name, PETSC_MAX_PATH_LEN, "spectral_plane_%" PetscInt_FMT, p));
280: PetscCall(DMGetLabel(dm, name, &label));
281: PetscCall(DMLabelGetStratumIS(label, 1, &stratum));
282: PetscCall(ISGetLocalSize(stratum, &n));
283: PetscCall(PetscMPIIntCast(n, &in));
284: PetscCall(ISGetIndices(stratum, &points));
285: PetscCall(PetscMalloc2(n, &ray, n, &svals));
286: for (i = 0; i < n; ++i) {
287: PetscCall(PetscSectionGetOffset(coordSection, points[i], &off));
288: PetscCall(PetscSectionGetOffset(section, points[i], &offu));
289: ray[i] = PetscRealPart(coords[off + ((planeDir[p] + 1) % 2)]);
290: svals[i] = array[offu];
291: }
292: /* Gather the ray data to proc 0 */
293: if (size > 1) {
294: PetscMPIInt *cnt, *displs;
296: PetscCall(PetscCalloc2(size, &cnt, size, &displs));
297: PetscCallMPI(MPI_Gather(&n, 1, MPIU_INT, cnt, 1, MPIU_INT, 0, comm));
298: for (PetscInt p = 1; p < size; ++p) displs[p] = displs[p - 1] + cnt[p - 1];
299: N = displs[size - 1] + cnt[size - 1];
300: PetscCall(PetscMalloc2(N, &gray, N, &gsvals));
301: PetscCallMPI(MPI_Gatherv(ray, in, MPIU_REAL, gray, cnt, displs, MPIU_REAL, 0, comm));
302: PetscCallMPI(MPI_Gatherv(svals, in, MPIU_SCALAR, gsvals, cnt, displs, MPIU_SCALAR, 0, comm));
303: PetscCall(PetscFree2(cnt, displs));
304: } else {
305: N = n;
306: gray = ray;
307: gsvals = svals;
308: }
309: if (rank == 0) {
310: /* Sort point along ray */
311: PetscCall(PetscMalloc2(N, &perm, N, &nperm));
312: for (i = 0; i < N; ++i) perm[i] = i;
313: PetscCall(PetscSortRealWithPermutation(N, gray, perm));
314: /* Count duplicates and squish mapping */
315: nperm[0] = perm[0];
316: for (i = 1, j = 1; i < N; ++i) {
317: if (PetscAbsReal(gray[perm[i]] - gray[perm[i - 1]]) > PETSC_SMALL) nperm[j++] = perm[i];
318: }
319: /* Create FFT structs */
320: PetscCall(MatCreateFFT(PETSC_COMM_SELF, 1, &j, MATFFTW, &F));
321: PetscCall(MatCreateVecs(F, &x, &y));
322: PetscCall(PetscObjectSetName((PetscObject)y, name));
323: PetscCall(VecGetArray(x, &rvals));
324: for (i = 0, j = 0; i < N; ++i) {
325: if (i > 0 && PetscAbsReal(gray[perm[i]] - gray[perm[i - 1]]) < PETSC_SMALL) continue;
326: rvals[j] = gsvals[nperm[j]];
327: ++j;
328: }
329: PetscCall(PetscFree2(perm, nperm));
330: if (size > 1) PetscCall(PetscFree2(gray, gsvals));
331: PetscCall(VecRestoreArray(x, &rvals));
332: /* Do FFT along the ray */
333: PetscCall(MatMult(F, x, y));
334: /* Chop FFT */
335: PetscCall(VecFilter(y, PETSC_SMALL));
336: PetscCall(VecViewFromOptions(x, NULL, "-real_view"));
337: PetscCall(VecViewFromOptions(y, NULL, "-fft_view"));
338: PetscCall(VecDestroy(&x));
339: PetscCall(VecDestroy(&y));
340: PetscCall(MatDestroy(&F));
341: }
342: PetscCall(ISRestoreIndices(stratum, &points));
343: PetscCall(ISDestroy(&stratum));
344: PetscCall(PetscFree2(ray, svals));
345: }
346: PetscCall(VecRestoreArrayRead(coordinates, &coords));
347: PetscCall(VecRestoreArrayRead(uloc, &array));
348: PetscCall(DMRestoreLocalVector(dm, &uloc));
349: PetscFunctionReturn(PETSC_SUCCESS);
350: }
352: static PetscErrorCode ComputeAdjoint(Vec u, AppCtx *user)
353: {
354: PetscFunctionBegin;
355: if (!user->adjoint) PetscFunctionReturn(PETSC_SUCCESS);
356: DM dm, dmAdj;
357: SNES snesAdj;
358: Vec uAdj;
360: PetscCall(VecGetDM(u, &dm));
361: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snesAdj));
362: PetscCall(PetscObjectSetOptionsPrefix((PetscObject)snesAdj, "adjoint_"));
363: PetscCall(DMClone(dm, &dmAdj));
364: PetscCall(SNESSetDM(snesAdj, dmAdj));
365: PetscCall(SetupDiscretization(dmAdj, "adjoint", SetupAdjointProblem, user));
366: PetscCall(DMCreateGlobalVector(dmAdj, &uAdj));
367: PetscCall(PetscObjectSetName((PetscObject)uAdj, "adjoint"));
368: PetscCall(DMPlexSetSNESLocalFEM(dmAdj, PETSC_FALSE, &user));
369: PetscCall(SNESSetFromOptions(snesAdj));
370: PetscCall(SNESSolve(snesAdj, NULL, uAdj));
371: PetscCall(SNESGetSolution(snesAdj, &uAdj));
372: PetscCall(VecViewFromOptions(uAdj, NULL, "-adjoint_view"));
373: /* Error representation */
374: {
375: DM dmErr, dmErrAux, dms[2];
376: Vec errorEst, errorL2, uErr, uErrLoc, uAdjLoc, uAdjProj;
377: IS *subis;
378: PetscReal errorEstTot, errorL2Norm, errorL2Tot;
379: PetscInt N;
380: PetscErrorCode (*funcs[1])(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *) = {user->homogeneous ? trig_homogeneous_u : trig_inhomogeneous_u};
381: void (*identity[1])(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]) = {f0_identityaux_u};
382: PetscCtx ctxs[1] = {0};
384: ctxs[0] = user;
385: PetscCall(DMClone(dm, &dmErr));
386: PetscCall(SetupDiscretization(dmErr, "error", SetupErrorProblem, user));
387: PetscCall(DMGetGlobalVector(dmErr, &errorEst));
388: PetscCall(DMGetGlobalVector(dmErr, &errorL2));
389: /* Compute auxiliary data (solution and projection of adjoint solution) */
390: PetscCall(DMGetLocalVector(dmAdj, &uAdjLoc));
391: PetscCall(DMGlobalToLocalBegin(dmAdj, uAdj, INSERT_VALUES, uAdjLoc));
392: PetscCall(DMGlobalToLocalEnd(dmAdj, uAdj, INSERT_VALUES, uAdjLoc));
393: PetscCall(DMGetGlobalVector(dm, &uAdjProj));
394: PetscCall(DMSetAuxiliaryVec(dm, NULL, 0, 0, uAdjLoc));
395: PetscCall(DMProjectField(dm, 0.0, u, identity, INSERT_VALUES, uAdjProj));
396: PetscCall(DMSetAuxiliaryVec(dm, NULL, 0, 0, NULL));
397: PetscCall(DMRestoreLocalVector(dmAdj, &uAdjLoc));
398: /* Attach auxiliary data */
399: dms[0] = dm;
400: dms[1] = dm;
401: PetscCall(DMCreateSuperDM(dms, 2, &subis, &dmErrAux));
402: if (0) {
403: PetscSection sec;
405: PetscCall(DMGetLocalSection(dms[0], &sec));
406: PetscCall(PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD));
407: PetscCall(DMGetLocalSection(dms[1], &sec));
408: PetscCall(PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD));
409: PetscCall(DMGetLocalSection(dmErrAux, &sec));
410: PetscCall(PetscSectionView(sec, PETSC_VIEWER_STDOUT_WORLD));
411: }
412: PetscCall(DMViewFromOptions(dmErrAux, NULL, "-dm_err_view"));
413: PetscCall(ISViewFromOptions(subis[0], NULL, "-super_is_view"));
414: PetscCall(ISViewFromOptions(subis[1], NULL, "-super_is_view"));
415: PetscCall(DMGetGlobalVector(dmErrAux, &uErr));
416: PetscCall(VecViewFromOptions(u, NULL, "-map_vec_view"));
417: PetscCall(VecViewFromOptions(uAdjProj, NULL, "-map_vec_view"));
418: PetscCall(VecViewFromOptions(uErr, NULL, "-map_vec_view"));
419: PetscCall(VecISCopy(uErr, subis[0], SCATTER_FORWARD, u));
420: PetscCall(VecISCopy(uErr, subis[1], SCATTER_FORWARD, uAdjProj));
421: PetscCall(DMRestoreGlobalVector(dm, &uAdjProj));
422: for (PetscInt i = 0; i < 2; ++i) PetscCall(ISDestroy(&subis[i]));
423: PetscCall(PetscFree(subis));
424: PetscCall(DMGetLocalVector(dmErrAux, &uErrLoc));
425: PetscCall(DMGlobalToLocalBegin(dm, uErr, INSERT_VALUES, uErrLoc));
426: PetscCall(DMGlobalToLocalEnd(dm, uErr, INSERT_VALUES, uErrLoc));
427: PetscCall(DMRestoreGlobalVector(dmErrAux, &uErr));
428: PetscCall(DMSetAuxiliaryVec(dmAdj, NULL, 0, 0, uErrLoc));
429: /* Compute cellwise error estimate */
430: PetscCall(VecSet(errorEst, 0.0));
431: PetscCall(DMPlexComputeCellwiseIntegralFEM(dmAdj, uAdj, errorEst, user));
432: PetscCall(DMSetAuxiliaryVec(dmAdj, NULL, 0, 0, NULL));
433: PetscCall(DMRestoreLocalVector(dmErrAux, &uErrLoc));
434: PetscCall(DMDestroy(&dmErrAux));
435: /* Plot cellwise error vector */
436: PetscCall(VecViewFromOptions(errorEst, NULL, "-error_view"));
437: /* Compute ratio of estimate (sum over cells) with actual L_2 error */
438: PetscCall(DMComputeL2Diff(dm, 0.0, funcs, ctxs, u, &errorL2Norm));
439: PetscCall(DMPlexComputeL2DiffVec(dm, 0.0, funcs, ctxs, u, errorL2));
440: PetscCall(VecViewFromOptions(errorL2, NULL, "-l2_error_view"));
441: PetscCall(VecNorm(errorL2, NORM_INFINITY, &errorL2Tot));
442: PetscCall(VecNorm(errorEst, NORM_INFINITY, &errorEstTot));
443: PetscCall(VecGetSize(errorEst, &N));
444: PetscCall(VecPointwiseDivide(errorEst, errorEst, errorL2));
445: PetscCall(PetscObjectSetName((PetscObject)errorEst, "Error ratio"));
446: PetscCall(VecViewFromOptions(errorEst, NULL, "-error_ratio_view"));
447: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "N: %" PetscInt_FMT " L2 error: %g Error Ratio: %g/%g = %g\n", N, (double)errorL2Norm, (double)errorEstTot, (double)PetscSqrtReal(errorL2Tot), (double)(errorEstTot / PetscSqrtReal(errorL2Tot))));
448: PetscCall(DMRestoreGlobalVector(dmErr, &errorEst));
449: PetscCall(DMRestoreGlobalVector(dmErr, &errorL2));
450: PetscCall(DMDestroy(&dmErr));
451: }
452: PetscCall(DMDestroy(&dmAdj));
453: PetscCall(VecDestroy(&uAdj));
454: PetscCall(SNESDestroy(&snesAdj));
455: PetscFunctionReturn(PETSC_SUCCESS);
456: }
458: static PetscErrorCode ErrorView(Vec u, AppCtx *user)
459: {
460: PetscErrorCode (*sol)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar[], void *);
461: void *ctx;
462: DM dm;
463: PetscDS ds;
464: PetscReal error;
465: PetscInt N;
467: PetscFunctionBegin;
468: if (!user->viewError) PetscFunctionReturn(PETSC_SUCCESS);
469: PetscCall(VecGetDM(u, &dm));
470: PetscCall(DMGetDS(dm, &ds));
471: PetscCall(PetscDSGetExactSolution(ds, 0, &sol, &ctx));
472: PetscCall(VecGetSize(u, &N));
473: PetscCall(DMComputeL2Diff(dm, 0.0, &sol, &ctx, u, &error));
474: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "N: %" PetscInt_FMT " L2 error: %g\n", N, (double)error));
475: PetscFunctionReturn(PETSC_SUCCESS);
476: }
478: int main(int argc, char **argv)
479: {
480: DM dm; /* Problem specification */
481: SNES snes; /* Nonlinear solver */
482: Vec u; /* Solutions */
483: AppCtx user; /* User-defined work context */
484: PetscInt planeDir[2] = {0, 1};
485: PetscReal planeCoord[2] = {0., 1.};
487: PetscFunctionBeginUser;
488: PetscCall(PetscInitialize(&argc, &argv, NULL, help));
489: PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
490: /* Primal system */
491: PetscCall(SNESCreate(PETSC_COMM_WORLD, &snes));
492: PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
493: PetscCall(SNESSetDM(snes, dm));
494: PetscCall(SetupDiscretization(dm, "potential", SetupPrimalProblem, &user));
495: PetscCall(DMCreateGlobalVector(dm, &u));
496: PetscCall(PetscObjectSetName((PetscObject)u, "potential"));
497: PetscCall(DMPlexSetSNESLocalFEM(dm, PETSC_FALSE, &user));
498: PetscCall(SNESSetFromOptions(snes));
499: PetscCall(SNESSolve(snes, NULL, u));
500: PetscCall(SNESGetSolution(snes, &u));
501: PetscCall(VecViewFromOptions(u, NULL, "-potential_view"));
502: PetscCall(ErrorView(u, &user));
503: PetscCall(ComputeSpectral(u, 2, planeDir, planeCoord, &user));
504: PetscCall(ComputeAdjoint(u, &user));
505: /* Cleanup */
506: PetscCall(VecDestroy(&u));
507: PetscCall(SNESDestroy(&snes));
508: PetscCall(DMDestroy(&dm));
509: PetscCall(PetscFinalize());
510: return 0;
511: }
513: /*TEST
515: test:
516: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9
517: suffix: 2d_p1_conv
518: requires: triangle
519: args: -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2
520: test:
521: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9
522: suffix: 2d_p2_conv
523: requires: triangle
524: args: -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2
525: test:
526: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9
527: suffix: 2d_p3_conv
528: requires: triangle
529: args: -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 2
530: test:
531: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9
532: suffix: 2d_q1_conv
533: args: -dm_plex_simplex 0 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2
534: test:
535: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9
536: suffix: 2d_q2_conv
537: args: -dm_plex_simplex 0 -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2
538: test:
539: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9
540: suffix: 2d_q3_conv
541: args: -dm_plex_simplex 0 -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 2
542: test:
543: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9
544: suffix: 2d_q1_ceed_conv
545: requires: libceed
546: args: -dm_plex_use_ceed -dm_plex_simplex 0 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2
547: test:
548: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9
549: suffix: 2d_q2_ceed_conv
550: requires: libceed
551: args: -dm_plex_use_ceed -dm_plex_simplex 0 -potential_petscspace_degree 2 -cdm_default_quadrature_order 2 \
552: -snes_convergence_estimate -convest_num_refine 2
553: test:
554: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9
555: suffix: 2d_q3_ceed_conv
556: requires: libceed
557: args: -dm_plex_use_ceed -dm_plex_simplex 0 -potential_petscspace_degree 3 -cdm_default_quadrature_order 3 \
558: -snes_convergence_estimate -convest_num_refine 2
559: test:
560: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.9
561: suffix: 2d_q1_shear_conv
562: args: -dm_plex_simplex 0 -shear -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 2
563: test:
564: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.9
565: suffix: 2d_q2_shear_conv
566: args: -dm_plex_simplex 0 -shear -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 2
567: test:
568: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 3.9
569: suffix: 2d_q3_shear_conv
570: args: -dm_plex_simplex 0 -shear -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 2
571: test:
572: # Using -convest_num_refine 3 we get L_2 convergence rate: 1.7
573: suffix: 3d_p1_conv
574: requires: ctetgen
575: args: -dm_plex_dim 3 -dm_refine 1 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1
576: test:
577: # Using -dm_refine 1 -convest_num_refine 3 we get L_2 convergence rate: 2.8
578: suffix: 3d_p2_conv
579: requires: ctetgen
580: args: -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 1
581: test:
582: # Using -dm_refine 1 -convest_num_refine 3 we get L_2 convergence rate: 4.0
583: suffix: 3d_p3_conv
584: requires: ctetgen
585: args: -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 1
586: test:
587: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 1.8
588: suffix: 3d_q1_conv
589: args: -dm_plex_dim 3 -dm_plex_simplex 0 -dm_refine 1 -potential_petscspace_degree 1 -snes_convergence_estimate -convest_num_refine 1
590: test:
591: # Using -dm_refine 2 -convest_num_refine 3 we get L_2 convergence rate: 2.8
592: suffix: 3d_q2_conv
593: args: -dm_plex_dim 3 -dm_plex_simplex 0 -potential_petscspace_degree 2 -snes_convergence_estimate -convest_num_refine 1
594: test:
595: # Using -dm_refine 1 -convest_num_refine 3 we get L_2 convergence rate: 3.8
596: suffix: 3d_q3_conv
597: args: -dm_plex_dim 3 -dm_plex_simplex 0 -potential_petscspace_degree 3 -snes_convergence_estimate -convest_num_refine 1
598: test:
599: suffix: 2d_p1_fas_full
600: requires: triangle
601: args: -potential_petscspace_degree 1 -dm_refine_hierarchy 5 \
602: -snes_max_it 1 -snes_type fas -snes_fas_levels 5 -snes_fas_type full -snes_fas_full_total \
603: -fas_coarse_snes_monitor -fas_coarse_snes_max_it 1 -fas_coarse_ksp_atol 1.e-13 \
604: -fas_levels_snes_monitor -fas_levels_snes_max_it 1 -fas_levels_snes_type newtonls \
605: -fas_levels_pc_type none -fas_levels_ksp_max_it 2 -fas_levels_ksp_converged_maxits -fas_levels_ksp_type chebyshev \
606: -fas_levels_esteig_ksp_type cg -fas_levels_ksp_chebyshev_esteig 0,0.25,0,1.1 -fas_levels_esteig_ksp_max_it 10
607: test:
608: suffix: 2d_p1_fas_full_homogeneous
609: requires: triangle
610: args: -homogeneous -potential_petscspace_degree 1 -dm_refine_hierarchy 5 \
611: -snes_max_it 1 -snes_type fas -snes_fas_levels 5 -snes_fas_type full \
612: -fas_coarse_snes_monitor -fas_coarse_snes_max_it 1 -fas_coarse_ksp_atol 1.e-13 \
613: -fas_levels_snes_monitor -fas_levels_snes_max_it 1 -fas_levels_snes_type newtonls \
614: -fas_levels_pc_type none -fas_levels_ksp_max_it 2 -fas_levels_ksp_converged_maxits -fas_levels_ksp_type chebyshev \
615: -fas_levels_esteig_ksp_type cg -fas_levels_ksp_chebyshev_esteig 0,0.25,0,1.1 -fas_levels_esteig_ksp_max_it 10
617: test:
618: suffix: 2d_p1_scalable
619: requires: triangle
620: args: -potential_petscspace_degree 1 -dm_refine 3 \
621: -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned \
622: -pc_type gamg -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 \
623: -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 \
624: -pc_gamg_coarse_eq_limit 1000 \
625: -pc_gamg_threshold 0.05 \
626: -pc_gamg_threshold_scale .0 \
627: -mg_levels_ksp_type chebyshev \
628: -mg_levels_ksp_max_it 1 \
629: -mg_levels_pc_type jacobi \
630: -matptap_via scalable
631: output_file: output/empty.out
632: test:
633: suffix: 2d_p1_gmg_vcycle
634: requires: triangle
635: output_file: output/empty.out
636: args: -potential_petscspace_degree 1 -dm_plex_box_faces 2,2 -dm_refine_hierarchy 3 \
637: -ksp_rtol 5e-10 -pc_type mg \
638: -mg_levels_ksp_max_it 1 \
639: -mg_levels_esteig_ksp_type cg \
640: -mg_levels_esteig_ksp_max_it 10 \
641: -mg_levels_ksp_chebyshev_esteig 0,0.1,0,1.1 \
642: -mg_levels_pc_type jacobi
643: # Run with -dm_refine_hierarchy 3 to get a better idea of the solver
644: testset:
645: args: -potential_petscspace_degree 1 -dm_refine_hierarchy 2 \
646: -ksp_rtol 5e-10 -pc_type mg -pc_mg_type full \
647: -mg_levels_ksp_max_it 2 \
648: -mg_levels_esteig_ksp_type cg \
649: -mg_levels_esteig_ksp_max_it 10 \
650: -mg_levels_ksp_chebyshev_esteig 0,0.1,0,1.1 \
651: -mg_levels_pc_type jacobi
652: output_file: output/empty.out
653: test:
654: suffix: 2d_p1_gmg_fcycle
655: requires: triangle
656: args: -dm_plex_box_faces 2,2
657: test:
658: suffix: 2d_q1_gmg_fcycle
659: args: -dm_plex_simplex 0 -dm_plex_box_faces 2,2
660: test:
661: suffix: 3d_p1_gmg_fcycle
662: requires: ctetgen
663: args: -dm_plex_dim 3 -dm_plex_box_faces 2,2,1
664: test:
665: suffix: 3d_q1_gmg_fcycle
666: args: -dm_plex_dim 3 -dm_plex_simplex 0 -dm_plex_box_faces 2,2,1
667: test:
668: suffix: 2d_p1_gmg_vcycle_adapt
669: requires: triangle
670: output_file: output/empty.out
671: args: -petscpartitioner_type simple -potential_petscspace_degree 1 -dm_plex_box_faces 2,2 -dm_refine_hierarchy 3 \
672: -ksp_rtol 5e-10 -pc_type mg -pc_mg_galerkin -pc_mg_adapt_interp_coarse_space harmonic -pc_mg_adapt_interp_n 8 \
673: -mg_levels_ksp_max_it 1 \
674: -mg_levels_esteig_ksp_type cg \
675: -mg_levels_esteig_ksp_max_it 10 \
676: -mg_levels_ksp_chebyshev_esteig 0,0.1,0,1.1 \
677: -mg_levels_pc_type jacobi
678: test:
679: suffix: 2d_p1_spectral_0
680: requires: triangle fftw !complex
681: args: -dm_plex_box_faces 1,1 -potential_petscspace_degree 1 -dm_refine 6 -spectral -fft_view
682: test:
683: suffix: 2d_p1_spectral_1
684: requires: triangle fftw !complex
685: nsize: 2
686: args: -dm_plex_box_faces 4,4 -potential_petscspace_degree 1 -spectral -fft_view
687: test:
688: suffix: 2d_p1_adj_0
689: requires: triangle
690: args: -potential_petscspace_degree 1 -dm_refine 1 -adjoint -adjoint_petscspace_degree 1 -error_petscspace_degree 0
691: test:
692: nsize: 2
693: requires: kokkos_kernels
694: suffix: kokkos
695: args: -dm_plex_dim 3 -dm_plex_box_faces 2,3,6 -petscpartitioner_type simple -dm_plex_simplex 0 -potential_petscspace_degree 1 \
696: -dm_refine 0 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -pc_type gamg -pc_gamg_coarse_eq_limit 1000 -pc_gamg_threshold 0.0 \
697: -pc_gamg_threshold_scale .5 -mg_levels_ksp_type chebyshev -mg_levels_ksp_max_it 2 -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 \
698: -ksp_monitor -snes_monitor -dm_view -dm_mat_type aijkokkos -dm_vec_type kokkos
700: TEST*/