Actual source code: ex77.c

  1: static char help[] = "Nonlinear elasticity problem in 3d with simplicial finite elements.\n\
2: We solve a nonlinear elasticity problem, modelled as an incompressible Neo-Hookean solid, \n\
3:  with pressure loading in a rectangular domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n";

5: /*
6: Nonlinear elasticity problem, which we discretize using the finite
7: element method on an unstructured mesh. This uses both Dirichlet boundary conditions (fixed faces)
9: The Lagrangian density (modulo boundary conditions) for this problem is given by
10:
11:   \frac{\mu}{2} (\mathrm{Tr}{C}-3) + J p + \frac{\kappa}{2} (J-1).
12:

14: Discretization:

16: We use PetscFE to generate a tabulation of the finite element basis functions
17: at quadrature points. We can currently generate an arbitrary order Lagrange
18: element.

20: Field Data:

22:   DMPLEX data is organized by point, and the closure operation just stacks up the
23: data from each sieve point in the closure. Thus, for a P_2-P_1 Stokes element, we
24: have

26:   cl{e} = {f e_0 e_1 e_2 v_0 v_1 v_2}
27:   x     = [u_{e_0} v_{e_0} u_{e_1} v_{e_1} u_{e_2} v_{e_2} u_{v_0} v_{v_0} p_{v_0} u_{v_1} v_{v_1} p_{v_1} u_{v_2} v_{v_2} p_{v_2}]

29: The problem here is that we would like to loop over each field separately for
30: integration. Therefore, the closure visitor in DMPlexVecGetClosure() reorders
31: the data so that each field is contiguous

33:   x'    = [u_{e_0} v_{e_0} u_{e_1} v_{e_1} u_{e_2} v_{e_2} u_{v_0} v_{v_0} u_{v_1} v_{v_1} u_{v_2} v_{v_2} p_{v_0} p_{v_1} p_{v_2}]

35: Likewise, DMPlexVecSetClosure() takes data partitioned by field, and correctly
36: puts it into the Sieve ordering.

38: */

40: #include <petscdmplex.h>
41: #include <petscsnes.h>
42: #include <petscds.h>

44: typedef enum {RUN_FULL, RUN_TEST} RunType;

46: typedef struct {
47:   RunType   runType; /* Whether to run tests, or solve the full problem */
48:   PetscReal mu;      /* The shear modulus */
49:   PetscReal p_wall;  /* The wall pressure */
50: } AppCtx;

52: #if 0
53: PETSC_STATIC_INLINE void Det2D(PetscReal *detJ, const PetscReal J[])
54: {
55:   *detJ = J[0]*J[3] - J[1]*J[2];
56: }
57: #endif

59: PETSC_STATIC_INLINE void Det3D(PetscReal *detJ, const PetscScalar J[])
60: {
61:   *detJ = PetscRealPart(J[0*3+0]*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]) +
62:                         J[0*3+1]*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]) +
63:                         J[0*3+2]*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]));
64: }

66: #if 0
67: PETSC_STATIC_INLINE void Cof2D(PetscReal C[], const PetscReal A[])
68: {
69:   C[0] =  A[3];
70:   C[1] = -A[2];
71:   C[2] = -A[1];
72:   C[3] =  A[0];
73: }
74: #endif

76: PETSC_STATIC_INLINE void Cof3D(PetscReal C[], const PetscScalar A[])
77: {
78:   C[0*3+0] = PetscRealPart(A[1*3+1]*A[2*3+2] - A[1*3+2]*A[2*3+1]);
79:   C[0*3+1] = PetscRealPart(A[1*3+2]*A[2*3+0] - A[1*3+0]*A[2*3+2]);
80:   C[0*3+2] = PetscRealPart(A[1*3+0]*A[2*3+1] - A[1*3+1]*A[2*3+0]);
81:   C[1*3+0] = PetscRealPart(A[0*3+2]*A[2*3+1] - A[0*3+1]*A[2*3+2]);
82:   C[1*3+1] = PetscRealPart(A[0*3+0]*A[2*3+2] - A[0*3+2]*A[2*3+0]);
83:   C[1*3+2] = PetscRealPart(A[0*3+1]*A[2*3+0] - A[0*3+0]*A[2*3+1]);
84:   C[2*3+0] = PetscRealPart(A[0*3+1]*A[1*3+2] - A[0*3+2]*A[1*3+1]);
85:   C[2*3+1] = PetscRealPart(A[0*3+2]*A[1*3+0] - A[0*3+0]*A[1*3+2]);
86:   C[2*3+2] = PetscRealPart(A[0*3+0]*A[1*3+1] - A[0*3+1]*A[1*3+0]);
87: }

89: PetscErrorCode zero_scalar(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
90: {
91:   u[0] = 0.0;
92:   return 0;
93: }

95: PetscErrorCode zero_vector(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
96: {
97:   const PetscInt Ncomp = dim;

99:   PetscInt       comp;
100:   for (comp = 0; comp < Ncomp; ++comp) u[comp] = 0.0;
101:   return 0;
102: }

104: PetscErrorCode coordinates(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
105: {
106:   const PetscInt Ncomp = dim;

108:   PetscInt       comp;
109:   for (comp = 0; comp < Ncomp; ++comp) u[comp] = x[comp];
110:   return 0;
111: }

113: PetscErrorCode elasticityMaterial(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
114: {
115:   AppCtx *user = (AppCtx *) ctx;
116:   u[0] = user->mu;
117:   return 0;
118: }

120: PetscErrorCode wallPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
121: {
122:   AppCtx *user = (AppCtx *) ctx;
123:   u[0] = user->p_wall;
124:   return 0;
125: }

127: void f1_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
128:           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
129:           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
130:           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
131: {
132:   const PetscInt  Ncomp = dim;
133:   const PetscReal mu = PetscRealPart(a[0]), kappa = 3.0;
134:   PetscReal       cofu_x[9/*Ncomp*dim*/], detu_x, p = PetscRealPart(u[Ncomp]);
135:   PetscInt        comp, d;

137:   Cof3D(cofu_x, u_x);
138:   Det3D(&detu_x, u_x);
139:   p += kappa * (detu_x - 1.0);

141:   /* f1 is the first Piola-Kirchhoff tensor */
142:   for (comp = 0; comp < Ncomp; ++comp) {
143:     for (d = 0; d < dim; ++d) {
144:       f1[comp*dim+d] = mu * u_x[comp*dim+d] + p * cofu_x[comp*dim+d];
145:     }
146:   }
147: }

149: void g3_uu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
150:           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
151:           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
152:           PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
153: {
154:   const PetscInt  Ncomp = dim;
155:   const PetscReal mu = PetscRealPart(a[0]), kappa = 3.0;
156:   PetscReal       cofu_x[9/*Ncomp*dim*/], detu_x, pp, pm, p = PetscRealPart(u[Ncomp]);
157:   PetscInt        compI, compJ, d1, d2;

159:   Cof3D(cofu_x, u_x);
160:   Det3D(&detu_x, u_x);
161:   p += kappa * (detu_x - 1.0);
162:   pp = p/detu_x + kappa;
163:   pm = p/detu_x;

165:   /* g3 is the first elasticity tensor, i.e. A_i^I_j^J = S^{IJ} g_{ij} + C^{KILJ} F^k_K F^l_L g_{kj} g_{li} */
166:   for (compI = 0; compI < Ncomp; ++compI) {
167:     for (compJ = 0; compJ < Ncomp; ++compJ) {
168:       const PetscReal G = (compI == compJ) ? 1.0 : 0.0;

170:       for (d1 = 0; d1 < dim; ++d1) {
171:         for (d2 = 0; d2 < dim; ++d2) {
172:           const PetscReal g = (d1 == d2) ? 1.0 : 0.0;

174:           g3[((compI*Ncomp+compJ)*dim+d1)*dim+d2] = g * G * mu + pp * cofu_x[compI*dim+d1] * cofu_x[compJ*dim+d2] - pm * cofu_x[compI*dim+d2] * cofu_x[compJ*dim+d1];
175:         }
176:       }
177:     }
178:   }
179: }

181: void f0_bd_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
182:     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
183:     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
184:     PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
185: {
186:   const PetscInt    Ncomp = dim;
187:   const PetscScalar p = a[aOff[1]];
188:   PetscReal         cofu_x[9/*Ncomp*dim*/];
189:   PetscInt          comp, d;

191:   Cof3D(cofu_x, u_x);
192:   for (comp = 0; comp < Ncomp; ++comp) {
193:     for (d = 0, f0[comp] = 0.0; d < dim; ++d) f0[comp] += cofu_x[comp*dim+d] * n[d];
194:     f0[comp] *= p;
195:   }
196: }

198: void g1_bd_uu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
199:     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
200:     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
201:     PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
202: {
203:   const PetscInt Ncomp = dim;
204:   PetscScalar    p = a[aOff[1]];
205:   PetscReal      cofu_x[9/*Ncomp*dim*/], m[3/*Ncomp*/], detu_x;
206:   PetscInt       comp, compI, compJ, d;

208:   Cof3D(cofu_x, u_x);
209:   Det3D(&detu_x, u_x);
210:   p /= detu_x;

212:   for (comp = 0; comp < Ncomp; ++comp) for (d = 0, m[comp] = 0.0; d < dim; ++d) m[comp] += cofu_x[comp*dim+d] * n[d];
213:   for (compI = 0; compI < Ncomp; ++compI) {
214:     for (compJ = 0; compJ < Ncomp; ++compJ) {
215:       for (d = 0; d < dim; ++d) {
216:         g1[(compI*Ncomp+compJ)*dim+d] = p * (m[compI] * cofu_x[compJ*dim+d] - cofu_x[compI*dim+d] * m[compJ]);
217:       }
218:     }
219:   }
220: }

222: void f0_p_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
223:           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
224:           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
225:           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
226: {
227:   PetscReal detu_x;
228:   Det3D(&detu_x, u_x);
229:   f0[0] = detu_x - 1.0;
230: }

232: void g1_pu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
233:            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
234:            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
235:            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
236: {
237:   PetscReal cofu_x[9/*Ncomp*dim*/];
238:   PetscInt  compI, d;

240:   Cof3D(cofu_x, u_x);
241:   for (compI = 0; compI < dim; ++compI)
242:     for (d = 0; d < dim; ++d) g1[compI*dim+d] = cofu_x[compI*dim+d];
243: }

245: void g2_up_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
246:            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
247:            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
248:            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
249: {
250:   PetscReal cofu_x[9/*Ncomp*dim*/];
251:   PetscInt  compI, d;

253:   Cof3D(cofu_x, u_x);
254:   for (compI = 0; compI < dim; ++compI)
255:     for (d = 0; d < dim; ++d) g2[compI*dim+d] = cofu_x[compI*dim+d];
256: }

258: PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
259: {
260:   const char    *runTypes[2] = {"full", "test"};
261:   PetscInt       run;

265:   options->runType      = RUN_FULL;
266:   options->mu           = 1.0;
267:   options->p_wall       = 0.4;

269:   PetscOptionsBegin(comm, "", "Nonlinear elasticity problem options", "DMPLEX");
270:   run  = options->runType;
271:   PetscOptionsEList("-run_type", "The run type", "ex77.c", runTypes, 2, runTypes[options->runType], &run, NULL);
272:   options->runType = (RunType) run;
273:   PetscOptionsReal("-shear_modulus", "The shear modulus", "ex77.c", options->mu, &options->mu, NULL);
274:   PetscOptionsReal("-wall_pressure", "The wall pressure", "ex77.c", options->p_wall, &options->p_wall, NULL);
275:   PetscOptionsEnd();
276:   return(0);
277: }

279: PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
280: {

284:   /* TODO The P1 coordinate space gives wrong results when compared to the affine version. Track this down */
285:   if (0) {
286:     DMPlexCreateBoxMesh(comm, 3, PETSC_TRUE, NULL, NULL, NULL, NULL, PETSC_TRUE, dm);
287:   } else {
288:     DMCreate(comm, dm);
289:     DMSetType(*dm, DMPLEX);
290:   }
291:   DMSetFromOptions(*dm);
292:   /* Label the faces (bit of a hack here, until it is properly implemented for simplices) */
293:   DMViewFromOptions(*dm, NULL, "-orig_dm_view");
294:   {
295:     DM              cdm;
296:     DMLabel         label;
297:     IS              is;
298:     PetscInt        d, dim, b, f, Nf;
299:     const PetscInt *faces;
300:     PetscInt        csize;
301:     PetscScalar    *coords = NULL;
302:     PetscSection    cs;
303:     Vec             coordinates ;

305:     DMGetDimension(*dm, &dim);
306:     DMCreateLabel(*dm, "boundary");
307:     DMGetLabel(*dm, "boundary", &label);
308:     DMPlexMarkBoundaryFaces(*dm, 1, label);
309:     DMGetStratumIS(*dm, "boundary", 1,  &is);
310:     if (is) {
311:       PetscReal faceCoord;
312:       PetscInt  v;

314:       ISGetLocalSize(is, &Nf);
315:       ISGetIndices(is, &faces);

317:       DMGetCoordinatesLocal(*dm, &coordinates);
318:       DMGetCoordinateDM(*dm, &cdm);
319:       DMGetLocalSection(cdm, &cs);

321:       /* Check for each boundary face if any component of its centroid is either 0.0 or 1.0 */
322:       for (f = 0; f < Nf; ++f) {
323:         DMPlexVecGetClosure(cdm, cs, coordinates, faces[f], &csize, &coords);
324:         /* Calculate mean coordinate vector */
325:         for (d = 0; d < dim; ++d) {
326:           const PetscInt Nv = csize/dim;
327:           faceCoord = 0.0;
328:           for (v = 0; v < Nv; ++v) faceCoord += PetscRealPart(coords[v*dim+d]);
329:           faceCoord /= Nv;
330:           for (b = 0; b < 2; ++b) {
331:             if (PetscAbs(faceCoord - b*1.0) < PETSC_SMALL) {
332:               DMSetLabelValue(*dm, "Faces", faces[f], d*2+b+1);
333:             }
334:           }
335:         }
336:         DMPlexVecRestoreClosure(cdm, cs, coordinates, faces[f], &csize, &coords);
337:       }
338:       ISRestoreIndices(is, &faces);
339:     }
340:     ISDestroy(&is);
341:   }
342:   DMViewFromOptions(*dm, NULL, "-dm_view");
343:   return(0);
344: }

346: PetscErrorCode SetupProblem(DM dm, PetscInt dim, AppCtx *user)
347: {
348:   PetscDS        ds;
349:   PetscWeakForm  wf;
350:   DMLabel        label;
351:   PetscInt       bd;

355:   DMGetDS(dm, &ds);
356:   PetscDSSetResidual(ds, 0, NULL, f1_u_3d);
357:   PetscDSSetResidual(ds, 1, f0_p_3d, NULL);
358:   PetscDSSetJacobian(ds, 0, 0, NULL, NULL,  NULL,  g3_uu_3d);
359:   PetscDSSetJacobian(ds, 0, 1, NULL, NULL,  g2_up_3d, NULL);
360:   PetscDSSetJacobian(ds, 1, 0, NULL, g1_pu_3d, NULL,  NULL);

362:   DMGetLabel(dm, "Faces", &label);
363:   DMAddBoundary(dm, DM_BC_NATURAL, "pressure", label, 0, NULL, 0, 0, NULL, NULL, NULL, user, &bd);
364:   PetscDSGetBoundary(ds, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
365:   PetscWeakFormSetIndexBdResidual(wf, label, 1, 0, 0, 0, f0_bd_u_3d, 0, NULL);
366:   PetscWeakFormSetIndexBdJacobian(wf, label, 1, 0, 0, 0, 0, NULL, 0, g1_bd_uu_3d, 0, NULL, 0, NULL);

368:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "fixed", label, 0, NULL, 0, 0, NULL, (void (*)(void)) coordinates, NULL, user, NULL);
369:   return(0);
370: }

372: PetscErrorCode SetupMaterial(DM dm, DM dmAux, AppCtx *user)
373: {
374:   PetscErrorCode (*matFuncs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx) = {elasticityMaterial, wallPressure};
375:   Vec            A;
376:   void          *ctxs[2];

380:   ctxs[0] = user; ctxs[1] = user;
381:   DMCreateLocalVector(dmAux, &A);
382:   DMProjectFunctionLocal(dmAux, 0.0, matFuncs, ctxs, INSERT_ALL_VALUES, A);
383:   DMSetAuxiliaryVec(dm, NULL, 0, A);
384:   VecDestroy(&A);
385:   return(0);
386: }

388: PetscErrorCode SetupNearNullSpace(DM dm, AppCtx *user)
389: {
390:   /* Set up the near null space (a.k.a. rigid body modes) that will be used by the multigrid preconditioner */
391:   DM             subdm;
392:   MatNullSpace   nearNullSpace;
393:   PetscInt       fields = 0;
394:   PetscObject    deformation;

398:   DMCreateSubDM(dm, 1, &fields, NULL, &subdm);
399:   DMPlexCreateRigidBody(subdm, 0, &nearNullSpace);
400:   DMGetField(dm, 0, NULL, &deformation);
401:   PetscObjectCompose(deformation, "nearnullspace", (PetscObject) nearNullSpace);
402:   DMDestroy(&subdm);
403:   MatNullSpaceDestroy(&nearNullSpace);
404:   return(0);
405: }

407: static PetscErrorCode SetupAuxDM(DM dm, PetscInt NfAux, PetscFE feAux[], AppCtx *user)
408: {
409:   DM             dmAux, coordDM;
410:   PetscInt       f;

414:   /* MUST call DMGetCoordinateDM() in order to get p4est setup if present */
415:   DMGetCoordinateDM(dm, &coordDM);
416:   if (!feAux) return(0);
417:   DMClone(dm, &dmAux);
418:   DMSetCoordinateDM(dmAux, coordDM);
419:   for (f = 0; f < NfAux; ++f) {DMSetField(dmAux, f, NULL, (PetscObject) feAux[f]);}
420:   DMCreateDS(dmAux);
421:   SetupMaterial(dm, dmAux, user);
422:   DMDestroy(&dmAux);
423:   return(0);
424: }

426: PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
427: {
428:   DM              cdm = dm;
429:   PetscFE         fe[2], feAux[2];
430:   PetscBool       simplex;
431:   PetscInt        dim;
432:   MPI_Comm        comm;
433:   PetscErrorCode  ierr;

436:   PetscObjectGetComm((PetscObject) dm, &comm);
437:   DMGetDimension(dm, &dim);
438:   DMPlexIsSimplex(dm, &simplex);
439:   /* Create finite element */
440:   PetscFECreateDefault(comm, dim, dim, simplex, "def_", PETSC_DEFAULT, &fe[0]);
441:   PetscObjectSetName((PetscObject) fe[0], "deformation");
442:   PetscFECreateDefault(comm, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]);

445:   PetscObjectSetName((PetscObject) fe[1], "pressure");

447:   PetscFECreateDefault(comm, dim, 1, simplex, "elastMat_", PETSC_DEFAULT, &feAux[0]);
448:   PetscObjectSetName((PetscObject) feAux[0], "elasticityMaterial");
450:   /* It is not yet possible to define a field on a submesh (e.g. a boundary), so we will use a normal finite element */
451:   PetscFECreateDefault(comm, dim, 1, simplex, "wall_pres_", PETSC_DEFAULT, &feAux[1]);
452:   PetscObjectSetName((PetscObject) feAux[1], "wall_pressure");

455:   /* Set discretization and boundary conditions for each mesh */
456:   DMSetField(dm, 0, NULL, (PetscObject) fe[0]);
457:   DMSetField(dm, 1, NULL, (PetscObject) fe[1]);
458:   DMCreateDS(dm);
459:   SetupProblem(dm, dim, user);
460:   while (cdm) {
461:     SetupAuxDM(cdm, 2, feAux, user);
462:     DMCopyDisc(dm, cdm);
463:     DMGetCoarseDM(cdm, &cdm);
464:   }
465:   PetscFEDestroy(&fe[0]);
466:   PetscFEDestroy(&fe[1]);
467:   PetscFEDestroy(&feAux[0]);
468:   PetscFEDestroy(&feAux[1]);
469:   return(0);
470: }

472: int main(int argc, char **argv)
473: {
474:   SNES           snes;                 /* nonlinear solver */
475:   DM             dm;                   /* problem definition */
476:   Vec            u,r;                  /* solution, residual vectors */
477:   Mat            A,J;                  /* Jacobian matrix */
478:   AppCtx         user;                 /* user-defined work context */
479:   PetscInt       its;                  /* iterations for convergence */

482:   PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
483:   ProcessOptions(PETSC_COMM_WORLD, &user);
484:   SNESCreate(PETSC_COMM_WORLD, &snes);
485:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
486:   SNESSetDM(snes, dm);
487:   DMSetApplicationContext(dm, &user);

489:   SetupDiscretization(dm, &user);
490:   DMPlexCreateClosureIndex(dm, NULL);
491:   SetupNearNullSpace(dm, &user);

493:   DMCreateGlobalVector(dm, &u);
494:   VecDuplicate(u, &r);

496:   DMSetMatType(dm,MATAIJ);
497:   DMCreateMatrix(dm, &J);
498:   A = J;

500:   DMPlexSetSNESLocalFEM(dm,&user,&user,&user);
501:   SNESSetJacobian(snes, A, J, NULL, NULL);

503:   SNESSetFromOptions(snes);

505:   {
506:     PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx);
507:     initialGuess[0] = coordinates; initialGuess[1] = zero_scalar;
508:     DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);
509:   }

511:   if (user.runType == RUN_FULL) {
512:     SNESSolve(snes, NULL, u);
513:     SNESGetIterationNumber(snes, &its);
514:     PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %D\n", its);
515:   } else {
516:     PetscReal res = 0.0;

518:     /* Check initial guess */
519:     PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");
520:     VecView(u, PETSC_VIEWER_STDOUT_WORLD);
521:     /* Check residual */
522:     SNESComputeFunction(snes, u, r);
523:     PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");
524:     VecChop(r, 1.0e-10);
525:     VecView(r, PETSC_VIEWER_STDOUT_WORLD);
526:     VecNorm(r, NORM_2, &res);
527:     PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);
528:     /* Check Jacobian */
529:     {
530:       Vec b;

532:       SNESComputeJacobian(snes, u, A, A);
533:       VecDuplicate(u, &b);
534:       VecSet(r, 0.0);
535:       SNESComputeFunction(snes, r, b);
536:       MatMult(A, u, r);
537:       VecAXPY(r, 1.0, b);
538:       VecDestroy(&b);
539:       PetscPrintf(PETSC_COMM_WORLD, "Au - b = Au + F(0)\n");
540:       VecChop(r, 1.0e-10);
541:       VecView(r, PETSC_VIEWER_STDOUT_WORLD);
542:       VecNorm(r, NORM_2, &res);
543:       PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", (double)res);
544:     }
545:   }
546:   VecViewFromOptions(u, NULL, "-sol_vec_view");

548:   if (A != J) {MatDestroy(&A);}
549:   MatDestroy(&J);
550:   VecDestroy(&u);
551:   VecDestroy(&r);
552:   SNESDestroy(&snes);
553:   DMDestroy(&dm);
554:   PetscFinalize();
555:   return ierr;
556: }

558: /*TEST

560:   build:
561:     requires: !complex

563:   testset:
564:     requires: ctetgen
565:     args: -run_type full -dm_plex_dim 3 \
566:           -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 \
567:           -snes_rtol 1e-05 -snes_monitor_short -snes_converged_reason \
568:           -ksp_type fgmres -ksp_rtol 1e-10 -ksp_monitor_short -ksp_converged_reason \
569:           -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper \
570:             -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu \
571:             -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi

573:     test:
574:       suffix: 0
575:       requires: !single
576:       args: -dm_refine 2 \
577:             -bc_fixed 1 -bc_pressure 2 -wall_pressure 0.4

579:     test:
580:       suffix: 1
581:       requires: superlu_dist
582:       nsize: 2
583:       args: -dm_distribute -dm_refine 0 -petscpartitioner_type simple \
584:             -bc_fixed 1 -bc_pressure 2 -wall_pressure 0.4
585:       timeoutfactor: 2

587:     test:
588:       suffix: 4
589:       requires: superlu_dist
590:       nsize: 2
591:       args: -dm_distribute -dm_refine 0 -petscpartitioner_type simple \
592:             -bc_fixed 1 -bc_pressure 2 -wall_pressure 0.4
593:       output_file: output/ex77_1.out

595:     test:
596:       suffix: 2
597:       requires: !single
598:       args: -dm_refine 2 \
599:             -bc_fixed 3,4,5,6 -bc_pressure 2 -wall_pressure 1.0

601:     test:
602:       suffix: 2_par
603:       requires: superlu_dist !single
604:       nsize: 4
605:       args: -dm_distribute -dm_refine 2 -petscpartitioner_type simple \
606:             -bc_fixed 3,4,5,6 -bc_pressure 2 -wall_pressure 1.0
607:       output_file: output/ex77_2.out

609: TEST*/