Actual source code: ex77.c

petsc-master 2020-06-03
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  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)
8: and nonlinear Neumann boundary conditions (pressure loading).
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:   PetscInt      debug;             /* The debugging level */
48:   RunType       runType;           /* Whether to run tests, or solve the full problem */
49:   PetscLogEvent createMeshEvent;
50:   PetscBool     showInitial, showSolution;
51:   /* Domain and mesh definition */
52:   PetscInt      dim;               /* The topological mesh dimension */
53:   PetscBool     interpolate;       /* Generate intermediate mesh elements */
54:   PetscBool     simplex;           /* Use simplices or tensor product cells */
55:   PetscReal     refinementLimit;   /* The largest allowable cell volume */
56:   PetscBool     testPartition;     /* Use a fixed partitioning for testing */
57:   PetscReal     mu;                /* The shear modulus */
58:   PetscReal     p_wall;            /* The wall pressure */
59: } AppCtx;

61: #if 0
62: PETSC_STATIC_INLINE void Det2D(PetscReal *detJ, const PetscReal J[])
63: {
64:   *detJ = J[0]*J[3] - J[1]*J[2];
65: }
66: #endif

68: PETSC_STATIC_INLINE void Det3D(PetscReal *detJ, const PetscScalar J[])
69: {
70:   *detJ = PetscRealPart(J[0*3+0]*(J[1*3+1]*J[2*3+2] - J[1*3+2]*J[2*3+1]) +
71:                         J[0*3+1]*(J[1*3+2]*J[2*3+0] - J[1*3+0]*J[2*3+2]) +
72:                         J[0*3+2]*(J[1*3+0]*J[2*3+1] - J[1*3+1]*J[2*3+0]));
73: }

75: #if 0
76: PETSC_STATIC_INLINE void Cof2D(PetscReal C[], const PetscReal A[])
77: {
78:   C[0] =  A[3];
79:   C[1] = -A[2];
80:   C[2] = -A[1];
81:   C[3] =  A[0];
82: }
83: #endif

85: PETSC_STATIC_INLINE void Cof3D(PetscReal C[], const PetscScalar A[])
86: {
87:   C[0*3+0] = PetscRealPart(A[1*3+1]*A[2*3+2] - A[1*3+2]*A[2*3+1]);
88:   C[0*3+1] = PetscRealPart(A[1*3+2]*A[2*3+0] - A[1*3+0]*A[2*3+2]);
89:   C[0*3+2] = PetscRealPart(A[1*3+0]*A[2*3+1] - A[1*3+1]*A[2*3+0]);
90:   C[1*3+0] = PetscRealPart(A[0*3+2]*A[2*3+1] - A[0*3+1]*A[2*3+2]);
91:   C[1*3+1] = PetscRealPart(A[0*3+0]*A[2*3+2] - A[0*3+2]*A[2*3+0]);
92:   C[1*3+2] = PetscRealPart(A[0*3+1]*A[2*3+0] - A[0*3+0]*A[2*3+1]);
93:   C[2*3+0] = PetscRealPart(A[0*3+1]*A[1*3+2] - A[0*3+2]*A[1*3+1]);
94:   C[2*3+1] = PetscRealPart(A[0*3+2]*A[1*3+0] - A[0*3+0]*A[1*3+2]);
95:   C[2*3+2] = PetscRealPart(A[0*3+0]*A[1*3+1] - A[0*3+1]*A[1*3+0]);
96: }

98: PetscErrorCode zero_scalar(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
99: {
100:   u[0] = 0.0;
101:   return 0;
102: }

104: PetscErrorCode zero_vector(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] = 0.0;
110:   return 0;
111: }

113: PetscErrorCode coordinates(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
114: {
115:   const PetscInt Ncomp = dim;

117:   PetscInt       comp;
118:   for (comp = 0; comp < Ncomp; ++comp) u[comp] = x[comp];
119:   return 0;
120: }

122: PetscErrorCode elasticityMaterial(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
123: {
124:   AppCtx *user = (AppCtx *) ctx;
125:   u[0] = user->mu;
126:   return 0;
127: }

129: PetscErrorCode wallPressure(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
130: {
131:   AppCtx *user = (AppCtx *) ctx;
132:   u[0] = user->p_wall;
133:   return 0;
134: }

136: void f1_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
137:           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
138:           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
139:           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
140: {
141:   const PetscInt  Ncomp = dim;
142:   const PetscReal mu = PetscRealPart(a[0]), kappa = 3.0;
143:   PetscReal       cofu_x[9/*Ncomp*dim*/], detu_x, p = PetscRealPart(u[Ncomp]);
144:   PetscInt        comp, d;

146:   Cof3D(cofu_x, u_x);
147:   Det3D(&detu_x, u_x);
148:   p += kappa * (detu_x - 1.0);

150:   /* f1 is the first Piola-Kirchhoff tensor */
151:   for (comp = 0; comp < Ncomp; ++comp) {
152:     for (d = 0; d < dim; ++d) {
153:       f1[comp*dim+d] = mu * u_x[comp*dim+d] + p * cofu_x[comp*dim+d];
154:     }
155:   }
156: }

158: void g3_uu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
159:           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
160:           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
161:           PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
162: {
163:   const PetscInt  Ncomp = dim;
164:   const PetscReal mu = PetscRealPart(a[0]), kappa = 3.0;
165:   PetscReal       cofu_x[9/*Ncomp*dim*/], detu_x, pp, pm, p = PetscRealPart(u[Ncomp]);
166:   PetscInt        compI, compJ, d1, d2;

168:   Cof3D(cofu_x, u_x);
169:   Det3D(&detu_x, u_x);
170:   p += kappa * (detu_x - 1.0);
171:   pp = p/detu_x + kappa;
172:   pm = p/detu_x;

174:   /* 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} */
175:   for (compI = 0; compI < Ncomp; ++compI) {
176:     for (compJ = 0; compJ < Ncomp; ++compJ) {
177:       const PetscReal G = (compI == compJ) ? 1.0 : 0.0;

179:       for (d1 = 0; d1 < dim; ++d1) {
180:         for (d2 = 0; d2 < dim; ++d2) {
181:           const PetscReal g = (d1 == d2) ? 1.0 : 0.0;

183:           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];
184:         }
185:       }
186:     }
187:   }
188: }

190: void f0_bd_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
191:     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
192:     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
193:     PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
194: {
195:   const PetscInt    Ncomp = dim;
196:   const PetscScalar p = a[aOff[1]];
197:   PetscReal         cofu_x[9/*Ncomp*dim*/];
198:   PetscInt          comp, d;

200:   Cof3D(cofu_x, u_x);
201:   for (comp = 0; comp < Ncomp; ++comp) {
202:     for (d = 0, f0[comp] = 0.0; d < dim; ++d) f0[comp] += cofu_x[comp*dim+d] * n[d];
203:     f0[comp] *= p;
204:   }
205: }

207: void g1_bd_uu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
208:     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
209:     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
210:     PetscReal t, PetscReal u_tShift, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
211: {
212:   const PetscInt Ncomp = dim;
213:   PetscScalar    p = a[aOff[1]];
214:   PetscReal      cofu_x[9/*Ncomp*dim*/], m[3/*Ncomp*/], detu_x;
215:   PetscInt       comp, compI, compJ, d;

217:   Cof3D(cofu_x, u_x);
218:   Det3D(&detu_x, u_x);
219:   p /= detu_x;

221:   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];
222:   for (compI = 0; compI < Ncomp; ++compI) {
223:     for (compJ = 0; compJ < Ncomp; ++compJ) {
224:       for (d = 0; d < dim; ++d) {
225:         g1[(compI*Ncomp+compJ)*dim+d] = p * (m[compI] * cofu_x[compJ*dim+d] - cofu_x[compI*dim+d] * m[compJ]);
226:       }
227:     }
228:   }
229: }

231: void f0_p_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
232:           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
233:           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
234:           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
235: {
236:   PetscReal detu_x;
237:   Det3D(&detu_x, u_x);
238:   f0[0] = detu_x - 1.0;
239: }

241: void g1_pu_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
242:            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
243:            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
244:            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g1[])
245: {
246:   PetscReal cofu_x[9/*Ncomp*dim*/];
247:   PetscInt  compI, d;

249:   Cof3D(cofu_x, u_x);
250:   for (compI = 0; compI < dim; ++compI)
251:     for (d = 0; d < dim; ++d) g1[compI*dim+d] = cofu_x[compI*dim+d];
252: }

254: void g2_up_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
255:            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
256:            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
257:            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g2[])
258: {
259:   PetscReal cofu_x[9/*Ncomp*dim*/];
260:   PetscInt  compI, d;

262:   Cof3D(cofu_x, u_x);
263:   for (compI = 0; compI < dim; ++compI)
264:     for (d = 0; d < dim; ++d) g2[compI*dim+d] = cofu_x[compI*dim+d];
265: }

267: PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
268: {
269:   const char    *runTypes[2] = {"full", "test"};
270:   PetscInt       run;

274:   options->debug           = 0;
275:   options->runType         = RUN_FULL;
276:   options->dim             = 3;
277:   options->interpolate     = PETSC_FALSE;
278:   options->simplex         = PETSC_TRUE;
279:   options->refinementLimit = 0.0;
280:   options->mu              = 1.0;
281:   options->p_wall          = 0.4;
282:   options->testPartition   = PETSC_FALSE;
283:   options->showInitial     = PETSC_FALSE;
284:   options->showSolution    = PETSC_TRUE;

286:   PetscOptionsBegin(comm, "", "Nonlinear elasticity problem options", "DMPLEX");
287:   PetscOptionsInt("-debug", "The debugging level", "ex77.c", options->debug, &options->debug, NULL);
288:   run  = options->runType;
289:   PetscOptionsEList("-run_type", "The run type", "ex77.c", runTypes, 2, runTypes[options->runType], &run, NULL);

291:   options->runType = (RunType) run;

293:   PetscOptionsInt("-dim", "The topological mesh dimension", "ex77.c", options->dim, &options->dim, NULL);
294:   PetscOptionsBool("-interpolate", "Generate intermediate mesh elements", "ex77.c", options->interpolate, &options->interpolate, NULL);
295:   PetscOptionsBool("-simplex", "Use simplices or tensor product cells", "ex77.c", options->simplex, &options->simplex, NULL);
296:   PetscOptionsReal("-refinement_limit", "The largest allowable cell volume", "ex77.c", options->refinementLimit, &options->refinementLimit, NULL);
297:   PetscOptionsBool("-test_partition", "Use a fixed partition for testing", "ex77.c", options->testPartition, &options->testPartition, NULL);
298:   PetscOptionsReal("-shear_modulus", "The shear modulus", "ex77.c", options->mu, &options->mu, NULL);
299:   PetscOptionsReal("-wall_pressure", "The wall pressure", "ex77.c", options->p_wall, &options->p_wall, NULL);

301:   PetscOptionsBool("-show_initial", "Output the initial guess for verification", "ex77.c", options->showInitial, &options->showInitial, NULL);
302:   PetscOptionsBool("-show_solution", "Output the solution for verification", "ex77.c", options->showSolution, &options->showSolution, NULL);
303:   PetscOptionsEnd();

305:   PetscLogEventRegister("CreateMesh", DM_CLASSID, &options->createMeshEvent);
306:   return(0);
307: }

309: PetscErrorCode DMVecViewLocal(DM dm, Vec v, PetscViewer viewer)
310: {
311:   Vec            lv;
312:   PetscInt       p;
313:   PetscMPIInt    rank, size;

317:   MPI_Comm_rank(PetscObjectComm((PetscObject)dm), &rank);
318:   MPI_Comm_size(PetscObjectComm((PetscObject)dm), &size);
319:   DMGetLocalVector(dm, &lv);
320:   DMGlobalToLocalBegin(dm, v, INSERT_VALUES, lv);
321:   DMGlobalToLocalEnd(dm, v, INSERT_VALUES, lv);
322:   PetscPrintf(PETSC_COMM_WORLD, "Local function\n");
323:   for (p = 0; p < size; ++p) {
324:     if (p == rank) {VecView(lv, PETSC_VIEWER_STDOUT_SELF);}
325:     PetscBarrier((PetscObject) dm);
326:   }
327:   DMRestoreLocalVector(dm, &lv);
328:   return(0);
329: }

331: PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
332: {
333:   PetscInt       dim             = user->dim;
334:   PetscBool      interpolate     = user->interpolate;
335:   PetscReal      refinementLimit = user->refinementLimit;
336:   const PetscInt cells[3]        = {3, 3, 3};

340:   PetscLogEventBegin(user->createMeshEvent,0,0,0,0);
341:   DMPlexCreateBoxMesh(comm, dim, user->simplex, user->simplex ? NULL : cells, NULL, NULL, NULL, interpolate, dm);
342:   /* Label the faces (bit of a hack here, until it is properly implemented for simplices) */
343:   {
344:     DM              cdm;
345:     DMLabel         label;
346:     IS              is;
347:     PetscInt        d, dim = user->dim, b, f, Nf;
348:     const PetscInt *faces;
349:     PetscInt        csize;
350:     PetscScalar    *coords = NULL;
351:     PetscSection    cs;
352:     Vec             coordinates ;

354:     DMCreateLabel(*dm, "boundary");
355:     DMGetLabel(*dm, "boundary", &label);
356:     DMPlexMarkBoundaryFaces(*dm, 1, label);
357:     DMGetStratumIS(*dm, "boundary", 1,  &is);
358:     if (is) {
359:       PetscReal faceCoord;
360:       PetscInt  v;

362:       ISGetLocalSize(is, &Nf);
363:       ISGetIndices(is, &faces);

365:       DMGetCoordinatesLocal(*dm, &coordinates);
366:       DMGetCoordinateDM(*dm, &cdm);
367:       DMGetLocalSection(cdm, &cs);

369:       /* Check for each boundary face if any component of its centroid is either 0.0 or 1.0 */
370:       for (f = 0; f < Nf; ++f) {
371:         DMPlexVecGetClosure(cdm, cs, coordinates, faces[f], &csize, &coords);
372:         /* Calculate mean coordinate vector */
373:         for (d = 0; d < dim; ++d) {
374:           const PetscInt Nv = csize/dim;
375:           faceCoord = 0.0;
376:           for (v = 0; v < Nv; ++v) faceCoord += PetscRealPart(coords[v*dim+d]);
377:           faceCoord /= Nv;
378:           for (b = 0; b < 2; ++b) {
379:             if (PetscAbs(faceCoord - b*1.0) < PETSC_SMALL) {
380:               DMSetLabelValue(*dm, "Faces", faces[f], d*2+b+1);
381:             }
382:           }
383:         }
384:         DMPlexVecRestoreClosure(cdm, cs, coordinates, faces[f], &csize, &coords);
385:       }
386:       ISRestoreIndices(is, &faces);
387:     }
388:     ISDestroy(&is);
389:   }
390:   {
391:     DM refinedMesh     = NULL;
392:     DM distributedMesh = NULL;
393:     PetscPartitioner part;

395:     DMPlexGetPartitioner(*dm, &part);

397:     /* Refine mesh using a volume constraint */
398:     DMPlexSetRefinementLimit(*dm, refinementLimit);
399:     if (user->simplex) {DMRefine(*dm, comm, &refinedMesh);}
400:     if (refinedMesh) {
401:       DMDestroy(dm);
402:       *dm  = refinedMesh;
403:     }
404:     /* Setup test partitioning */
405:     if (user->testPartition) {
406:       PetscInt         triSizes_n2[2]       = {4, 4};
407:       PetscInt         triPoints_n2[8]      = {3, 5, 6, 7, 0, 1, 2, 4};
408:       PetscInt         triSizes_n3[3]       = {2, 3, 3};
409:       PetscInt         triPoints_n3[8]      = {3, 5, 1, 6, 7, 0, 2, 4};
410:       PetscInt         triSizes_n5[5]       = {1, 2, 2, 1, 2};
411:       PetscInt         triPoints_n5[8]      = {3, 5, 6, 4, 7, 0, 1, 2};
412:       PetscInt         triSizes_ref_n2[2]   = {8, 8};
413:       PetscInt         triPoints_ref_n2[16] = {1, 5, 6, 7, 10, 11, 14, 15, 0, 2, 3, 4, 8, 9, 12, 13};
414:       PetscInt         triSizes_ref_n3[3]   = {5, 6, 5};
415:       PetscInt         triPoints_ref_n3[16] = {1, 7, 10, 14, 15, 2, 6, 8, 11, 12, 13, 0, 3, 4, 5, 9};
416:       PetscInt         triSizes_ref_n5[5]   = {3, 4, 3, 3, 3};
417:       PetscInt         triPoints_ref_n5[16] = {1, 7, 10, 2, 11, 13, 14, 5, 6, 15, 0, 8, 9, 3, 4, 12};
418:       PetscInt         tetSizes_n2[2]       = {3, 3};
419:       PetscInt         tetPoints_n2[6]      = {1, 2, 3, 0, 4, 5};
420:       const PetscInt  *sizes = NULL;
421:       const PetscInt  *points = NULL;
422:       PetscInt         cEnd;
423:       PetscMPIInt      rank, size;

425:       MPI_Comm_rank(comm, &rank);
426:       MPI_Comm_size(comm, &size);
427:       DMPlexGetHeightStratum(*dm, 0, NULL, &cEnd);
428:       if (!rank) {
429:         if (dim == 2 && user->simplex && size == 2 && cEnd == 8) {
430:            sizes = triSizes_n2; points = triPoints_n2;
431:         } else if (dim == 2 && user->simplex && size == 3 && cEnd == 8) {
432:           sizes = triSizes_n3; points = triPoints_n3;
433:         } else if (dim == 2 && user->simplex && size == 5 && cEnd == 8) {
434:           sizes = triSizes_n5; points = triPoints_n5;
435:         } else if (dim == 2 && user->simplex && size == 2 && cEnd == 16) {
436:            sizes = triSizes_ref_n2; points = triPoints_ref_n2;
437:         } else if (dim == 2 && user->simplex && size == 3 && cEnd == 16) {
438:           sizes = triSizes_ref_n3; points = triPoints_ref_n3;
439:         } else if (dim == 2 && user->simplex && size == 5 && cEnd == 16) {
440:           sizes = triSizes_ref_n5; points = triPoints_ref_n5;
441:         } else if (dim == 3 && user->simplex && size == 2 && cEnd == 6) {
442:           sizes = tetSizes_n2; points = tetPoints_n2;
443:         } else SETERRQ(comm, PETSC_ERR_ARG_WRONG, "No stored partition matching run parameters");
444:       }
445:       PetscPartitionerSetType(part, PETSCPARTITIONERSHELL);
446:       PetscPartitionerShellSetPartition(part, size, sizes, points);
447:     } else {
448:       PetscPartitionerSetFromOptions(part);
449:     }
450:     /* Distribute mesh over processes */
451:     DMPlexDistribute(*dm, 0, NULL, &distributedMesh);
452:     if (distributedMesh) {
453:       DMDestroy(dm);
454:       *dm  = distributedMesh;
455:     }
456:   }
457:   DMSetFromOptions(*dm);
458:   DMViewFromOptions(*dm, NULL, "-dm_view");

460:   PetscLogEventEnd(user->createMeshEvent,0,0,0,0);
461:   return(0);
462: }

464: PetscErrorCode SetupProblem(DM dm, PetscInt dim, AppCtx *user)
465: {
466:   PetscDS        prob;

470:   DMGetDS(dm, &prob);
471:   PetscDSSetResidual(prob, 0, NULL, f1_u_3d);
472:   PetscDSSetResidual(prob, 1, f0_p_3d, NULL);
473:   PetscDSSetJacobian(prob, 0, 0, NULL, NULL,  NULL,  g3_uu_3d);
474:   PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  g2_up_3d, NULL);
475:   PetscDSSetJacobian(prob, 1, 0, NULL, g1_pu_3d, NULL,  NULL);

477:   PetscDSSetBdResidual(prob, 0, f0_bd_u_3d, NULL);
478:   PetscDSSetBdJacobian(prob, 0, 0, NULL, g1_bd_uu_3d, NULL, NULL);

480:   DMAddBoundary(dm, DM_BC_ESSENTIAL, "fixed", "Faces", 0, 0, NULL, (void (*)(void)) coordinates, 0, NULL, user);
481:   DMAddBoundary(dm, DM_BC_NATURAL, "pressure", "Faces", 0, 0, NULL, NULL, 0, NULL, user);
482:   return(0);
483: }

485: PetscErrorCode SetupMaterial(DM dm, DM dmAux, AppCtx *user)
486: {
487:   PetscErrorCode (*matFuncs[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar u[], void *ctx) = {elasticityMaterial, wallPressure};
488:   Vec            A;
489:   void          *ctxs[2];

493:   ctxs[0] = user; ctxs[1] = user;
494:   DMCreateLocalVector(dmAux, &A);
495:   DMProjectFunctionLocal(dmAux, 0.0, matFuncs, ctxs, INSERT_ALL_VALUES, A);
496:   PetscObjectCompose((PetscObject) dm, "A", (PetscObject) A);
497:   VecDestroy(&A);
498:   return(0);
499: }

501: PetscErrorCode SetupNearNullSpace(DM dm, AppCtx *user)
502: {
503:   /* Set up the near null space (a.k.a. rigid body modes) that will be used by the multigrid preconditioner */
504:   DM             subdm;
505:   MatNullSpace   nearNullSpace;
506:   PetscInt       fields = 0;
507:   PetscObject    deformation;

511:   DMCreateSubDM(dm, 1, &fields, NULL, &subdm);
512:   DMPlexCreateRigidBody(subdm, &nearNullSpace);
513:   DMGetField(dm, 0, NULL, &deformation);
514:   PetscObjectCompose(deformation, "nearnullspace", (PetscObject) nearNullSpace);
515:   DMDestroy(&subdm);
516:   MatNullSpaceDestroy(&nearNullSpace);
517:   return(0);
518: }

520: static PetscErrorCode SetupAuxDM(DM dm, PetscInt NfAux, PetscFE feAux[], AppCtx *user)
521: {
522:   DM             dmAux, coordDM;
523:   PetscInt       f;

527:   /* MUST call DMGetCoordinateDM() in order to get p4est setup if present */
528:   DMGetCoordinateDM(dm, &coordDM);
529:   if (!feAux) return(0);
530:   DMClone(dm, &dmAux);
531:   PetscObjectCompose((PetscObject) dm, "dmAux", (PetscObject) dmAux);
532:   DMSetCoordinateDM(dmAux, coordDM);
533:   for (f = 0; f < NfAux; ++f) {DMSetField(dmAux, f, NULL, (PetscObject) feAux[f]);}
534:   DMCreateDS(dmAux);
535:   SetupMaterial(dm, dmAux, user);
536:   DMDestroy(&dmAux);
537:   return(0);
538: }

540: PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
541: {
542:   DM              cdm   = dm;
543:   const PetscInt  dim   = user->dim;
544:   const PetscBool simplex = user->simplex;
545:   PetscFE         fe[2], feAux[2];
546:   MPI_Comm        comm;
547:   PetscErrorCode  ierr;

550:   PetscObjectGetComm((PetscObject) dm, &comm);
551:   /* Create finite element */
552:   PetscFECreateDefault(comm, dim, dim, simplex, "def_", PETSC_DEFAULT, &fe[0]);
553:   PetscObjectSetName((PetscObject) fe[0], "deformation");
554:   PetscFECreateDefault(comm, dim, 1, simplex, "pres_", PETSC_DEFAULT, &fe[1]);

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

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

567:   /* Set discretization and boundary conditions for each mesh */
568:   DMSetField(dm, 0, NULL, (PetscObject) fe[0]);
569:   DMSetField(dm, 1, NULL, (PetscObject) fe[1]);
570:   DMCreateDS(dm);
571:   SetupProblem(dm, dim, user);
572:   while (cdm) {
573:     SetupAuxDM(cdm, 2, feAux, user);
574:     DMCopyDisc(dm, cdm);
575:     DMGetCoarseDM(cdm, &cdm);
576:   }
577:   PetscFEDestroy(&fe[0]);
578:   PetscFEDestroy(&fe[1]);
579:   PetscFEDestroy(&feAux[0]);
580:   PetscFEDestroy(&feAux[1]);
581:   return(0);
582: }

585: int main(int argc, char **argv)
586: {
587:   SNES           snes;                 /* nonlinear solver */
588:   DM             dm;                   /* problem definition */
589:   Vec            u,r;                  /* solution, residual vectors */
590:   Mat            A,J;                  /* Jacobian matrix */
591:   AppCtx         user;                 /* user-defined work context */
592:   PetscInt       its;                  /* iterations for convergence */

595:   PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
596:   ProcessOptions(PETSC_COMM_WORLD, &user);
597:   SNESCreate(PETSC_COMM_WORLD, &snes);
598:   CreateMesh(PETSC_COMM_WORLD, &user, &dm);
599:   SNESSetDM(snes, dm);
600:   DMSetApplicationContext(dm, &user);

602:   SetupDiscretization(dm, &user);
603:   DMPlexCreateClosureIndex(dm, NULL);
604:   SetupNearNullSpace(dm, &user);

606:   DMCreateGlobalVector(dm, &u);
607:   VecDuplicate(u, &r);

609:   DMSetMatType(dm,MATAIJ);
610:   DMCreateMatrix(dm, &J);
611:   A = J;

613:   DMPlexSetSNESLocalFEM(dm,&user,&user,&user);
614:   SNESSetJacobian(snes, A, J, NULL, NULL);

616:   SNESSetFromOptions(snes);

618:   {
619:     PetscErrorCode (*initialGuess[2])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void* ctx);
620:     initialGuess[0] = coordinates; initialGuess[1] = zero_scalar;
621:     DMProjectFunction(dm, 0.0, initialGuess, NULL, INSERT_VALUES, u);
622:   }
623:   if (user.showInitial) {DMVecViewLocal(dm, u, PETSC_VIEWER_STDOUT_SELF);}

625:   if (user.runType == RUN_FULL) {
626:     if (user.debug) {
627:       PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");
628:       VecView(u, PETSC_VIEWER_STDOUT_WORLD);
629:     }
630:     SNESSolve(snes, NULL, u);
631:     SNESGetIterationNumber(snes, &its);
632:     PetscPrintf(PETSC_COMM_WORLD, "Number of SNES iterations = %D\n", its);
633:     if (user.showSolution) {
634:       PetscPrintf(PETSC_COMM_WORLD, "Solution\n");
635:       VecChop(u, 3.0e-9);
636:       VecView(u, PETSC_VIEWER_STDOUT_WORLD);
637:     }
638:   } else {
639:     PetscReal res = 0.0;

641:     /* Check initial guess */
642:     PetscPrintf(PETSC_COMM_WORLD, "Initial guess\n");
643:     VecView(u, PETSC_VIEWER_STDOUT_WORLD);
644:     /* Check residual */
645:     SNESComputeFunction(snes, u, r);
646:     PetscPrintf(PETSC_COMM_WORLD, "Initial Residual\n");
647:     VecChop(r, 1.0e-10);
648:     VecView(r, PETSC_VIEWER_STDOUT_WORLD);
649:     VecNorm(r, NORM_2, &res);
650:     PetscPrintf(PETSC_COMM_WORLD, "L_2 Residual: %g\n", (double)res);
651:     /* Check Jacobian */
652:     {
653:       Vec b;

655:       SNESComputeJacobian(snes, u, A, A);
656:       VecDuplicate(u, &b);
657:       VecSet(r, 0.0);
658:       SNESComputeFunction(snes, r, b);
659:       MatMult(A, u, r);
660:       VecAXPY(r, 1.0, b);
661:       VecDestroy(&b);
662:       PetscPrintf(PETSC_COMM_WORLD, "Au - b = Au + F(0)\n");
663:       VecChop(r, 1.0e-10);
664:       VecView(r, PETSC_VIEWER_STDOUT_WORLD);
665:       VecNorm(r, NORM_2, &res);
666:       PetscPrintf(PETSC_COMM_WORLD, "Linear L_2 Residual: %g\n", (double)res);
667:     }
668:   }
669:   VecViewFromOptions(u, NULL, "-sol_vec_view");

671:   if (A != J) {MatDestroy(&A);}
672:   MatDestroy(&J);
673:   VecDestroy(&u);
674:   VecDestroy(&r);
675:   SNESDestroy(&snes);
676:   DMDestroy(&dm);
677:   PetscFinalize();
678:   return ierr;
679: }

681: /*TEST

683:   build:
684:     requires: !complex

686:   test:
687:     suffix: 0
688:     requires: ctetgen !single
689:     args: -run_type full -dim 3 -dm_refine 2 -interpolate 1 -bc_fixed 1 -bc_pressure 2 -wall_pressure 0.4 -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 -snes_rtol 1e-05 -ksp_type fgmres -ksp_rtol 1e-10 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi -snes_monitor_short -ksp_monitor_short -snes_converged_reason -ksp_converged_reason -show_solution 0

691:   test:
692:     suffix: 1
693:     requires: ctetgen superlu_dist
694:     nsize: 2
695:     args: -run_type full -dim 3 -dm_refine 0 -interpolate 1 -test_partition -bc_fixed 1 -bc_pressure 2 -wall_pressure 0.4 -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 -snes_rtol 1e-05 -ksp_type fgmres -ksp_rtol 1e-10 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi -snes_monitor_short -ksp_monitor_short -snes_converged_reason -ksp_converged_reason -show_solution 0
696:     timeoutfactor: 2

698:   test:
699:     suffix: 2
700:     requires: ctetgen !single
701:     args: -run_type full -dim 3 -dm_refine 2 -interpolate 1 -bc_fixed 3,4,5,6 -bc_pressure 2 -wall_pressure 1.0 -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 -snes_rtol 1e-05 -ksp_type fgmres -ksp_rtol 1e-10 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi -snes_monitor_short -ksp_monitor_short -snes_converged_reason -ksp_converged_reason -show_solution 0

703:   test:
704:     requires: ctetgen superlu_dist
705:     suffix: 4
706:     nsize: 2
707:     args: -run_type full -dim 3 -dm_refine 0 -interpolate 1 -test_partition -bc_fixed 1 -bc_pressure 2 -wall_pressure 0.4 -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 -snes_rtol 1e-05 -ksp_type fgmres -ksp_rtol 1e-10 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi -snes_monitor_short -ksp_monitor_short -snes_converged_reason -ksp_converged_reason -show_solution 0
708:     output_file: output/ex77_1.out

710:   test:
711:     requires: ctetgen !single
712:     suffix: 3
713:     args: -run_type full -dim 3 -dm_refine 2 -interpolate 1 -bc_fixed 3,4,5,6 -bc_pressure 2 -wall_pressure 1.0 -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 -snes_rtol 1e-05 -ksp_type fgmres -ksp_rtol 1e-10 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi -snes_monitor_short -ksp_monitor_short -snes_converged_reason -ksp_converged_reason -show_solution 0
714:     output_file: output/ex77_2.out

716:   #TODO: this example deadlocks for me when using ParMETIS
717:   test:
718:     requires: ctetgen superlu_dist !single
719:     suffix: 2_par
720:     nsize: 4
721:     args: -run_type full -dim 3 -dm_refine 2 -interpolate 1 -bc_fixed 3,4,5,6 -bc_pressure 2 -wall_pressure 1.0 -def_petscspace_degree 2 -pres_petscspace_degree 1 -elastMat_petscspace_degree 0 -wall_pres_petscspace_degree 0 -snes_rtol 1e-05 -ksp_type fgmres -ksp_rtol 1e-10 -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type upper -fieldsplit_deformation_ksp_type preonly -fieldsplit_deformation_pc_type lu -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi -snes_monitor_short -ksp_monitor_short -snes_converged_reason -ksp_converged_reason -show_solution 0 -petscpartitioner_type simple
722:     output_file: output/ex77_2.out

724: TEST*/