Actual source code: ex56.c

petsc-main 2021-04-15
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  1: static char help[] = "3D, tri-quadratic hexahedra (Q1), displacement finite element formulation\n\
  2: of linear elasticity.  E=1.0, nu=1/3.\n\
  3: Unit cube domain with Dirichlet boundary\n\n";

  5: #include <petscdmplex.h>
  6: #include <petscsnes.h>
  7: #include <petscds.h>
  8: #include <petscdmforest.h>

 10: static PetscReal s_soft_alpha=1.e-3;
 11: static PetscReal s_mu=0.4;
 12: static PetscReal s_lambda=0.4;

 14: static void f0_bd_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 15:                        const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 16:                        const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 17:                        PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
 18: {
 19:   f0[0] = 1;     /* x direction pull */
 20:   f0[1] = -x[2]; /* add a twist around x-axis */
 21:   f0[2] =  x[1];
 22: }

 24: static void f1_bd_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 25:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 26:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 27:                     PetscReal t, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 28: {
 29:   const PetscInt Ncomp = dim;
 30:   PetscInt       comp, d;
 31:   for (comp = 0; comp < Ncomp; ++comp) {
 32:     for (d = 0; d < dim; ++d) {
 33:       f1[comp*dim+d] = 0.0;
 34:     }
 35:   }
 36: }

 38: /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
 39: static void f1_u_3d_alpha(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 40:                           const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 41:                           const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 42:                           PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 43: {
 44:   PetscReal trace,mu=s_mu,lambda=s_lambda,rad;
 45:   PetscInt i,j;
 46:   for (i=0,rad=0.;i<dim;i++) {
 47:     PetscReal t=x[i];
 48:     rad += t*t;
 49:   }
 50:   rad = PetscSqrtReal(rad);
 51:   if (rad>0.25) {
 52:     mu *= s_soft_alpha;
 53:     lambda *= s_soft_alpha; /* we could keep the bulk the same like rubberish */
 54:   }
 55:   for (i=0,trace=0; i < dim; ++i) {
 56:     trace += PetscRealPart(u_x[i*dim+i]);
 57:   }
 58:   for (i=0; i < dim; ++i) {
 59:     for (j=0; j < dim; ++j) {
 60:       f1[i*dim+j] = mu*(u_x[i*dim+j]+u_x[j*dim+i]);
 61:     }
 62:     f1[i*dim+i] += lambda*trace;
 63:   }
 64: }

 66: /* gradU[comp*dim+d] = {u_x, u_y} or {u_x, u_y, u_z} */
 67: static void f1_u_3d(PetscInt dim, PetscInt Nf, PetscInt NfAux,
 68:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
 69:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
 70:                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
 71: {
 72:   PetscReal trace,mu=s_mu,lambda=s_lambda;
 73:   PetscInt i,j;
 74:   for (i=0,trace=0; i < dim; ++i) {
 75:     trace += PetscRealPart(u_x[i*dim+i]);
 76:   }
 77:   for (i=0; i < dim; ++i) {
 78:     for (j=0; j < dim; ++j) {
 79:       f1[i*dim+j] = mu*(u_x[i*dim+j]+u_x[j*dim+i]);
 80:     }
 81:     f1[i*dim+i] += lambda*trace;
 82:   }
 83: }

 85: /* 3D elasticity */
 86: #define IDX(ii,jj,kk,ll) (27*ii+9*jj+3*kk+ll)

 88: void g3_uu_3d_private( PetscScalar g3[], const PetscReal mu, const PetscReal lambda)
 89: {
 90:   if (1) {
 91:     g3[0] += lambda;
 92:     g3[0] += mu;
 93:     g3[0] += mu;
 94:     g3[4] += lambda;
 95:     g3[8] += lambda;
 96:     g3[10] += mu;
 97:     g3[12] += mu;
 98:     g3[20] += mu;
 99:     g3[24] += mu;
100:     g3[28] += mu;
101:     g3[30] += mu;
102:     g3[36] += lambda;
103:     g3[40] += lambda;
104:     g3[40] += mu;
105:     g3[40] += mu;
106:     g3[44] += lambda;
107:     g3[50] += mu;
108:     g3[52] += mu;
109:     g3[56] += mu;
110:     g3[60] += mu;
111:     g3[68] += mu;
112:     g3[70] += mu;
113:     g3[72] += lambda;
114:     g3[76] += lambda;
115:     g3[80] += lambda;
116:     g3[80] += mu;
117:     g3[80] += mu;
118:   } else {
119:     int        i,j,k,l;
120:     static int cc=-1;
121:     cc++;
122:     for (i = 0; i < 3; ++i) {
123:       for (j = 0; j < 3; ++j) {
124:         for (k = 0; k < 3; ++k) {
125:           for (l = 0; l < 3; ++l) {
126:             if (k==l && i==j) g3[IDX(i,j,k,l)] += lambda;
127:             if (i==k && j==l) g3[IDX(i,j,k,l)] += mu;
128:             if (i==l && j==k) g3[IDX(i,j,k,l)] += mu;
129:             if (k==l && i==j && !cc) (void) PetscPrintf(PETSC_COMM_WORLD,"g3[%d] += lambda;\n",IDX(i,j,k,l));
130:             if (i==k && j==l && !cc) (void) PetscPrintf(PETSC_COMM_WORLD,"g3[%d] += mu;\n",IDX(i,j,k,l));
131:             if (i==l && j==k && !cc) (void) PetscPrintf(PETSC_COMM_WORLD,"g3[%d] += mu;\n",IDX(i,j,k,l));
132:           }
133:         }
134:       }
135:     }
136:   }
137: }

139: static void g3_uu_3d_alpha(PetscInt dim, PetscInt Nf, PetscInt NfAux,
140:                            const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
141:                            const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
142:                            PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g3[])
143: {
144:   PetscReal mu=s_mu, lambda=s_lambda,rad;
145:   PetscInt i;
146:   for (i=0,rad=0.;i<dim;i++) {
147:     PetscReal t=x[i];
148:     rad += t*t;
149:   }
150:   rad = PetscSqrtReal(rad);
151:   if (rad>0.25) {
152:     mu *= s_soft_alpha;
153:     lambda *= s_soft_alpha; /* we could keep the bulk the same like rubberish */
154:   }
155:   g3_uu_3d_private(g3,mu,lambda);
156: }

158: static 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:   g3_uu_3d_private(g3,s_mu,s_lambda);
164: }

166: static void f0_u(PetscInt dim, PetscInt Nf, PetscInt NfAux,
167:                  const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
168:                  const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
169:                  PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
170: {
171:   const    PetscInt Ncomp = dim;
172:   PetscInt comp;

174:   for (comp = 0; comp < Ncomp; ++comp) f0[comp] = 0.0;
175: }

177: /* PI_i (x_i^4 - x_i^2) */
178: static void f0_u_x4(PetscInt dim, PetscInt Nf, PetscInt NfAux,
179:                     const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[],
180:                     const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[],
181:                     PetscReal t, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
182: {
183:   const    PetscInt Ncomp = dim;
184:   PetscInt comp,i;

186:   for (comp = 0; comp < Ncomp; ++comp) {
187:     f0[comp] = 1e5;
188:     for (i = 0; i < Ncomp; ++i) {
189:       f0[comp] *= /* (comp+1)* */(x[i]*x[i]*x[i]*x[i] - x[i]*x[i]); /* assumes (0,1]^D domain */
190:     }
191:   }
192: }

194: PetscErrorCode zero(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)
195: {
196:   const PetscInt Ncomp = dim;
197:   PetscInt       comp;

199:   for (comp = 0; comp < Ncomp; ++comp) u[comp] = 0;
200:   return 0;
201: }

203: int main(int argc,char **args)
204: {
205:   Mat                Amat;
206:   PetscErrorCode     ierr;
207:   SNES               snes;
208:   KSP                ksp;
209:   MPI_Comm           comm;
210:   PetscMPIInt        rank;
211: #if defined(PETSC_USE_LOG)
212:   PetscLogStage      stage[17];
213: #endif
214:   PetscBool          test_nonzero_cols = PETSC_FALSE,use_nearnullspace = PETSC_TRUE,attach_nearnullspace = PETSC_FALSE;
215:   Vec                xx,bb;
216:   PetscInt           iter,i,N,dim = 3,cells[3] = {1,1,1},max_conv_its,local_sizes[7],run_type = 1;
217:   DM                 dm,distdm,basedm;
218:   PetscBool          flg;
219:   char               convType[256];
220:   PetscReal          Lx,mdisp[10],err[10];
221:   const char * const options[10] = {"-ex56_dm_refine 0",
222:                                     "-ex56_dm_refine 1",
223:                                     "-ex56_dm_refine 2",
224:                                     "-ex56_dm_refine 3",
225:                                     "-ex56_dm_refine 4",
226:                                     "-ex56_dm_refine 5",
227:                                     "-ex56_dm_refine 6",
228:                                     "-ex56_dm_refine 7",
229:                                     "-ex56_dm_refine 8",
230:                                     "-ex56_dm_refine 9"};
232:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
233:   comm = PETSC_COMM_WORLD;
234:   MPI_Comm_rank(comm, &rank);
235:   /* options */
236:   PetscOptionsBegin(comm,NULL,"3D bilinear Q1 elasticity options","");
237:   {
238:     i = 3;
239:     PetscOptionsIntArray("-cells", "Number of (flux tube) processor in each dimension", "ex56.c", cells, &i, NULL);

241:     Lx = 1.; /* or ne for rod */
242:     max_conv_its = 3;
243:     PetscOptionsInt("-max_conv_its","Number of iterations in convergence study","",max_conv_its,&max_conv_its,NULL);
244:     if (max_conv_its<=0 || max_conv_its>7) SETERRQ1(PETSC_COMM_WORLD, PETSC_ERR_USER, "Bad number of iterations for convergence test (%D)",max_conv_its);
245:     PetscOptionsReal("-lx","Length of domain","",Lx,&Lx,NULL);
246:     PetscOptionsReal("-alpha","material coefficient inside circle","",s_soft_alpha,&s_soft_alpha,NULL);
247:     PetscOptionsBool("-test_nonzero_cols","nonzero test","",test_nonzero_cols,&test_nonzero_cols,NULL);
248:     PetscOptionsBool("-use_mat_nearnullspace","MatNearNullSpace API test","",use_nearnullspace,&use_nearnullspace,NULL);
249:     PetscOptionsBool("-attach_mat_nearnullspace","MatNearNullSpace API test (via MatSetNearNullSpace)","",attach_nearnullspace,&attach_nearnullspace,NULL);
250:     PetscOptionsInt("-run_type","0: twisting load on cantalever, 1: 3rd order accurate convergence test","",run_type,&run_type,NULL);
251:   }
252:   PetscOptionsEnd();
253:   PetscLogStageRegister("Mesh Setup", &stage[16]);
254:   for (iter=0 ; iter<max_conv_its ; iter++) {
255:     char str[] = "Solve 0";
256:     str[6] += iter;
257:     PetscLogStageRegister(str, &stage[iter]);
258:   }
259:   /* create DM, Plex calls DMSetup */
260:   PetscLogStagePush(stage[16]);
261:   DMPlexCreateBoxMesh(comm, dim, PETSC_FALSE, cells, NULL, NULL, NULL, PETSC_TRUE, &dm);
262:   {
263:     DMLabel         label;
264:     IS              is;
265:     DMCreateLabel(dm, "boundary");
266:     DMGetLabel(dm, "boundary", &label);
267:     DMPlexMarkBoundaryFaces(dm, 1, label);
268:     if (!run_type) {
269:       DMGetStratumIS(dm, "boundary", 1,  &is);
270:       DMCreateLabel(dm,"Faces");
271:       if (is) {
272:         PetscInt        d, f, Nf;
273:         const PetscInt *faces;
274:         PetscInt        csize;
275:         PetscSection    cs;
276:         Vec             coordinates ;
277:         DM              cdm;
278:         ISGetLocalSize(is, &Nf);
279:         ISGetIndices(is, &faces);
280:         DMGetCoordinatesLocal(dm, &coordinates);
281:         DMGetCoordinateDM(dm, &cdm);
282:         DMGetLocalSection(cdm, &cs);
283:         /* Check for each boundary face if any component of its centroid is either 0.0 or 1.0 */
284:         for (f = 0; f < Nf; ++f) {
285:           PetscReal   faceCoord;
286:           PetscInt    b,v;
287:           PetscScalar *coords = NULL;
288:           PetscInt    Nv;
289:           DMPlexVecGetClosure(cdm, cs, coordinates, faces[f], &csize, &coords);
290:           Nv   = csize/dim; /* Calculate mean coordinate vector */
291:           for (d = 0; d < dim; ++d) {
292:             faceCoord = 0.0;
293:             for (v = 0; v < Nv; ++v) faceCoord += PetscRealPart(coords[v*dim+d]);
294:             faceCoord /= Nv;
295:             for (b = 0; b < 2; ++b) {
296:               if (PetscAbs(faceCoord - b) < PETSC_SMALL) { /* domain have not been set yet, still [0,1]^3 */
297:                 DMSetLabelValue(dm, "Faces", faces[f], d*2+b+1);
298:               }
299:             }
300:           }
301:           DMPlexVecRestoreClosure(cdm, cs, coordinates, faces[f], &csize, &coords);
302:         }
303:         ISRestoreIndices(is, &faces);
304:       }
305:       ISDestroy(&is);
306:       DMGetLabel(dm, "Faces", &label);
307:       DMPlexLabelComplete(dm, label);
308:     }
309:   }
310:   {
311:     PetscInt    dimEmbed, i;
312:     PetscInt    nCoords;
313:     PetscScalar *coords,bounds[] = {0,1,-.5,.5,-.5,.5,}; /* x_min,x_max,y_min,y_max */
314:     Vec         coordinates;
315:     bounds[1] = Lx;
316:     if (run_type==1) {
317:       for (i = 0; i < 2*dim; i++) bounds[i] = (i%2) ? 1 : 0;
318:     }
319:     DMGetCoordinatesLocal(dm,&coordinates);
320:     DMGetCoordinateDim(dm,&dimEmbed);
321:     if (dimEmbed != dim) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"dimEmbed != dim %D",dimEmbed);
322:     VecGetLocalSize(coordinates,&nCoords);
323:     if (nCoords % dimEmbed) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Coordinate vector the wrong size");
324:     VecGetArray(coordinates,&coords);
325:     for (i = 0; i < nCoords; i += dimEmbed) {
326:       PetscInt    j;
327:       PetscScalar *coord = &coords[i];
328:       for (j = 0; j < dimEmbed; j++) {
329:         coord[j] = bounds[2 * j] + coord[j] * (bounds[2 * j + 1] - bounds[2 * j]);
330:       }
331:     }
332:     VecRestoreArray(coordinates,&coords);
333:     DMSetCoordinatesLocal(dm,coordinates);
334:   }

336:   /* convert to p4est, and distribute */

338:   PetscOptionsBegin(comm, "", "Mesh conversion options", "DMPLEX");
339:   PetscOptionsFList("-dm_type","Convert DMPlex to another format (should not be Plex!)","ex56.c",DMList,DMPLEX,convType,256,&flg);
340:   PetscOptionsEnd();
341:   if (flg) {
342:     DM newdm;
343:     DMConvert(dm,convType,&newdm);
344:     if (newdm) {
345:       const char *prefix;
346:       PetscBool isForest;
347:       PetscObjectGetOptionsPrefix((PetscObject)dm,&prefix);
348:       PetscObjectSetOptionsPrefix((PetscObject)newdm,prefix);
349:       DMIsForest(newdm,&isForest);
350:       if (!isForest) SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Converted to non Forest?");
351:       DMDestroy(&dm);
352:       dm   = newdm;
353:     } else SETERRQ(PETSC_COMM_WORLD, PETSC_ERR_USER, "Convert failed?");
354:   } else {
355:     PetscPartitioner part;
356:     /* Plex Distribute mesh over processes */
357:     DMPlexGetPartitioner(dm,&part);
358:     PetscPartitionerSetFromOptions(part);
359:     DMPlexDistribute(dm, 0, NULL, &distdm);
360:     if (distdm) {
361:       const char *prefix;
362:       PetscObjectGetOptionsPrefix((PetscObject)dm,&prefix);
363:       PetscObjectSetOptionsPrefix((PetscObject)distdm,prefix);
364:       DMDestroy(&dm);
365:       dm   = distdm;
366:     }
367:   }
368:   PetscLogStagePop();
369:   basedm = dm; dm = NULL;

371:   for (iter=0 ; iter<max_conv_its ; iter++) {
372:     PetscLogStagePush(stage[16]);
373:     /* make new DM */
374:     DMClone(basedm, &dm);
375:     PetscObjectSetOptionsPrefix((PetscObject) dm, "ex56_");
376:     PetscObjectSetName( (PetscObject)dm,"Mesh");
377:     if (max_conv_its > 1) {
378:       /* If max_conv_its == 1, then we are not doing a convergence study. */
379:       PetscOptionsInsertString(NULL,options[iter]);
380:     }
381:     DMSetFromOptions(dm); /* refinement done here in Plex, p4est */
382:     /* snes */
383:     SNESCreate(comm, &snes);
384:     SNESSetDM(snes, dm);
385:     /* fem */
386:     {
387:       const PetscInt Ncomp = dim;
388:       const PetscInt components[] = {0,1,2};
389:       const PetscInt Nfid = 1, Npid = 1;
390:       const PetscInt fid[] = {1}; /* The fixed faces (x=0) */
391:       const PetscInt pid[] = {2}; /* The faces with loading (x=L_x) */
392:       PetscFE        fe;
393:       PetscDS        prob;
394:       DMLabel        label;
395:       DM             cdm = dm;

397:       PetscFECreateDefault(PetscObjectComm((PetscObject) dm), dim, dim, PETSC_FALSE, NULL, PETSC_DECIDE, &fe); /* elasticity */
398:       PetscObjectSetName((PetscObject) fe, "deformation");
399:       /* FEM prob */
400:       DMSetField(dm, 0, NULL, (PetscObject) fe);
401:       DMCreateDS(dm);
402:       DMGetDS(dm, &prob);
403:       /* setup problem */
404:       if (run_type==1) {
405:         PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu_3d);
406:         PetscDSSetResidual(prob, 0, f0_u_x4, f1_u_3d);
407:       } else {
408:         PetscWeakForm wf;
409:         PetscInt      bd, i;

411:         PetscDSSetJacobian(prob, 0, 0, NULL, NULL, NULL, g3_uu_3d_alpha);
412:         PetscDSSetResidual(prob, 0, f0_u, f1_u_3d_alpha);

414:         DMGetLabel(dm, "Faces", &label);
415:         DMAddBoundary(dm, DM_BC_NATURAL, "traction", label, Npid, pid, 0, Ncomp, components, NULL, NULL, NULL, &bd);
416:         PetscDSGetBoundary(prob, bd, &wf, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL);
417:         for (i = 0; i < Npid; ++i) {PetscWeakFormSetIndexBdResidual(wf, label, pid[i], 0, 0, f0_bd_u_3d, 0, f1_bd_u);}
418:       }
419:       /* bcs */
420:       if (run_type==1) {
421:         PetscInt id = 1;
422:         DMGetLabel(dm, "boundary", &label);
423:         DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 1, &id, 0, 0, NULL, (void (*)(void)) zero, NULL, NULL, NULL);
424:       } else {
425:         DMGetLabel(dm, "Faces", &label);
426:         DMAddBoundary(dm, DM_BC_ESSENTIAL, "fixed", label, Nfid, fid, 0, Ncomp, components, (void (*)(void)) zero, NULL, NULL, NULL);
427:       }
428:       while (cdm) {
429:         DMCopyDisc(dm, cdm);
430:         DMGetCoarseDM(cdm, &cdm);
431:       }
432:       PetscFEDestroy(&fe);
433:     }
434:     /* vecs & mat */
435:     DMCreateGlobalVector(dm,&xx);
436:     VecDuplicate(xx, &bb);
437:     PetscObjectSetName((PetscObject) bb, "b");
438:     PetscObjectSetName((PetscObject) xx, "u");
439:     DMCreateMatrix(dm, &Amat);
440:     MatSetOption(Amat,MAT_SYMMETRIC,PETSC_TRUE);        /* Some matrix kernels can take advantage of symmetry if we set this. */
441:     MatSetOption(Amat,MAT_SYMMETRY_ETERNAL,PETSC_TRUE); /* Inform PETSc that Amat is always symmetric, so info set above isn't lost. */
442:     MatSetBlockSize(Amat,3);
443:     MatSetOption(Amat,MAT_SPD,PETSC_TRUE);
444:     VecGetSize(bb,&N);
445:     local_sizes[iter] = N;
446:     PetscInfo2(snes,"%D global equations, %D vertices\n",N,N/dim);
447:     if ((use_nearnullspace || attach_nearnullspace) && N/dim > 1) {
448:       /* Set up the near null space (a.k.a. rigid body modes) that will be used by the multigrid preconditioner */
449:       DM           subdm;
450:       MatNullSpace nearNullSpace;
451:       PetscInt     fields = 0;
452:       PetscObject  deformation;
453:       DMCreateSubDM(dm, 1, &fields, NULL, &subdm);
454:       DMPlexCreateRigidBody(subdm, 0, &nearNullSpace);
455:       DMGetField(dm, 0, NULL, &deformation);
456:       PetscObjectCompose(deformation, "nearnullspace", (PetscObject) nearNullSpace);
457:       DMDestroy(&subdm);
458:       if (attach_nearnullspace) {
459:         MatSetNearNullSpace(Amat,nearNullSpace);
460:       }
461:       MatNullSpaceDestroy(&nearNullSpace); /* created by DM and destroyed by Mat */
462:     }
463:     DMPlexSetSNESLocalFEM(dm,NULL,NULL,NULL);
464:     SNESSetJacobian(snes, Amat, Amat, NULL, NULL);
465:     SNESSetFromOptions(snes);
466:     DMSetUp(dm);
467:     PetscLogStagePop();
468:     PetscLogStagePush(stage[16]);
469:     /* ksp */
470:     SNESGetKSP(snes, &ksp);
471:     KSPSetComputeSingularValues(ksp,PETSC_TRUE);
472:     /* test BCs */
473:     VecZeroEntries(xx);
474:     if (test_nonzero_cols) {
475:       if (!rank) {
476:         VecSetValue(xx,0,1.0,INSERT_VALUES);
477:       }
478:       VecAssemblyBegin(xx);
479:       VecAssemblyEnd(xx);
480:     }
481:     VecZeroEntries(bb);
482:     VecGetSize(bb,&i);
483:     local_sizes[iter] = i;
484:     PetscInfo2(snes,"%D equations in vector, %D vertices\n",i,i/dim);
485:     PetscLogStagePop();
486:     /* solve */
487:     PetscLogStagePush(stage[iter]);
488:     SNESSolve(snes, bb, xx);
489:     PetscLogStagePop();
490:     VecNorm(xx,NORM_INFINITY,&mdisp[iter]);
491:     DMViewFromOptions(dm, NULL, "-dm_view");
492:     {
493:       PetscViewer       viewer = NULL;
494:       PetscViewerFormat fmt;
495:       PetscOptionsGetViewer(comm,NULL,"ex56_","-vec_view",&viewer,&fmt,&flg);
496:       if (flg) {
497:         PetscViewerPushFormat(viewer,fmt);
498:         VecView(xx,viewer);
499:         VecView(bb,viewer);
500:         PetscViewerPopFormat(viewer);
501:       }
502:       PetscViewerDestroy(&viewer);
503:     }
504:     /* Free work space */
505:     DMDestroy(&dm);
506:     SNESDestroy(&snes);
507:     VecDestroy(&xx);
508:     VecDestroy(&bb);
509:     MatDestroy(&Amat);
510:   }
511:   DMDestroy(&basedm);
512:   if (run_type==1) err[0] = 59.975208 - mdisp[0]; /* error with what I think is the exact solution */
513:   else             err[0] = 171.038 - mdisp[0];
514:   for (iter=1 ; iter<max_conv_its ; iter++) {
515:     if (run_type==1) err[iter] = 59.975208 - mdisp[iter];
516:     else             err[iter] = 171.038 - mdisp[iter];
517:     PetscPrintf(PETSC_COMM_WORLD,"[%d] %D) N=%12D, max displ=%9.7e, disp diff=%9.2e, error=%4.3e, rate=%3.2g\n",rank,iter,local_sizes[iter],(double)mdisp[iter],
518:                        (double)(mdisp[iter]-mdisp[iter-1]),(double)err[iter],(double)(PetscLogReal(err[iter-1]/err[iter])/PetscLogReal(2.)));
519:   }

521:   PetscFinalize();
522:   return ierr;
523: }

525: /*TEST

527:   test:
528:     suffix: 0
529:     nsize: 4
530:     requires: !single
531:     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-10 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -ksp_converged_reason -snes_monitor_short -ksp_monitor_short -snes_converged_reason -use_mat_nearnullspace true -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.1 -mg_levels_pc_type jacobi -petscpartitioner_type simple -matptap_via scalable -ex56_dm_view
532:     timeoutfactor: 2

534:   # HYPRE PtAP broken with complex numbers
535:   test:
536:     suffix: hypre
537:     requires: hypre !single !complex
538:     nsize: 4
539:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -pc_type hypre -pc_hypre_type boomeramg -pc_hypre_boomeramg_no_CF true -pc_hypre_boomeramg_agg_nl 1 -pc_hypre_boomeramg_coarsen_type HMIS -pc_hypre_boomeramg_interp_type ext+i -ksp_converged_reason -use_mat_nearnullspace true -petscpartitioner_type simple

541:   test:
542:     suffix: ml
543:     requires: ml !single
544:     nsize: 4
545:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_converged_reason -ksp_rtol 1.e-8 -pc_type ml -mg_levels_ksp_type chebyshev -mg_levels_ksp_max_it 3 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type sor -petscpartitioner_type simple -use_mat_nearnullspace

547:   test:
548:     suffix: hpddm
549:     requires: hpddm slepc !single define(PETSC_HAVE_DYNAMIC_LIBRARIES) define(PETSC_USE_SHARED_LIBRARIES)
550:     nsize: 4
551:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type fgmres -ksp_monitor_short -ksp_converged_reason -ksp_rtol 1.e-8 -pc_type hpddm -petscpartitioner_type simple -pc_hpddm_levels_1_sub_pc_type lu -pc_hpddm_levels_1_eps_nev 6 -pc_hpddm_coarse_p 1 -pc_hpddm_coarse_pc_type svd

553:   test:
554:     nsize: 4
555:     requires: parmetis !single
556:     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-10 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -use_mat_nearnullspace true -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type jacobi -pc_gamg_mat_partitioning_type parmetis -pc_gamg_repartition true -snes_converged_reason

558:   test:
559:     suffix: bddc
560:     nsize: 4
561:     requires: !single
562:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type {{sbaij baij aij}} -pc_type bddc

564:   testset:
565:     nsize: 4
566:     requires: !single
567:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-10 -ksp_converged_reason -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type aij -pc_type bddc -attach_mat_nearnullspace {{0 1}separate output}
568:     test:
569:       suffix: bddc_approx_gamg
570:       args: -pc_bddc_switch_static -prefix_push pc_bddc_dirichlet_ -approximate -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -prefix_pop -prefix_push pc_bddc_neumann_ -approximate -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -prefix_pop
571:     # HYPRE PtAP broken with complex numbers
572:     test:
573:       requires: hypre !complex
574:       suffix: bddc_approx_hypre
575:       args: -pc_bddc_switch_static -prefix_push pc_bddc_dirichlet_ -pc_type hypre -pc_hypre_boomeramg_no_CF true -pc_hypre_boomeramg_strong_threshold 0.75 -pc_hypre_boomeramg_agg_nl 1 -pc_hypre_boomeramg_coarsen_type HMIS -pc_hypre_boomeramg_interp_type ext+i -prefix_pop -prefix_push pc_bddc_neumann_ -pc_type hypre -pc_hypre_boomeramg_no_CF true -pc_hypre_boomeramg_strong_threshold 0.75 -pc_hypre_boomeramg_agg_nl 1 -pc_hypre_boomeramg_coarsen_type HMIS -pc_hypre_boomeramg_interp_type ext+i -prefix_pop
576:     test:
577:       requires: ml
578:       suffix: bddc_approx_ml
579:       args: -pc_bddc_switch_static -prefix_push pc_bddc_dirichlet_ -approximate -pc_type ml -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -prefix_pop -prefix_push pc_bddc_neumann_ -approximate -pc_type ml -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -prefix_pop

581:   test:
582:     suffix: fetidp
583:     nsize: 4
584:     requires: !single
585:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type fetidp -fetidp_ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type {{sbaij baij aij}}

587:   test:
588:     suffix: bddc_elast
589:     nsize: 4
590:     requires: !single
591:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type sbaij -pc_type bddc -pc_bddc_monolithic -attach_mat_nearnullspace

593:   test:
594:     suffix: fetidp_elast
595:     nsize: 4
596:     requires: !single
597:     args: -cells 2,2,1 -max_conv_its 2 -lx 1. -alpha .01 -petscspace_degree 2 -ksp_type fetidp -fetidp_ksp_type cg -ksp_monitor_short -ksp_rtol 1.e-8 -ksp_converged_reason -petscpartitioner_type simple -ex56_dm_mat_type is -matis_localmat_type sbaij -fetidp_bddc_pc_bddc_monolithic -attach_mat_nearnullspace

599:   test:
600:     suffix: cuda
601:     nsize: 4
602:     requires: cuda !single
603:     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-10 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -use_mat_nearnullspace true -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type jacobi -ex56_dm_mat_type aijcusparse -ex56_dm_vec_type cuda -ksp_monitor_short -ksp_converged_reason -snes_converged_reason -snes_monitor_short -ex56_dm_view -petscpartitioner_type simple -pc_gamg_process_eq_limit 20

605:   test:
606:     suffix: viennacl
607:     nsize: 4
608:     requires: viennacl !single
609:     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-10 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 10 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -use_mat_nearnullspace true -mg_levels_ksp_max_it 2 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.05 -mg_levels_pc_type jacobi -ex56_dm_mat_type aijviennacl -ex56_dm_vec_type viennacl -ksp_monitor_short -ksp_converged_reason -snes_converged_reason -snes_monitor_short -ex56_dm_view -petscpartitioner_type simple -pc_gamg_process_eq_limit 20


612:   # Don't run AIJMKL caes with complex scalars because of convergence issues.
613:   # Note that we need to test both single and multiple MPI rank cases, because these use different sparse MKL routines to implement the PtAP operation.
614:   test:
615:     suffix: seqaijmkl
616:     nsize: 1
617:     requires: define(PETSC_HAVE_MKL_SPARSE_OPTIMIZE) !single !complex
618:     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 1000 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -ksp_converged_reason -snes_monitor_short -ksp_monitor_short -snes_converged_reason -use_mat_nearnullspace true -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.1 -mg_levels_pc_type jacobi -petscpartitioner_type simple -mat_block_size 3 -ex56_dm_view -run_type 1 -mat_seqaij_type seqaijmkl
619:     timeoutfactor: 2

621:   test:
622:     suffix: mpiaijmkl
623:     nsize: 2
624:     requires: define(PETSC_HAVE_MKL_SPARSE_OPTIMIZE) !single !complex
625:     args: -cells 2,2,1 -max_conv_its 2 -petscspace_degree 2 -snes_max_it 2 -ksp_max_it 100 -ksp_type cg -ksp_rtol 1.e-11 -ksp_norm_type unpreconditioned -snes_rtol 1.e-10 -pc_type gamg -pc_gamg_type agg -pc_gamg_agg_nsmooths 1 -pc_gamg_coarse_eq_limit 1000 -pc_gamg_reuse_interpolation true -pc_gamg_square_graph 1 -pc_gamg_threshold 0.05 -pc_gamg_threshold_scale .0 -ksp_converged_reason -snes_monitor_short -ksp_monitor_short -snes_converged_reason -use_mat_nearnullspace true -mg_levels_ksp_max_it 1 -mg_levels_ksp_type chebyshev -pc_gamg_esteig_ksp_type cg -pc_gamg_esteig_ksp_max_it 10 -mg_levels_ksp_chebyshev_esteig 0,0.05,0,1.1 -mg_levels_pc_type jacobi -petscpartitioner_type simple -mat_block_size 3 -ex56_dm_view -run_type 1 -mat_seqaij_type seqaijmkl
626:     timeoutfactor: 2


629: TEST*/