Actual source code: ex59.c

petsc-master 2019-08-22
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  1: static char help[] =  "This example illustrates the use of PCBDDC/FETI-DP and its customization.\n\n\
  2: Discrete system: 1D, 2D or 3D laplacian, discretized with spectral elements.\n\
  3: Spectral degree can be specified by passing values to -p option.\n\
  4: Global problem either with dirichlet boundary conditions on one side or in the pure neumann case (depending on runtime parameters).\n\
  5: Domain is [-nex,nex]x[-ney,ney]x[-nez,nez]: ne_ number of elements in _ direction.\n\
  6: Exaple usage: \n\
  7: 1D: mpiexec -n 4 ex59 -nex 7\n\
  8: 2D: mpiexec -n 4 ex59 -npx 2 -npy 2 -nex 2 -ney 2\n\
  9: 3D: mpiexec -n 4 ex59 -npx 2 -npy 2 -npz 1 -nex 2 -ney 2 -nez 1\n\
 10: Subdomain decomposition can be specified with -np_ parameters.\n\
 11: Dirichlet boundaries on one side by default:\n\
 12: it does not iterate on dirichlet nodes by default: if -usezerorows is passed in, it also iterates on Dirichlet nodes.\n\
 13: Pure Neumann case can be requested by passing in -pureneumann.\n\
 14: In the latter case, in order to avoid runtime errors during factorization, please specify also -coarse_redundant_pc_factor_zeropivot 0\n\n";

 16:  #include <petscksp.h>
 17:  #include <petscpc.h>
 18:  #include <petscdm.h>
 19:  #include <petscdmda.h>
 20:  #include <petscblaslapack.h>
 21: #define DEBUG 0

 23: /* structure holding domain data */
 24: typedef struct {
 25:   /* communicator */
 26:   MPI_Comm gcomm;
 27:   /* space dimension */
 28:   PetscInt dim;
 29:   /* spectral degree */
 30:   PetscInt p;
 31:   /* subdomains per dimension */
 32:   PetscInt npx,npy,npz;
 33:   /* subdomain index in cartesian dimensions */
 34:   PetscInt ipx,ipy,ipz;
 35:   /* elements per dimension */
 36:   PetscInt nex,ney,nez;
 37:   /* local elements per dimension */
 38:   PetscInt nex_l,ney_l,nez_l;
 39:   /* global number of dofs per dimension */
 40:   PetscInt xm,ym,zm;
 41:   /* local number of dofs per dimension */
 42:   PetscInt xm_l,ym_l,zm_l;
 43:   /* starting global indexes for subdomain in lexicographic ordering */
 44:   PetscInt startx,starty,startz;
 45:   /* pure Neumann problem */
 46:   PetscBool pure_neumann;
 47:   /* Dirichlet BC implementation */
 48:   PetscBool DBC_zerorows;
 49:   /* Scaling factor for subdomain */
 50:   PetscScalar scalingfactor;
 51:   PetscBool   testkspfetidp;
 52: } DomainData;

 54: /* structure holding GLL data */
 55: typedef struct {
 56:   /* GLL nodes */
 57:   PetscReal   *zGL;
 58:   /* GLL weights */
 59:   PetscScalar *rhoGL;
 60:   /* aux_mat */
 61:   PetscScalar **A;
 62:   /* Element matrix */
 63:   Mat elem_mat;
 64: } GLLData;


 67: static PetscErrorCode BuildCSRGraph(DomainData dd, PetscInt **xadj, PetscInt **adjncy)
 68: {
 70:   PetscInt       *xadj_temp,*adjncy_temp;
 71:   PetscInt       i,j,k,ii,jj,kk,iindex,count_adj;
 72:   PetscInt       istart_csr,iend_csr,jstart_csr,jend_csr,kstart_csr,kend_csr;
 73:   PetscBool      internal_node;

 75:   /* first count dimension of adjncy */
 76:   count_adj=0;
 77:   for (k=0; k<dd.zm_l; k++) {
 78:     internal_node = PETSC_TRUE;
 79:     kstart_csr    = k>0 ? k-1 : k;
 80:     kend_csr      = k<dd.zm_l-1 ? k+2 : k+1;
 81:     if (k == 0 || k == dd.zm_l-1) {
 82:       internal_node = PETSC_FALSE;
 83:       kstart_csr    = k;
 84:       kend_csr      = k+1;
 85:     }
 86:     for (j=0; j<dd.ym_l; j++) {
 87:       jstart_csr = j>0 ? j-1 : j;
 88:       jend_csr   = j<dd.ym_l-1 ? j+2 : j+1;
 89:       if (j == 0 || j == dd.ym_l-1) {
 90:         internal_node = PETSC_FALSE;
 91:         jstart_csr    = j;
 92:         jend_csr      = j+1;
 93:       }
 94:       for (i=0; i<dd.xm_l; i++) {
 95:         istart_csr = i>0 ? i-1 : i;
 96:         iend_csr   = i<dd.xm_l-1 ? i+2 : i+1;
 97:         if (i == 0 || i == dd.xm_l-1) {
 98:           internal_node = PETSC_FALSE;
 99:           istart_csr    = i;
100:           iend_csr      = i+1;
101:         }
102:         if (internal_node) {
103:           istart_csr = i;
104:           iend_csr   = i+1;
105:           jstart_csr = j;
106:           jend_csr   = j+1;
107:           kstart_csr = k;
108:           kend_csr   = k+1;
109:         }
110:         for (kk=kstart_csr;kk<kend_csr;kk++) {
111:           for (jj=jstart_csr;jj<jend_csr;jj++) {
112:             for (ii=istart_csr;ii<iend_csr;ii++) {
113:               count_adj=count_adj+1;
114:             }
115:           }
116:         }
117:       }
118:     }
119:   }
120:   PetscMalloc1(dd.xm_l*dd.ym_l*dd.zm_l+1,&xadj_temp);
121:   PetscMalloc1(count_adj,&adjncy_temp);

123:   /* now fill CSR data structure */
124:   count_adj=0;
125:   for (k=0; k<dd.zm_l; k++) {
126:     internal_node = PETSC_TRUE;
127:     kstart_csr    = k>0 ? k-1 : k;
128:     kend_csr      = k<dd.zm_l-1 ? k+2 : k+1;
129:     if (k == 0 || k == dd.zm_l-1) {
130:       internal_node = PETSC_FALSE;
131:       kstart_csr    = k;
132:       kend_csr      = k+1;
133:     }
134:     for (j=0; j<dd.ym_l; j++) {
135:       jstart_csr = j>0 ? j-1 : j;
136:       jend_csr   = j<dd.ym_l-1 ? j+2 : j+1;
137:       if (j == 0 || j == dd.ym_l-1) {
138:         internal_node = PETSC_FALSE;
139:         jstart_csr    = j;
140:         jend_csr      = j+1;
141:       }
142:       for (i=0; i<dd.xm_l; i++) {
143:         istart_csr = i>0 ? i-1 : i;
144:         iend_csr   = i<dd.xm_l-1 ? i+2 : i+1;
145:         if (i == 0 || i == dd.xm_l-1) {
146:           internal_node = PETSC_FALSE;
147:           istart_csr    = i;
148:           iend_csr      = i+1;
149:         }
150:         iindex            = k*dd.xm_l*dd.ym_l+j*dd.xm_l+i;
151:         xadj_temp[iindex] = count_adj;
152:         if (internal_node) {
153:           istart_csr = i;
154:           iend_csr   = i+1;
155:           jstart_csr = j;
156:           jend_csr   = j+1;
157:           kstart_csr = k;
158:           kend_csr   = k+1;
159:         }
160:         for (kk=kstart_csr; kk<kend_csr; kk++) {
161:           for (jj=jstart_csr; jj<jend_csr; jj++) {
162:             for (ii=istart_csr; ii<iend_csr; ii++) {
163:               iindex = kk*dd.xm_l*dd.ym_l+jj*dd.xm_l+ii;

165:               adjncy_temp[count_adj] = iindex;
166:               count_adj              = count_adj+1;
167:             }
168:           }
169:         }
170:       }
171:     }
172:   }
173:   xadj_temp[dd.xm_l*dd.ym_l*dd.zm_l] = count_adj;

175:   *xadj   = xadj_temp;
176:   *adjncy = adjncy_temp;
177:   return(0);
178: }

180: static PetscErrorCode ComputeSpecialBoundaryIndices(DomainData dd,IS *dirichlet,IS *neumann)
181: {
183:   IS             temp_dirichlet=0,temp_neumann=0;
184:   PetscInt       localsize,i,j,k,*indices;
185:   PetscBool      *touched;

188:   localsize = dd.xm_l*dd.ym_l*dd.zm_l;

190:   PetscMalloc1(localsize,&indices);
191:   PetscMalloc1(localsize,&touched);
192:   for (i=0; i<localsize; i++) touched[i] = PETSC_FALSE;

194:   if (dirichlet) {
195:     i = 0;
196:     /* west boundary */
197:     if (dd.ipx == 0) {
198:       for (k=0;k<dd.zm_l;k++) {
199:         for (j=0;j<dd.ym_l;j++) {
200:           indices[i]=k*dd.ym_l*dd.xm_l+j*dd.xm_l;
201:           touched[indices[i]]=PETSC_TRUE;
202:           i++;
203:         }
204:       }
205:     }
206:     ISCreateGeneral(dd.gcomm,i,indices,PETSC_COPY_VALUES,&temp_dirichlet);
207:   }
208:   if (neumann) {
209:     i = 0;
210:     /* west boundary */
211:     if (dd.ipx == 0) {
212:       for (k=0;k<dd.zm_l;k++) {
213:         for (j=0;j<dd.ym_l;j++) {
214:           indices[i]=k*dd.ym_l*dd.xm_l+j*dd.xm_l;
215:           if (!touched[indices[i]]) {
216:             touched[indices[i]]=PETSC_TRUE;
217:             i++;
218:           }
219:         }
220:       }
221:     }
222:     /* east boundary */
223:     if (dd.ipx == dd.npx-1) {
224:       for (k=0;k<dd.zm_l;k++) {
225:         for (j=0;j<dd.ym_l;j++) {
226:           indices[i]=k*dd.ym_l*dd.xm_l+j*dd.xm_l+dd.xm_l-1;
227:           if (!touched[indices[i]]) {
228:             touched[indices[i]]=PETSC_TRUE;
229:             i++;
230:           }
231:         }
232:       }
233:     }
234:     /* south boundary */
235:     if (dd.ipy == 0 && dd.dim > 1) {
236:       for (k=0;k<dd.zm_l;k++) {
237:         for (j=0;j<dd.xm_l;j++) {
238:           indices[i]=k*dd.ym_l*dd.xm_l+j;
239:           if (!touched[indices[i]]) {
240:             touched[indices[i]]=PETSC_TRUE;
241:             i++;
242:           }
243:         }
244:       }
245:     }
246:     /* north boundary */
247:     if (dd.ipy == dd.npy-1 && dd.dim > 1) {
248:       for (k=0;k<dd.zm_l;k++) {
249:         for (j=0;j<dd.xm_l;j++) {
250:           indices[i]=k*dd.ym_l*dd.xm_l+(dd.ym_l-1)*dd.xm_l+j;
251:           if (!touched[indices[i]]) {
252:             touched[indices[i]]=PETSC_TRUE;
253:             i++;
254:           }
255:         }
256:       }
257:     }
258:     /* bottom boundary */
259:     if (dd.ipz == 0 && dd.dim > 2) {
260:       for (k=0;k<dd.ym_l;k++) {
261:         for (j=0;j<dd.xm_l;j++) {
262:           indices[i]=k*dd.xm_l+j;
263:           if (!touched[indices[i]]) {
264:             touched[indices[i]]=PETSC_TRUE;
265:             i++;
266:           }
267:         }
268:       }
269:     }
270:     /* top boundary */
271:     if (dd.ipz == dd.npz-1 && dd.dim > 2) {
272:       for (k=0;k<dd.ym_l;k++) {
273:         for (j=0;j<dd.xm_l;j++) {
274:           indices[i]=(dd.zm_l-1)*dd.ym_l*dd.xm_l+k*dd.xm_l+j;
275:           if (!touched[indices[i]]) {
276:             touched[indices[i]]=PETSC_TRUE;
277:             i++;
278:           }
279:         }
280:       }
281:     }
282:     ISCreateGeneral(dd.gcomm,i,indices,PETSC_COPY_VALUES,&temp_neumann);
283:   }
284:   if (dirichlet) *dirichlet = temp_dirichlet;
285:   if (neumann) *neumann = temp_neumann;
286:   PetscFree(indices);
287:   PetscFree(touched);
288:   return(0);
289: }

291: static PetscErrorCode ComputeMapping(DomainData dd,ISLocalToGlobalMapping *isg2lmap)
292: {
293:   PetscErrorCode         ierr;
294:   DM                     da;
295:   AO                     ao;
296:   DMBoundaryType         bx = DM_BOUNDARY_NONE,by = DM_BOUNDARY_NONE, bz = DM_BOUNDARY_NONE;
297:   DMDAStencilType        stype = DMDA_STENCIL_BOX;
298:   ISLocalToGlobalMapping temp_isg2lmap;
299:   PetscInt               i,j,k,ig,jg,kg,lindex,gindex,localsize;
300:   PetscInt               *global_indices;

303:   /* Not an efficient mapping: this function computes a very simple lexicographic mapping
304:      just to illustrate the creation of a MATIS object */
305:   localsize = dd.xm_l*dd.ym_l*dd.zm_l;
306:   PetscMalloc1(localsize,&global_indices);
307:   for (k=0; k<dd.zm_l; k++) {
308:     kg=dd.startz+k;
309:     for (j=0; j<dd.ym_l; j++) {
310:       jg=dd.starty+j;
311:       for (i=0; i<dd.xm_l; i++) {
312:         ig                    =dd.startx+i;
313:         lindex                =k*dd.xm_l*dd.ym_l+j*dd.xm_l+i;
314:         gindex                =kg*dd.xm*dd.ym+jg*dd.xm+ig;
315:         global_indices[lindex]=gindex;
316:       }
317:     }
318:   }
319:   if (dd.dim==3) {
320:     DMDACreate3d(dd.gcomm,bx,by,bz,stype,dd.xm,dd.ym,dd.zm,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,NULL,&da);
321:   } else if (dd.dim==2) {
322:     DMDACreate2d(dd.gcomm,bx,by,stype,dd.xm,dd.ym,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);
323:   } else {
324:     DMDACreate1d(dd.gcomm,bx,dd.xm,1,1,NULL,&da);
325:   }
326:   DMSetFromOptions(da);
327:   DMSetUp(da);
328:   DMDASetAOType(da,AOMEMORYSCALABLE);
329:   DMDAGetAO(da,&ao);
330:   AOApplicationToPetsc(ao,dd.xm_l*dd.ym_l*dd.zm_l,global_indices);
331:   ISLocalToGlobalMappingCreate(dd.gcomm,1,localsize,global_indices,PETSC_OWN_POINTER,&temp_isg2lmap);
332:   DMDestroy(&da);
333:   *isg2lmap = temp_isg2lmap;
334:   return(0);
335: }
336: static PetscErrorCode ComputeSubdomainMatrix(DomainData dd, GLLData glldata, Mat *local_mat)
337: {
339:   PetscInt       localsize,zloc,yloc,xloc,auxnex,auxney,auxnez;
340:   PetscInt       ie,je,ke,i,j,k,ig,jg,kg,ii,ming;
341:   PetscInt       *indexg,*cols,*colsg;
342:   PetscScalar    *vals;
343:   Mat            temp_local_mat,elem_mat_DBC=0,*usedmat;
344:   IS             submatIS;

347:   MatGetSize(glldata.elem_mat,&i,&j);
348:   PetscMalloc1(i,&indexg);
349:   PetscMalloc1(i,&colsg);
350:   /* get submatrix of elem_mat without dirichlet nodes */
351:   if (!dd.pure_neumann && !dd.DBC_zerorows && !dd.ipx) {
352:     xloc = dd.p+1;
353:     yloc = 1;
354:     zloc = 1;
355:     if (dd.dim>1) yloc = dd.p+1;
356:     if (dd.dim>2) zloc = dd.p+1;
357:     ii = 0;
358:     for (k=0;k<zloc;k++) {
359:       for (j=0;j<yloc;j++) {
360:         for (i=1;i<xloc;i++) {
361:           indexg[ii]=k*xloc*yloc+j*xloc+i;
362:           ii++;
363:         }
364:       }
365:     }
366:     ISCreateGeneral(PETSC_COMM_SELF,ii,indexg,PETSC_COPY_VALUES,&submatIS);
367:     MatCreateSubMatrix(glldata.elem_mat,submatIS,submatIS,MAT_INITIAL_MATRIX,&elem_mat_DBC);
368:     ISDestroy(&submatIS);
369:   }

371:   /* Assemble subdomain matrix */
372:   localsize = dd.xm_l*dd.ym_l*dd.zm_l;
373:   MatCreate(PETSC_COMM_SELF,&temp_local_mat);
374:   MatSetSizes(temp_local_mat,localsize,localsize,localsize,localsize);
375:   MatSetOptionsPrefix(temp_local_mat,"subdomain_");
376:   /* set local matrices type: here we use SEQSBAIJ primarily for testing purpose */
377:   /* in order to avoid conversions inside the BDDC code, use SeqAIJ if possible */
378:   if (dd.DBC_zerorows && !dd.ipx) { /* in this case, we need to zero out some of the rows, so use seqaij */
379:     MatSetType(temp_local_mat,MATSEQAIJ);
380:   } else {
381:     MatSetType(temp_local_mat,MATSEQSBAIJ);
382:   }
383:   MatSetFromOptions(temp_local_mat);

385:   i = PetscPowRealInt(3.0*(dd.p+1.0),dd.dim);

387:   MatSeqAIJSetPreallocation(temp_local_mat,i,NULL);      /* very overestimated */
388:   MatSeqSBAIJSetPreallocation(temp_local_mat,1,i,NULL);      /* very overestimated */
389:   MatSeqBAIJSetPreallocation(temp_local_mat,1,i,NULL);      /* very overestimated */
390:   MatSetOption(temp_local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);

392:   yloc = dd.p+1;
393:   zloc = dd.p+1;
394:   if (dd.dim < 3) zloc = 1;
395:   if (dd.dim < 2) yloc = 1;

397:   auxnez = dd.nez_l;
398:   auxney = dd.ney_l;
399:   auxnex = dd.nex_l;
400:   if (dd.dim < 3) auxnez = 1;
401:   if (dd.dim < 2) auxney = 1;

403:   for (ke=0; ke<auxnez; ke++) {
404:     for (je=0; je<auxney; je++) {
405:       for (ie=0; ie<auxnex; ie++) {
406:         /* customize element accounting for BC */
407:         xloc    = dd.p+1;
408:         ming    = 0;
409:         usedmat = &glldata.elem_mat;
410:         if (!dd.pure_neumann && !dd.DBC_zerorows && !dd.ipx) {
411:           if (ie == 0) {
412:             xloc    = dd.p;
413:             usedmat = &elem_mat_DBC;
414:           } else {
415:             ming    = -1;
416:             usedmat = &glldata.elem_mat;
417:           }
418:         }
419:         /* local to the element/global to the subdomain indexing */
420:         for (k=0; k<zloc; k++) {
421:           kg = ke*dd.p+k;
422:           for (j=0; j<yloc; j++) {
423:             jg = je*dd.p+j;
424:             for (i=0; i<xloc; i++) {
425:               ig         = ie*dd.p+i+ming;
426:               ii         = k*xloc*yloc+j*xloc+i;
427:               indexg[ii] = kg*dd.xm_l*dd.ym_l+jg*dd.xm_l+ig;
428:             }
429:           }
430:         }
431:         /* Set values */
432:         for (i=0; i<xloc*yloc*zloc; i++) {
433:           MatGetRow(*usedmat,i,&j,(const PetscInt**)&cols,(const PetscScalar**)&vals);
434:           for (k=0; k<j; k++) colsg[k] = indexg[cols[k]];
435:           MatSetValues(temp_local_mat,1,&indexg[i],j,colsg,vals,ADD_VALUES);
436:           MatRestoreRow(*usedmat,i,&j,(const PetscInt**)&cols,(const PetscScalar**)&vals);
437:         }
438:       }
439:     }
440:   }
441:   PetscFree(indexg);
442:   PetscFree(colsg);
443:   MatAssemblyBegin(temp_local_mat,MAT_FINAL_ASSEMBLY);
444:   MatAssemblyEnd  (temp_local_mat,MAT_FINAL_ASSEMBLY);
445: #if DEBUG
446:   {
447:     Vec       lvec,rvec;
448:     PetscReal norm;
449:     MatCreateVecs(temp_local_mat,&lvec,&rvec);
450:     VecSet(lvec,1.0);
451:     MatMult(temp_local_mat,lvec,rvec);
452:     VecNorm(rvec,NORM_INFINITY,&norm);
453:     VecDestroy(&lvec);
454:     VecDestroy(&rvec);
455:   }
456: #endif
457:   *local_mat = temp_local_mat;
458:   MatDestroy(&elem_mat_DBC);
459:   return(0);
460: }

462: static PetscErrorCode GLLStuffs(DomainData dd, GLLData *glldata)
463: {
465:   PetscReal      *M,si;
466:   PetscScalar    x,z0,z1,z2,Lpj,Lpr,rhoGLj,rhoGLk;
467:   PetscBLASInt   pm1,lierr;
468:   PetscInt       i,j,n,k,s,r,q,ii,jj,p=dd.p;
469:   PetscInt       xloc,yloc,zloc,xyloc,xyzloc;

472:   /* Gauss-Lobatto-Legendre nodes zGL on [-1,1] */
473:   PetscCalloc1(p+1,&glldata->zGL);

475:   glldata->zGL[0]=-1.0;
476:   glldata->zGL[p]= 1.0;
477:   if (p > 1) {
478:     if (p == 2) glldata->zGL[1]=0.0;
479:     else {
480:       PetscMalloc1(p-1,&M);
481:       for (i=0; i<p-1; i++) {
482:         si  = (PetscReal)(i+1.0);
483:         M[i]=0.5*PetscSqrtReal(si*(si+2.0)/((si+0.5)*(si+1.5)));
484:       }
485:       pm1  = p-1;
486:       PetscFPTrapPush(PETSC_FP_TRAP_OFF);
487:       PetscStackCallBLAS("LAPACKsteqr",LAPACKsteqr_("N",&pm1,&glldata->zGL[1],M,&x,&pm1,M,&lierr));
488:       if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in STERF Lapack routine %d",(int)lierr);
489:       PetscFPTrapPop();
490:       PetscFree(M);
491:     }
492:   }

494:   /* Weights for 1D quadrature */
495:   PetscMalloc1(p+1,&glldata->rhoGL);

497:   glldata->rhoGL[0]=2.0/(PetscScalar)(p*(p+1.0));
498:   glldata->rhoGL[p]=glldata->rhoGL[0];
499:   z2 = -1;                      /* Dummy value to avoid -Wmaybe-initialized */
500:   for (i=1; i<p; i++) {
501:     x  = glldata->zGL[i];
502:     z0 = 1.0;
503:     z1 = x;
504:     for (n=1; n<p; n++) {
505:       z2 = x*z1*(2.0*n+1.0)/(n+1.0)-z0*(PetscScalar)(n/(n+1.0));
506:       z0 = z1;
507:       z1 = z2;
508:     }
509:     glldata->rhoGL[i]=2.0/(p*(p+1.0)*z2*z2);
510:   }

512:   /* Auxiliary mat for laplacian */
513:   PetscMalloc1(p+1,&glldata->A);
514:   PetscMalloc1((p+1)*(p+1),&glldata->A[0]);
515:   for (i=1; i<p+1; i++) glldata->A[i]=glldata->A[i-1]+p+1;

517:   for (j=1; j<p; j++) {
518:     x =glldata->zGL[j];
519:     z0=1.0;
520:     z1=x;
521:     for (n=1; n<p; n++) {
522:       z2=x*z1*(2.0*n+1.0)/(n+1.0)-z0*(PetscScalar)(n/(n+1.0));
523:       z0=z1;
524:       z1=z2;
525:     }
526:     Lpj=z2;
527:     for (r=1; r<p; r++) {
528:       if (r == j) {
529:         glldata->A[j][j]=2.0/(3.0*(1.0-glldata->zGL[j]*glldata->zGL[j])*Lpj*Lpj);
530:       } else {
531:         x  = glldata->zGL[r];
532:         z0 = 1.0;
533:         z1 = x;
534:         for (n=1; n<p; n++) {
535:           z2=x*z1*(2.0*n+1.0)/(n+1.0)-z0*(PetscScalar)(n/(n+1.0));
536:           z0=z1;
537:           z1=z2;
538:         }
539:         Lpr             = z2;
540:         glldata->A[r][j]=4.0/(p*(p+1.0)*Lpj*Lpr*(glldata->zGL[j]-glldata->zGL[r])*(glldata->zGL[j]-glldata->zGL[r]));
541:       }
542:     }
543:   }
544:   for (j=1; j<p+1; j++) {
545:     x  = glldata->zGL[j];
546:     z0 = 1.0;
547:     z1 = x;
548:     for (n=1; n<p; n++) {
549:       z2=x*z1*(2.0*n+1.0)/(n+1.0)-z0*(PetscScalar)(n/(n+1.0));
550:       z0=z1;
551:       z1=z2;
552:     }
553:     Lpj             = z2;
554:     glldata->A[j][0]=4.0*PetscPowRealInt(-1.0,p)/(p*(p+1.0)*Lpj*(1.0+glldata->zGL[j])*(1.0+glldata->zGL[j]));
555:     glldata->A[0][j]=glldata->A[j][0];
556:   }
557:   for (j=0; j<p; j++) {
558:     x  = glldata->zGL[j];
559:     z0 = 1.0;
560:     z1 = x;
561:     for (n=1; n<p; n++) {
562:       z2=x*z1*(2.0*n+1.0)/(n+1.0)-z0*(PetscScalar)(n/(n+1.0));
563:       z0=z1;
564:       z1=z2;
565:     }
566:     Lpj=z2;

568:     glldata->A[p][j]=4.0/(p*(p+1.0)*Lpj*(1.0-glldata->zGL[j])*(1.0-glldata->zGL[j]));
569:     glldata->A[j][p]=glldata->A[p][j];
570:   }
571:   glldata->A[0][0]=0.5+(p*(p+1.0)-2.0)/6.0;
572:   glldata->A[p][p]=glldata->A[0][0];

574:   /* compute element matrix */
575:   xloc = p+1;
576:   yloc = p+1;
577:   zloc = p+1;
578:   if (dd.dim<2) yloc=1;
579:   if (dd.dim<3) zloc=1;
580:   xyloc  = xloc*yloc;
581:   xyzloc = xloc*yloc*zloc;

583:   MatCreate(PETSC_COMM_SELF,&glldata->elem_mat);
584:   MatSetSizes(glldata->elem_mat,xyzloc,xyzloc,xyzloc,xyzloc);
585:   MatSetType(glldata->elem_mat,MATSEQAIJ);
586:   MatSeqAIJSetPreallocation(glldata->elem_mat,xyzloc,NULL); /* overestimated */
587:   MatZeroEntries(glldata->elem_mat);
588:   MatSetOption(glldata->elem_mat,MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);

590:   for (k=0; k<zloc; k++) {
591:     if (dd.dim>2) rhoGLk=glldata->rhoGL[k];
592:     else rhoGLk=1.0;

594:     for (j=0; j<yloc; j++) {
595:       if (dd.dim>1) rhoGLj=glldata->rhoGL[j];
596:       else rhoGLj=1.0;

598:       for (i=0; i<xloc; i++) {
599:         ii = k*xyloc+j*xloc+i;
600:         s  = k;
601:         r  = j;
602:         for (q=0; q<xloc; q++) {
603:           jj   = s*xyloc+r*xloc+q;
604:           MatSetValue(glldata->elem_mat,jj,ii,glldata->A[i][q]*rhoGLj*rhoGLk,ADD_VALUES);
605:         }
606:         if (dd.dim>1) {
607:           s=k;
608:           q=i;
609:           for (r=0; r<yloc; r++) {
610:             jj   = s*xyloc+r*xloc+q;
611:             MatSetValue(glldata->elem_mat,jj,ii,glldata->A[j][r]*glldata->rhoGL[i]*rhoGLk,ADD_VALUES);
612:           }
613:         }
614:         if (dd.dim>2) {
615:           r=j;
616:           q=i;
617:           for (s=0; s<zloc; s++) {
618:             jj   = s*xyloc+r*xloc+q;
619:             MatSetValue(glldata->elem_mat,jj,ii,glldata->A[k][s]*rhoGLj*glldata->rhoGL[i],ADD_VALUES);
620:           }
621:         }
622:       }
623:     }
624:   }
625:   MatAssemblyBegin(glldata->elem_mat,MAT_FINAL_ASSEMBLY);
626:   MatAssemblyEnd  (glldata->elem_mat,MAT_FINAL_ASSEMBLY);
627: #if DEBUG
628:   {
629:     Vec       lvec,rvec;
630:     PetscReal norm;
631:     MatCreateVecs(glldata->elem_mat,&lvec,&rvec);
632:     VecSet(lvec,1.0);
633:     MatMult(glldata->elem_mat,lvec,rvec);
634:     VecNorm(rvec,NORM_INFINITY,&norm);
635:     VecDestroy(&lvec);
636:     VecDestroy(&rvec);
637:   }
638: #endif
639:   return(0);
640: }

642: static PetscErrorCode DomainDecomposition(DomainData *dd)
643: {
644:   PetscMPIInt rank;
645:   PetscInt    i,j,k;

648:   /* Subdomain index in cartesian coordinates */
649:   MPI_Comm_rank(dd->gcomm,&rank);
650:   dd->ipx = rank%dd->npx;
651:   if (dd->dim>1) dd->ipz = rank/(dd->npx*dd->npy);
652:   else dd->ipz = 0;

654:   dd->ipy = rank/dd->npx-dd->ipz*dd->npy;
655:   /* number of local elements */
656:   dd->nex_l = dd->nex/dd->npx;
657:   if (dd->ipx < dd->nex%dd->npx) dd->nex_l++;
658:   if (dd->dim>1) {
659:     dd->ney_l = dd->ney/dd->npy;
660:     if (dd->ipy < dd->ney%dd->npy) dd->ney_l++;
661:   } else {
662:     dd->ney_l = 0;
663:   }
664:   if (dd->dim>2) {
665:     dd->nez_l = dd->nez/dd->npz;
666:     if (dd->ipz < dd->nez%dd->npz) dd->nez_l++;
667:   } else {
668:     dd->nez_l = 0;
669:   }
670:   /* local and global number of dofs */
671:   dd->xm_l = dd->nex_l*dd->p+1;
672:   dd->xm   = dd->nex*dd->p+1;
673:   dd->ym_l = dd->ney_l*dd->p+1;
674:   dd->ym   = dd->ney*dd->p+1;
675:   dd->zm_l = dd->nez_l*dd->p+1;
676:   dd->zm   = dd->nez*dd->p+1;
677:   if (!dd->pure_neumann) {
678:     if (!dd->DBC_zerorows && !dd->ipx) dd->xm_l--;
679:     if (!dd->DBC_zerorows) dd->xm--;
680:   }

682:   /* starting global index for local dofs (simple lexicographic order) */
683:   dd->startx = 0;
684:   j          = dd->nex/dd->npx;
685:   for (i=0; i<dd->ipx; i++) {
686:     k = j;
687:     if (i<dd->nex%dd->npx) k++;
688:     dd->startx = dd->startx+k*dd->p;
689:   }
690:   if (!dd->pure_neumann && !dd->DBC_zerorows && dd->ipx) dd->startx--;

692:   dd->starty = 0;
693:   if (dd->dim > 1) {
694:     j = dd->ney/dd->npy;
695:     for (i=0; i<dd->ipy; i++) {
696:       k = j;
697:       if (i<dd->ney%dd->npy) k++;
698:       dd->starty = dd->starty+k*dd->p;
699:     }
700:   }
701:   dd->startz = 0;
702:   if (dd->dim > 2) {
703:     j = dd->nez/dd->npz;
704:     for (i=0; i<dd->ipz; i++) {
705:       k = j;
706:       if (i<dd->nez%dd->npz) k++;
707:       dd->startz = dd->startz+k*dd->p;
708:     }
709:   }
710:   return(0);
711: }
712: static PetscErrorCode ComputeMatrix(DomainData dd, Mat *A)
713: {
714:   PetscErrorCode         ierr;
715:   GLLData                gll;
716:   Mat                    local_mat  =0,temp_A=0;
717:   ISLocalToGlobalMapping matis_map  =0;
718:   IS                     dirichletIS=0;

721:   /* Compute some stuff of Gauss-Legendre-Lobatto quadrature rule */
722:   GLLStuffs(dd,&gll);
723:   /* Compute matrix of subdomain Neumann problem */
724:   ComputeSubdomainMatrix(dd,gll,&local_mat);
725:   /* Compute global mapping of local dofs */
726:   ComputeMapping(dd,&matis_map);
727:   /* Create MATIS object needed by BDDC */
728:   MatCreateIS(dd.gcomm,1,PETSC_DECIDE,PETSC_DECIDE,dd.xm*dd.ym*dd.zm,dd.xm*dd.ym*dd.zm,matis_map,NULL,&temp_A);
729:   /* Set local subdomain matrices into MATIS object */
730:   MatScale(local_mat,dd.scalingfactor);
731:   MatISSetLocalMat(temp_A,local_mat);
732:   /* Call assembly functions */
733:   MatAssemblyBegin(temp_A,MAT_FINAL_ASSEMBLY);
734:   MatAssemblyEnd(temp_A,MAT_FINAL_ASSEMBLY);

736:   if (dd.DBC_zerorows) {
737:     PetscInt dirsize;

739:     ComputeSpecialBoundaryIndices(dd,&dirichletIS,NULL);
740:     MatSetOption(local_mat,MAT_KEEP_NONZERO_PATTERN,PETSC_TRUE);
741:     MatZeroRowsColumnsLocalIS(temp_A,dirichletIS,1.0,NULL,NULL);
742:     ISGetLocalSize(dirichletIS,&dirsize);
743:     ISDestroy(&dirichletIS);
744:   }

746:   /* giving hints to local and global matrices could be useful for the BDDC */
747:   MatSetOption(local_mat,MAT_SYMMETRIC,PETSC_TRUE);
748:   MatSetOption(local_mat,MAT_SPD,PETSC_TRUE);
749: #if DEBUG
750:   {
751:     Vec       lvec,rvec;
752:     PetscReal norm;
753:     MatCreateVecs(temp_A,&lvec,&rvec);
754:     VecSet(lvec,1.0);
755:     MatMult(temp_A,lvec,rvec);
756:     VecNorm(rvec,NORM_INFINITY,&norm);
757:     VecDestroy(&lvec);
758:     VecDestroy(&rvec);
759:   }
760: #endif
761:   /* free allocated workspace */
762:   PetscFree(gll.zGL);
763:   PetscFree(gll.rhoGL);
764:   PetscFree(gll.A[0]);
765:   PetscFree(gll.A);
766:   MatDestroy(&gll.elem_mat);
767:   MatDestroy(&local_mat);
768:   ISLocalToGlobalMappingDestroy(&matis_map);
769:   /* give back the pointer to te MATIS object */
770:   *A = temp_A;
771:   return(0);
772: }

774: static PetscErrorCode ComputeKSPFETIDP(DomainData dd, KSP ksp_bddc, KSP *ksp_fetidp)
775: {
777:   KSP            temp_ksp;
778:   PC             pc;

781:   KSPGetPC(ksp_bddc,&pc);
782:   if (!dd.testkspfetidp) {
783:     PC  D;
784:     Mat F;

786:     PCBDDCCreateFETIDPOperators(pc,PETSC_TRUE,NULL,&F,&D);
787:     KSPCreate(PetscObjectComm((PetscObject)F),&temp_ksp);
788:     KSPSetOperators(temp_ksp,F,F);
789:     KSPSetType(temp_ksp,KSPCG);
790:     KSPSetPC(temp_ksp,D);
791:     KSPSetComputeSingularValues(temp_ksp,PETSC_TRUE);
792:     KSPSetOptionsPrefix(temp_ksp,"fluxes_");
793:     KSPSetFromOptions(temp_ksp);
794:     KSPSetUp(temp_ksp);
795:     MatDestroy(&F);
796:     PCDestroy(&D);
797:   } else {
798:     Mat A,Ap;

800:     KSPCreate(PetscObjectComm((PetscObject)ksp_bddc),&temp_ksp);
801:     KSPGetOperators(ksp_bddc,&A,&Ap);
802:     KSPSetOperators(temp_ksp,A,Ap);
803:     KSPSetOptionsPrefix(temp_ksp,"fluxes_");
804:     KSPSetType(temp_ksp,KSPFETIDP);
805:     KSPFETIDPSetInnerBDDC(temp_ksp,pc);
806:     KSPSetComputeSingularValues(temp_ksp,PETSC_TRUE);
807:     KSPSetFromOptions(temp_ksp);
808:     KSPSetUp(temp_ksp);
809:   }
810:   *ksp_fetidp = temp_ksp;
811:   return(0);
812: }


815: static PetscErrorCode ComputeKSPBDDC(DomainData dd,Mat A,KSP *ksp)
816: {
818:   KSP            temp_ksp;
819:   PC             pc;
820:   IS             primals,dirichletIS=0,neumannIS=0,*bddc_dofs_splitting;
821:   PetscInt       vidx[8],localsize,*xadj=NULL,*adjncy=NULL;
822:   MatNullSpace   near_null_space;

825:   KSPCreate(dd.gcomm,&temp_ksp);
826:   KSPSetOperators(temp_ksp,A,A);
827:   KSPSetType(temp_ksp,KSPCG);
828:   KSPGetPC(temp_ksp,&pc);
829:   PCSetType(pc,PCBDDC);

831:   localsize = dd.xm_l*dd.ym_l*dd.zm_l;

833:   /* BDDC customization */

835:   /* jumping coefficients case */
836:   PCISSetSubdomainScalingFactor(pc,dd.scalingfactor);

838:   /* Dofs splitting
839:      Simple stride-1 IS
840:      It is not needed since, by default, PCBDDC assumes a stride-1 split */
841:   PetscMalloc1(1,&bddc_dofs_splitting);
842: #if 1
843:   ISCreateStride(PETSC_COMM_WORLD,localsize,0,1,&bddc_dofs_splitting[0]);
844:   PCBDDCSetDofsSplittingLocal(pc,1,bddc_dofs_splitting);
845: #else
846:   /* examples for global ordering */

848:   /* each process lists the nodes it owns */
849:   PetscInt sr,er;
850:   MatGetOwnershipRange(A,&sr,&er);
851:   ISCreateStride(PETSC_COMM_WORLD,er-sr,sr,1,&bddc_dofs_splitting[0]);
852:   PCBDDCSetDofsSplitting(pc,1,bddc_dofs_splitting);
853:   /* Split can be passed in a more general way since any process can list any node */
854: #endif
855:   ISDestroy(&bddc_dofs_splitting[0]);
856:   PetscFree(bddc_dofs_splitting);

858:   /* Primal constraints implemented by using a near null space attached to A -> now it passes in only the constants
859:     (which in practice is not needed since by default PCBDDC builds the primal space using constants for quadrature formulas */
860: #if 0
861:   Vec vecs[2];
862:   PetscRandom rctx;
863:   MatCreateVecs(A,&vecs[0],&vecs[1]);
864:   PetscRandomCreate(dd.gcomm,&rctx);
865:   VecSetRandom(vecs[0],rctx);
866:   VecSetRandom(vecs[1],rctx);
867:   MatNullSpaceCreate(dd.gcomm,PETSC_TRUE,2,vecs,&near_null_space);
868:   VecDestroy(&vecs[0]);
869:   VecDestroy(&vecs[1]);
870:   PetscRandomDestroy(&rctx);
871: #else
872:   MatNullSpaceCreate(dd.gcomm,PETSC_TRUE,0,NULL,&near_null_space);
873: #endif
874:   MatSetNearNullSpace(A,near_null_space);
875:   MatNullSpaceDestroy(&near_null_space);

877:   /* CSR graph of subdomain dofs */
878:   BuildCSRGraph(dd,&xadj,&adjncy);
879:   PCBDDCSetLocalAdjacencyGraph(pc,localsize,xadj,adjncy,PETSC_OWN_POINTER);

881:   /* Prescribe user-defined primal vertices: in this case we use the 8 corners in 3D (for 2D and 1D, the indices are duplicated) */
882:   vidx[0] = 0*dd.xm_l+0;
883:   vidx[1] = 0*dd.xm_l+dd.xm_l-1;
884:   vidx[2] = (dd.ym_l-1)*dd.xm_l+0;
885:   vidx[3] = (dd.ym_l-1)*dd.xm_l+dd.xm_l-1;
886:   vidx[4] = (dd.zm_l-1)*dd.xm_l*dd.ym_l+0*dd.xm_l+0;
887:   vidx[5] = (dd.zm_l-1)*dd.xm_l*dd.ym_l+0*dd.xm_l+dd.xm_l-1;
888:   vidx[6] = (dd.zm_l-1)*dd.xm_l*dd.ym_l+(dd.ym_l-1)*dd.xm_l+0;
889:   vidx[7] = (dd.zm_l-1)*dd.xm_l*dd.ym_l+(dd.ym_l-1)*dd.xm_l+dd.xm_l-1;
890:   ISCreateGeneral(dd.gcomm,8,vidx,PETSC_COPY_VALUES,&primals);
891:   PCBDDCSetPrimalVerticesLocalIS(pc,primals);
892:   ISDestroy(&primals);

894:   /* Neumann/Dirichlet indices on the global boundary */
895:   if (dd.DBC_zerorows) {
896:     /* Only in case you eliminate some rows matrix with zerorows function, you need to set dirichlet indices into PCBDDC data */
897:     ComputeSpecialBoundaryIndices(dd,&dirichletIS,&neumannIS);
898:     PCBDDCSetNeumannBoundariesLocal(pc,neumannIS);
899:     PCBDDCSetDirichletBoundariesLocal(pc,dirichletIS);
900:   } else {
901:     if (dd.pure_neumann) {
902:       /* In such a case, all interface nodes lying on the global boundary are neumann nodes */
903:       ComputeSpecialBoundaryIndices(dd,NULL,&neumannIS);
904:       PCBDDCSetNeumannBoundariesLocal(pc,neumannIS);
905:     } else {
906:       /* It is wrong setting dirichlet indices without having zeroed the corresponding rows in the global matrix */
907:       /* But we can still compute them since nodes near the dirichlet boundaries does not need to be defined as neumann nodes */
908:       ComputeSpecialBoundaryIndices(dd,&dirichletIS,&neumannIS);
909:       PCBDDCSetNeumannBoundariesLocal(pc,neumannIS);
910:     }
911:   }

913:   /* Pass local null space information to local matrices (needed when using approximate local solvers) */
914:   if (dd.ipx || dd.pure_neumann) {
915:     MatNullSpace nsp;
916:     Mat          local_mat;

918:     MatISGetLocalMat(A,&local_mat);
919:     MatNullSpaceCreate(PETSC_COMM_SELF,PETSC_TRUE,0,NULL,&nsp);
920:     MatSetNullSpace(local_mat,nsp);
921:     MatNullSpaceDestroy(&nsp);
922:   }
923:   KSPSetComputeSingularValues(temp_ksp,PETSC_TRUE);
924:   KSPSetOptionsPrefix(temp_ksp,"physical_");
925:   KSPSetFromOptions(temp_ksp);
926:   KSPSetUp(temp_ksp);
927:   *ksp = temp_ksp;
928:   ISDestroy(&dirichletIS);
929:   ISDestroy(&neumannIS);
930:   return(0);
931: }

933: static PetscErrorCode InitializeDomainData(DomainData *dd)
934: {
936:   PetscMPIInt    sizes,rank;
937:   PetscInt       factor;

940:   dd->gcomm = PETSC_COMM_WORLD;
941:   MPI_Comm_size(dd->gcomm,&sizes);
942:   MPI_Comm_rank(dd->gcomm,&rank);
943:   /* Get informations from command line */
944:   /* Processors/subdomains per dimension */
945:   /* Default is 1d problem */
946:   dd->npx = sizes;
947:   dd->npy = 0;
948:   dd->npz = 0;
949:   dd->dim = 1;
950:   PetscOptionsGetInt(NULL,NULL,"-npx",&dd->npx,NULL);
951:   PetscOptionsGetInt(NULL,NULL,"-npy",&dd->npy,NULL);
952:   PetscOptionsGetInt(NULL,NULL,"-npz",&dd->npz,NULL);
953:   if (dd->npy) dd->dim++;
954:   if (dd->npz) dd->dim++;
955:   /* Number of elements per dimension */
956:   /* Default is one element per subdomain */
957:   dd->nex = dd->npx;
958:   dd->ney = dd->npy;
959:   dd->nez = dd->npz;
960:   PetscOptionsGetInt(NULL,NULL,"-nex",&dd->nex,NULL);
961:   PetscOptionsGetInt(NULL,NULL,"-ney",&dd->ney,NULL);
962:   PetscOptionsGetInt(NULL,NULL,"-nez",&dd->nez,NULL);
963:   if (!dd->npy) {
964:     dd->ney=0;
965:     dd->nez=0;
966:   }
967:   if (!dd->npz) dd->nez=0;
968:   /* Spectral degree */
969:   dd->p = 3;
970:   PetscOptionsGetInt(NULL,NULL,"-p",&dd->p,NULL);
971:   /* pure neumann problem? */
972:   dd->pure_neumann = PETSC_FALSE;
973:   PetscOptionsGetBool(NULL,NULL,"-pureneumann",&dd->pure_neumann,NULL);

975:   /* How to enforce dirichlet boundary conditions (in case pureneumann has not been requested explicitly) */
976:   dd->DBC_zerorows = PETSC_FALSE;

978:   PetscOptionsGetBool(NULL,NULL,"-usezerorows",&dd->DBC_zerorows,NULL);
979:   if (dd->pure_neumann) dd->DBC_zerorows = PETSC_FALSE;
980:   dd->scalingfactor = 1.0;

982:   factor = 0.0;
983:   PetscOptionsGetInt(NULL,NULL,"-jump",&factor,NULL);
984:   /* checkerboard pattern */
985:   dd->scalingfactor = PetscPowScalar(10.0,(PetscScalar)factor*PetscPowScalar(-1.0,(PetscScalar)rank));
986:   /* test data passed in */
987:   if (dd->dim==1) {
988:     if (sizes!=dd->npx) SETERRQ(dd->gcomm,PETSC_ERR_USER,"Number of mpi procs in 1D must be equal to npx");
989:     if (dd->nex<dd->npx) SETERRQ(dd->gcomm,PETSC_ERR_USER,"Number of elements per dim must be greater/equal than number of procs per dim");
990:   } else if (dd->dim==2) {
991:     if (sizes!=dd->npx*dd->npy) SETERRQ(dd->gcomm,PETSC_ERR_USER,"Number of mpi procs in 2D must be equal to npx*npy");
992:     if (dd->nex<dd->npx || dd->ney<dd->npy) SETERRQ(dd->gcomm,PETSC_ERR_USER,"Number of elements per dim must be greater/equal than number of procs per dim");
993:   } else {
994:     if (sizes!=dd->npx*dd->npy*dd->npz) SETERRQ(dd->gcomm,PETSC_ERR_USER,"Number of mpi procs in 3D must be equal to npx*npy*npz");
995:     if (dd->nex<dd->npx || dd->ney<dd->npy || dd->nez<dd->npz) SETERRQ(dd->gcomm,PETSC_ERR_USER,"Number of elements per dim must be greater/equal than number of procs per dim");
996:   }
997:   return(0);
998: }

1000: int main(int argc,char **args)
1001: {
1002:   PetscErrorCode     ierr;
1003:   DomainData         dd;
1004:   PetscReal          norm,maxeig,mineig;
1005:   PetscScalar        scalar_value;
1006:   PetscInt           ndofs,its;
1007:   Mat                A = NULL,F = NULL;
1008:   KSP                KSPwithBDDC = NULL,KSPwithFETIDP = NULL;
1009:   KSPConvergedReason reason;
1010:   Vec                exact_solution = NULL,bddc_solution = NULL,bddc_rhs = NULL;
1011:   PetscBool          testfetidp = PETSC_TRUE;

1013:   /* Init PETSc */
1014:   PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
1015:   /* Initialize DomainData */
1016:   InitializeDomainData(&dd);
1017:   /* Decompose domain */
1018:   DomainDecomposition(&dd);
1019: #if DEBUG
1020:   printf("Subdomain data\n");
1021:   printf("IPS   : %d %d %d\n",dd.ipx,dd.ipy,dd.ipz);
1022:   printf("NEG   : %d %d %d\n",dd.nex,dd.ney,dd.nez);
1023:   printf("NEL   : %d %d %d\n",dd.nex_l,dd.ney_l,dd.nez_l);
1024:   printf("LDO   : %d %d %d\n",dd.xm_l,dd.ym_l,dd.zm_l);
1025:   printf("SIZES : %d %d %d\n",dd.xm,dd.ym,dd.zm);
1026:   printf("STARTS: %d %d %d\n",dd.startx,dd.starty,dd.startz);
1027: #endif
1028:   dd.testkspfetidp = PETSC_TRUE;
1029:   PetscOptionsGetBool(NULL,NULL,"-testfetidp",&testfetidp,NULL);
1030:   PetscOptionsGetBool(NULL,NULL,"-testkspfetidp",&dd.testkspfetidp,NULL);
1031:   /* assemble global matrix */
1032:   ComputeMatrix(dd,&A);
1033:   /* get work vectors */
1034:   MatCreateVecs(A,&bddc_solution,NULL);
1035:   VecDuplicate(bddc_solution,&bddc_rhs);
1036:   VecDuplicate(bddc_solution,&exact_solution);
1037:   /* create and customize KSP/PC for BDDC */
1038:   ComputeKSPBDDC(dd,A,&KSPwithBDDC);
1039:   /* create KSP/PC for FETIDP */
1040:   if (testfetidp) {
1041:     ComputeKSPFETIDP(dd,KSPwithBDDC,&KSPwithFETIDP);
1042:   }
1043:   /* create random exact solution */
1044: #if defined(PETSC_USE_COMPLEX)
1045:   VecSet(exact_solution,1.0 + PETSC_i);
1046: #else
1047:   VecSetRandom(exact_solution,NULL);
1048: #endif
1049:   VecShift(exact_solution,-0.5);
1050:   VecScale(exact_solution,100.0);
1051:   VecGetSize(exact_solution,&ndofs);
1052:   if (dd.pure_neumann) {
1053:     VecSum(exact_solution,&scalar_value);
1054:     scalar_value = -scalar_value/(PetscScalar)ndofs;
1055:     VecShift(exact_solution,scalar_value);
1056:   }
1057:   /* assemble BDDC rhs */
1058:   MatMult(A,exact_solution,bddc_rhs);
1059:   /* test ksp with BDDC */
1060:   KSPSolve(KSPwithBDDC,bddc_rhs,bddc_solution);
1061:   KSPGetIterationNumber(KSPwithBDDC,&its);
1062:   KSPGetConvergedReason(KSPwithBDDC,&reason);
1063:   KSPComputeExtremeSingularValues(KSPwithBDDC,&maxeig,&mineig);
1064:   if (dd.pure_neumann) {
1065:     VecSum(bddc_solution,&scalar_value);
1066:     scalar_value = -scalar_value/(PetscScalar)ndofs;
1067:     VecShift(bddc_solution,scalar_value);
1068:   }
1069:   /* check exact_solution and BDDC solultion */
1070:   VecAXPY(bddc_solution,-1.0,exact_solution);
1071:   VecNorm(bddc_solution,NORM_INFINITY,&norm);
1072:   PetscPrintf(dd.gcomm,"---------------------BDDC stats-------------------------------\n");
1073:   PetscPrintf(dd.gcomm,"Number of degrees of freedom               : %8D\n",ndofs);
1074:   if (reason < 0) {
1075:     PetscPrintf(dd.gcomm,"Number of iterations                       : %8D\n",its);
1076:     PetscPrintf(dd.gcomm,"Converged reason                           : %s\n",KSPConvergedReasons[reason]);
1077:   }
1078:   if (0.95 <= mineig && mineig <= 1.05) mineig = 1.0;
1079:   PetscPrintf(dd.gcomm,"Eigenvalues preconditioned operator        : %1.1e %1.1e\n",(double)PetscFloorReal(100.*mineig)/100.,(double)PetscCeilReal(100.*maxeig)/100.);
1080:   if (norm > 1.e-1 || reason < 0) {
1081:     PetscPrintf(dd.gcomm,"Error betweeen exact and computed solution : %1.2e\n",(double)norm);
1082:   }
1083:   PetscPrintf(dd.gcomm,"--------------------------------------------------------------\n");
1084:   if (testfetidp) {
1085:     Vec fetidp_solution_all = NULL,fetidp_solution = NULL,fetidp_rhs = NULL;

1087:     VecDuplicate(bddc_solution,&fetidp_solution_all);
1088:     if (!dd.testkspfetidp) {
1089:       /* assemble fetidp rhs on the space of Lagrange multipliers */
1090:       KSPGetOperators(KSPwithFETIDP,&F,NULL);
1091:       MatCreateVecs(F,&fetidp_solution,&fetidp_rhs);
1092:       PCBDDCMatFETIDPGetRHS(F,bddc_rhs,fetidp_rhs);
1093:       VecSet(fetidp_solution,0.0);
1094:       /* test ksp with FETIDP */
1095:       KSPSolve(KSPwithFETIDP,fetidp_rhs,fetidp_solution);
1096:       /* assemble fetidp solution on physical domain */
1097:       PCBDDCMatFETIDPGetSolution(F,fetidp_solution,fetidp_solution_all);
1098:     } else {
1099:       KSP kspF;
1100:       KSPSolve(KSPwithFETIDP,bddc_rhs,fetidp_solution_all);
1101:       KSPFETIDPGetInnerKSP(KSPwithFETIDP,&kspF);
1102:       KSPGetOperators(kspF,&F,NULL);
1103:     }
1104:     MatGetSize(F,&ndofs,NULL);
1105:     KSPGetIterationNumber(KSPwithFETIDP,&its);
1106:     KSPGetConvergedReason(KSPwithFETIDP,&reason);
1107:     KSPComputeExtremeSingularValues(KSPwithFETIDP,&maxeig,&mineig);
1108:     /* check FETIDP sol */
1109:     if (dd.pure_neumann) {
1110:       VecSum(fetidp_solution_all,&scalar_value);
1111:       scalar_value = -scalar_value/(PetscScalar)ndofs;
1112:       VecShift(fetidp_solution_all,scalar_value);
1113:     }
1114:     VecAXPY(fetidp_solution_all,-1.0,exact_solution);
1115:     VecNorm(fetidp_solution_all,NORM_INFINITY,&norm);
1116:     PetscPrintf(dd.gcomm,"------------------FETI-DP stats-------------------------------\n");
1117:     PetscPrintf(dd.gcomm,"Number of degrees of freedom               : %8D\n",ndofs);
1118:     if (reason < 0) {
1119:       PetscPrintf(dd.gcomm,"Number of iterations                       : %8D\n",its);
1120:       PetscPrintf(dd.gcomm,"Converged reason                           : %D\n",reason);
1121:     }
1122:     if (0.95 <= mineig && mineig <= 1.05) mineig = 1.0;
1123:     PetscPrintf(dd.gcomm,"Eigenvalues preconditioned operator        : %1.1e %1.1e\n",(double)PetscFloorReal(100.*mineig)/100.,(double)PetscCeilReal(100.*maxeig)/100.);
1124:     if (norm > 1.e-1 || reason < 0) {
1125:       PetscPrintf(dd.gcomm,"Error betweeen exact and computed solution : %1.2e\n",(double)norm);
1126:     }
1127:     PetscPrintf(dd.gcomm,"--------------------------------------------------------------\n");
1128:     VecDestroy(&fetidp_solution);
1129:     VecDestroy(&fetidp_solution_all);
1130:     VecDestroy(&fetidp_rhs);
1131:   }
1132:   KSPDestroy(&KSPwithFETIDP);
1133:   VecDestroy(&exact_solution);
1134:   VecDestroy(&bddc_solution);
1135:   VecDestroy(&bddc_rhs);
1136:   MatDestroy(&A);
1137:   KSPDestroy(&KSPwithBDDC);
1138:   /* Quit PETSc */
1139:   PetscFinalize();
1140:   return ierr;
1141: }

1143: /*TEST

1145:  testset:
1146:    nsize: 4
1147:    args: -nex 7 -physical_pc_bddc_coarse_eqs_per_proc 3 -physical_pc_bddc_switch_static
1148:    output_file: output/ex59_bddc_fetidp_1.out
1149:    test:
1150:      suffix: bddc_fetidp_1
1151:    test:
1152:      requires: viennacl
1153:      suffix: bddc_fetidp_1_viennacl
1154:      args: -subdomain_mat_type aijviennacl
1155:    test:
1156:      requires: cuda
1157:      suffix: bddc_fetidp_1_cuda
1158:      args: -subdomain_mat_type aijcusparse -physical_pc_bddc_dirichlet_pc_factor_mat_solver_type cusparse

1160:  testset:
1161:    nsize: 4
1162:    args: -npx 2 -npy 2 -nex 6 -ney 6 -fluxes_ksp_max_it 10 -physical_ksp_max_it 10
1163:    requires: !single
1164:    test:
1165:      suffix: bddc_fetidp_2
1166:    test:
1167:      suffix: bddc_fetidp_3
1168:      args: -npz 1 -nez 1
1169:    test:
1170:      suffix: bddc_fetidp_4
1171:      args: -npz 1 -nez 1 -physical_pc_bddc_use_change_of_basis -physical_pc_bddc_use_deluxe_scaling -physical_pc_bddc_deluxe_singlemat -fluxes_fetidp_ksp_type cg

1173:  testset:
1174:    nsize: 8
1175:    suffix: bddc_fetidp_approximate
1176:    args: -npx 2 -npy 2 -npz 2 -p 2 -nex 8 -ney 7 -nez 9 -physical_ksp_max_it 20 -subdomain_mat_type aij -physical_pc_bddc_switch_static -physical_pc_bddc_dirichlet_approximate -physical_pc_bddc_neumann_approximate -physical_pc_bddc_dirichlet_pc_type gamg -physical_pc_bddc_dirichlet_mg_levels_ksp_max_it 3 -physical_pc_bddc_neumann_pc_type sor -physical_pc_bddc_neumann_approximate_scale -testfetidp 0

1178:  testset:
1179:    nsize: 4
1180:    args: -npx 2 -npy 2 -nex 6 -ney 6 -fluxes_ksp_max_it 10 -physical_ksp_max_it 10 -physical_ksp_view -physical_pc_bddc_levels 1
1181:    filter: grep -v "variant HERMITIAN"
1182:    requires: !single
1183:    test:
1184:      suffix: bddc_fetidp_ml_1
1185:      args: -physical_pc_bddc_coarsening_ratio 1
1186:    test:
1187:      suffix: bddc_fetidp_ml_2
1188:      args: -physical_pc_bddc_coarsening_ratio 2 -mat_partitioning_type average
1189:    test:
1190:      suffix: bddc_fetidp_ml_3
1191:      args: -physical_pc_bddc_coarsening_ratio 4

1193:  testset:
1194:    nsize: 9
1195:    args: -npx 3 -npy 3 -p 2 -nex 6 -ney 6 -physical_pc_bddc_deluxe_singlemat -physical_pc_bddc_use_deluxe_scaling -physical_pc_bddc_graph_maxcount 1 -physical_pc_bddc_levels 3 -physical_pc_bddc_coarsening_ratio 2 -physical_pc_bddc_coarse_ksp_type gmres
1196:    output_file: output/ex59_bddc_fetidp_ml_eqlimit.out
1197:    test:
1198:      suffix: bddc_fetidp_ml_eqlimit_1
1199:      args: -physical_pc_bddc_coarse_eqs_limit 31 -mat_partitioning_type average -physical_pc_bddc_coarse_pc_bddc_graph_maxcount 1
1200:    test:
1201:      suffix: bddc_fetidp_ml_eqlimit_2
1202:      args: -physical_pc_bddc_coarse_eqs_limit 46


1205: TEST*/