Actual source code: wb.c


  2: #include <petscdmda.h>
  3: #include <petsc/private/pcmgimpl.h>
  4: #include <petscctable.h>

  6: typedef struct {
  7:   PCExoticType type;
  8:   Mat          P;            /* the constructed interpolation matrix */
  9:   PetscBool    directSolve;  /* use direct LU factorization to construct interpolation */
 10:   KSP          ksp;
 11: } PC_Exotic;

 13: const char *const PCExoticTypes[] = {"face","wirebasket","PCExoticType","PC_Exotic",NULL};

 15: /*
 16:       DMDAGetWireBasketInterpolation - Gets the interpolation for a wirebasket based coarse space

 18: */
 19: PetscErrorCode DMDAGetWireBasketInterpolation(PC pc,DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
 20: {
 21:   PetscErrorCode         ierr;
 22:   PetscInt               dim,i,j,k,m,n,p,dof,Nint,Nface,Nwire,Nsurf,*Iint,*Isurf,cint = 0,csurf = 0,istart,jstart,kstart,*II,N,c = 0;
 23:   PetscInt               mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[26],*globals,Ng,*IIint,*IIsurf,Nt;
 24:   Mat                    Xint, Xsurf,Xint_tmp;
 25:   IS                     isint,issurf,is,row,col;
 26:   ISLocalToGlobalMapping ltg;
 27:   MPI_Comm               comm;
 28:   Mat                    A,Aii,Ais,Asi,*Aholder,iAii;
 29:   MatFactorInfo          info;
 30:   PetscScalar            *xsurf,*xint;
 31:   const PetscScalar      *rxint;
 32: #if defined(PETSC_USE_DEBUG_foo)
 33:   PetscScalar            tmp;
 34: #endif
 35:   PetscTable             ht;

 38:   DMDAGetInfo(da,&dim,NULL,NULL,NULL,&mp,&np,&pp,&dof,NULL,NULL,NULL,NULL,NULL);
 39:   if (dof != 1) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only for single field problems");
 40:   if (dim != 3) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only coded for 3d problems");
 41:   DMDAGetCorners(da,NULL,NULL,NULL,&m,&n,&p);
 42:   DMDAGetGhostCorners(da,&istart,&jstart,&kstart,&mwidth,&nwidth,&pwidth);
 43:   istart = istart ? -1 : 0;
 44:   jstart = jstart ? -1 : 0;
 45:   kstart = kstart ? -1 : 0;

 47:   /*
 48:     the columns of P are the interpolation of each coarse grid point (one for each vertex and edge)
 49:     to all the local degrees of freedom (this includes the vertices, edges and faces).

 51:     Xint are the subset of the interpolation into the interior

 53:     Xface are the interpolation onto faces but not into the interior

 55:     Xsurf are the interpolation onto the vertices and edges (the surfbasket)
 56:                                       Xint
 57:     Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
 58:                                       Xsurf
 59:   */
 60:   N     = (m - istart)*(n - jstart)*(p - kstart);
 61:   Nint  = (m-2-istart)*(n-2-jstart)*(p-2-kstart);
 62:   Nface = 2*((m-2-istart)*(n-2-jstart) + (m-2-istart)*(p-2-kstart) + (n-2-jstart)*(p-2-kstart));
 63:   Nwire = 4*((m-2-istart) + (n-2-jstart) + (p-2-kstart)) + 8;
 64:   Nsurf = Nface + Nwire;
 65:   MatCreateSeqDense(MPI_COMM_SELF,Nint,26,NULL,&Xint);
 66:   MatCreateSeqDense(MPI_COMM_SELF,Nsurf,26,NULL,&Xsurf);
 67:   MatDenseGetArray(Xsurf,&xsurf);

 69:   /*
 70:      Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
 71:      Xsurf will be all zero (thus making the coarse matrix singular).
 72:   */
 73:   if (m-istart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in X direction must be at least 3");
 74:   if (n-jstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Y direction must be at least 3");
 75:   if (p-kstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Z direction must be at least 3");

 77:   cnt = 0;

 79:   xsurf[cnt++] = 1;
 80:   for (i=1; i<m-istart-1; i++) xsurf[cnt++ + Nsurf] = 1;
 81:   xsurf[cnt++ + 2*Nsurf] = 1;

 83:   for (j=1; j<n-1-jstart; j++) {
 84:     xsurf[cnt++ + 3*Nsurf] = 1;
 85:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
 86:     xsurf[cnt++ + 5*Nsurf] = 1;
 87:   }

 89:   xsurf[cnt++ + 6*Nsurf] = 1;
 90:   for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 7*Nsurf] = 1;
 91:   xsurf[cnt++ + 8*Nsurf] = 1;

 93:   for (k=1; k<p-1-kstart; k++) {
 94:     xsurf[cnt++ + 9*Nsurf] = 1;
 95:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 10*Nsurf] = 1;
 96:     xsurf[cnt++ + 11*Nsurf] = 1;

 98:     for (j=1; j<n-1-jstart; j++) {
 99:       xsurf[cnt++ + 12*Nsurf] = 1;
100:       /* these are the interior nodes */
101:       xsurf[cnt++ + 13*Nsurf] = 1;
102:     }

104:     xsurf[cnt++ + 14*Nsurf] = 1;
105:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 15*Nsurf] = 1;
106:     xsurf[cnt++ + 16*Nsurf] = 1;
107:   }

109:   xsurf[cnt++ + 17*Nsurf] = 1;
110:   for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 18*Nsurf] = 1;
111:   xsurf[cnt++ + 19*Nsurf] = 1;

113:   for (j=1;j<n-1-jstart;j++) {
114:     xsurf[cnt++ + 20*Nsurf] = 1;
115:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 21*Nsurf] = 1;
116:     xsurf[cnt++ + 22*Nsurf] = 1;
117:   }

119:   xsurf[cnt++ + 23*Nsurf] = 1;
120:   for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 24*Nsurf] = 1;
121:   xsurf[cnt++ + 25*Nsurf] = 1;

123:   /* interpolations only sum to 1 when using direct solver */
124: #if defined(PETSC_USE_DEBUG_foo)
125:   for (i=0; i<Nsurf; i++) {
126:     tmp = 0.0;
127:     for (j=0; j<26; j++) tmp += xsurf[i+j*Nsurf];
128:     if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xsurf interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
129:   }
130: #endif
131:   MatDenseRestoreArray(Xsurf,&xsurf);
132:   /* MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);*/

134:   /*
135:        I are the indices for all the needed vertices (in global numbering)
136:        Iint are the indices for the interior values, I surf for the surface values
137:             (This is just for the part of the global matrix obtained with MatCreateSubMatrix(), it
138:              is NOT the local DMDA ordering.)
139:        IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
140:   */
141: #define Endpoint(a,start,b) (a == 0 || a == (b-1-start))
142:   PetscMalloc3(N,&II,Nint,&Iint,Nsurf,&Isurf);
143:   PetscMalloc2(Nint,&IIint,Nsurf,&IIsurf);
144:   for (k=0; k<p-kstart; k++) {
145:     for (j=0; j<n-jstart; j++) {
146:       for (i=0; i<m-istart; i++) {
147:         II[c++] = i + j*mwidth + k*mwidth*nwidth;

149:         if (!Endpoint(i,istart,m) && !Endpoint(j,jstart,n) && !Endpoint(k,kstart,p)) {
150:           IIint[cint]  = i + j*mwidth + k*mwidth*nwidth;
151:           Iint[cint++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
152:         } else {
153:           IIsurf[csurf]  = i + j*mwidth + k*mwidth*nwidth;
154:           Isurf[csurf++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
155:         }
156:       }
157:     }
158:   }
159:   if (c != N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"c != N");
160:   if (cint != Nint) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"cint != Nint");
161:   if (csurf != Nsurf) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csurf != Nsurf");
162:   DMGetLocalToGlobalMapping(da,&ltg);
163:   ISLocalToGlobalMappingApply(ltg,N,II,II);
164:   ISLocalToGlobalMappingApply(ltg,Nint,IIint,IIint);
165:   ISLocalToGlobalMappingApply(ltg,Nsurf,IIsurf,IIsurf);
166:   PetscObjectGetComm((PetscObject)da,&comm);
167:   ISCreateGeneral(comm,N,II,PETSC_COPY_VALUES,&is);
168:   ISCreateGeneral(PETSC_COMM_SELF,Nint,Iint,PETSC_COPY_VALUES,&isint);
169:   ISCreateGeneral(PETSC_COMM_SELF,Nsurf,Isurf,PETSC_COPY_VALUES,&issurf);
170:   PetscFree3(II,Iint,Isurf);

172:   MatCreateSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
173:   A    = *Aholder;
174:   PetscFree(Aholder);

176:   MatCreateSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
177:   MatCreateSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
178:   MatCreateSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);

180:   /*
181:      Solve for the interpolation onto the interior Xint
182:   */
183:   MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
184:   MatScale(Xint_tmp,-1.0);
185:   if (exotic->directSolve) {
186:     MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
187:     MatFactorInfoInitialize(&info);
188:     MatGetOrdering(Aii,MATORDERINGND,&row,&col);
189:     MatLUFactorSymbolic(iAii,Aii,row,col,&info);
190:     ISDestroy(&row);
191:     ISDestroy(&col);
192:     MatLUFactorNumeric(iAii,Aii,&info);
193:     MatMatSolve(iAii,Xint_tmp,Xint);
194:     MatDestroy(&iAii);
195:   } else {
196:     Vec         b,x;
197:     PetscScalar *xint_tmp;

199:     MatDenseGetArray(Xint,&xint);
200:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,NULL,&x);
201:     MatDenseGetArray(Xint_tmp,&xint_tmp);
202:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,NULL,&b);
203:     KSPSetOperators(exotic->ksp,Aii,Aii);
204:     for (i=0; i<26; i++) {
205:       VecPlaceArray(x,xint+i*Nint);
206:       VecPlaceArray(b,xint_tmp+i*Nint);
207:       KSPSolve(exotic->ksp,b,x);
208:       KSPCheckSolve(exotic->ksp,pc,x);
209:       VecResetArray(x);
210:       VecResetArray(b);
211:     }
212:     MatDenseRestoreArray(Xint,&xint);
213:     MatDenseRestoreArray(Xint_tmp,&xint_tmp);
214:     VecDestroy(&x);
215:     VecDestroy(&b);
216:   }
217:   MatDestroy(&Xint_tmp);

219: #if defined(PETSC_USE_DEBUG_foo)
220:   MatDenseGetArrayRead(Xint,&rxint);
221:   for (i=0; i<Nint; i++) {
222:     tmp = 0.0;
223:     for (j=0; j<26; j++) tmp += rxint[i+j*Nint];

225:     if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xint interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
226:   }
227:   MatDenseRestoreArrayRead(Xint,&rxint);
228:   /* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD); */
229: #endif

231:   /*         total vertices             total faces                                  total edges */
232:   Ntotal = (mp + 1)*(np + 1)*(pp + 1) + mp*np*(pp+1) + mp*pp*(np+1) + np*pp*(mp+1) + mp*(np+1)*(pp+1) + np*(mp+1)*(pp+1) +  pp*(mp+1)*(np+1);

234:   /*
235:       For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
236:   */
237:   cnt = 0;

239:   gl[cnt++] = 0;  { gl[cnt++] = 1;} gl[cnt++] = m-istart-1;
240:   { gl[cnt++] = mwidth;  { gl[cnt++] = mwidth+1;} gl[cnt++] = mwidth + m-istart-1;}
241:   gl[cnt++] = mwidth*(n-jstart-1);  { gl[cnt++] = mwidth*(n-jstart-1)+1;} gl[cnt++] = mwidth*(n-jstart-1) + m-istart-1;
242:   {
243:     gl[cnt++] = mwidth*nwidth;  { gl[cnt++] = mwidth*nwidth+1;}  gl[cnt++] = mwidth*nwidth+ m-istart-1;
244:     { gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;}
245:     gl[cnt++] = mwidth*nwidth+ mwidth*(n-jstart-1);   { gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1)+1;} gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1) + m-istart-1;
246:   }
247:   gl[cnt++] = mwidth*nwidth*(p-kstart-1); { gl[cnt++] = mwidth*nwidth*(p-kstart-1)+1;} gl[cnt++] = mwidth*nwidth*(p-kstart-1) +  m-istart-1;
248:   { gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth;   { gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth+1;} gl[cnt++] = mwidth*nwidth*(p-kstart-1)+mwidth+m-istart-1;}
249:   gl[cnt++] = mwidth*nwidth*(p-kstart-1) +  mwidth*(n-jstart-1);  { gl[cnt++] = mwidth*nwidth*(p-kstart-1)+ mwidth*(n-jstart-1)+1;} gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth*(n-jstart-1) + m-istart-1;

251:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
252:   /* convert that to global numbering and get them on all processes */
253:   ISLocalToGlobalMappingApply(ltg,26,gl,gl);
254:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
255:   PetscMalloc1(26*mp*np*pp,&globals);
256:   MPI_Allgather(gl,26,MPIU_INT,globals,26,MPIU_INT,PetscObjectComm((PetscObject)da));

258:   /* Number the coarse grid points from 0 to Ntotal */
259:   MatGetSize(Aglobal,&Nt,NULL);
260:   PetscTableCreate(Ntotal/3,Nt+1,&ht);
261:   for (i=0; i<26*mp*np*pp; i++) {
262:     PetscTableAddCount(ht,globals[i]+1);
263:   }
264:   PetscTableGetCount(ht,&cnt);
265:   if (cnt != Ntotal) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Hash table size %D not equal to total number coarse grid points %D",cnt,Ntotal);
266:   PetscFree(globals);
267:   for (i=0; i<26; i++) {
268:     PetscTableFind(ht,gl[i]+1,&gl[i]);
269:     gl[i]--;
270:   }
271:   PetscTableDestroy(&ht);
272:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */

274:   /* construct global interpolation matrix */
275:   MatGetLocalSize(Aglobal,&Ng,NULL);
276:   if (reuse == MAT_INITIAL_MATRIX) {
277:     MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint+Nsurf,NULL,P);
278:   } else {
279:     MatZeroEntries(*P);
280:   }
281:   MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
282:   MatDenseGetArrayRead(Xint,&rxint);
283:   MatSetValues(*P,Nint,IIint,26,gl,rxint,INSERT_VALUES);
284:   MatDenseRestoreArrayRead(Xint,&rxint);
285:   MatDenseGetArrayRead(Xsurf,&rxint);
286:   MatSetValues(*P,Nsurf,IIsurf,26,gl,rxint,INSERT_VALUES);
287:   MatDenseRestoreArrayRead(Xsurf,&rxint);
288:   MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
289:   MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
290:   PetscFree2(IIint,IIsurf);

292: #if defined(PETSC_USE_DEBUG_foo)
293:   {
294:     Vec         x,y;
295:     PetscScalar *yy;
296:     VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
297:     VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
298:     VecSet(x,1.0);
299:     MatMult(*P,x,y);
300:     VecGetArray(y,&yy);
301:     for (i=0; i<Ng; i++) {
302:       if (PetscAbsScalar(yy[i]-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong p interpolation at i %D value %g",i,(double)PetscAbsScalar(yy[i]));
303:     }
304:     VecRestoreArray(y,&yy);
305:     VecDestroy(x);
306:     VecDestroy(y);
307:   }
308: #endif

310:   MatDestroy(&Aii);
311:   MatDestroy(&Ais);
312:   MatDestroy(&Asi);
313:   MatDestroy(&A);
314:   ISDestroy(&is);
315:   ISDestroy(&isint);
316:   ISDestroy(&issurf);
317:   MatDestroy(&Xint);
318:   MatDestroy(&Xsurf);
319:   return(0);
320: }

322: /*
323:       DMDAGetFaceInterpolation - Gets the interpolation for a face based coarse space

325: */
326: PetscErrorCode DMDAGetFaceInterpolation(PC pc,DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
327: {
328:   PetscErrorCode         ierr;
329:   PetscInt               dim,i,j,k,m,n,p,dof,Nint,Nface,Nwire,Nsurf,*Iint,*Isurf,cint = 0,csurf = 0,istart,jstart,kstart,*II,N,c = 0;
330:   PetscInt               mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[6],*globals,Ng,*IIint,*IIsurf,Nt;
331:   Mat                    Xint, Xsurf,Xint_tmp;
332:   IS                     isint,issurf,is,row,col;
333:   ISLocalToGlobalMapping ltg;
334:   MPI_Comm               comm;
335:   Mat                    A,Aii,Ais,Asi,*Aholder,iAii;
336:   MatFactorInfo          info;
337:   PetscScalar            *xsurf,*xint;
338:   const PetscScalar      *rxint;
339: #if defined(PETSC_USE_DEBUG_foo)
340:   PetscScalar            tmp;
341: #endif
342:   PetscTable             ht;

345:   DMDAGetInfo(da,&dim,NULL,NULL,NULL,&mp,&np,&pp,&dof,NULL,NULL,NULL,NULL,NULL);
346:   if (dof != 1) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only for single field problems");
347:   if (dim != 3) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only coded for 3d problems");
348:   DMDAGetCorners(da,NULL,NULL,NULL,&m,&n,&p);
349:   DMDAGetGhostCorners(da,&istart,&jstart,&kstart,&mwidth,&nwidth,&pwidth);
350:   istart = istart ? -1 : 0;
351:   jstart = jstart ? -1 : 0;
352:   kstart = kstart ? -1 : 0;

354:   /*
355:     the columns of P are the interpolation of each coarse grid point (one for each vertex and edge)
356:     to all the local degrees of freedom (this includes the vertices, edges and faces).

358:     Xint are the subset of the interpolation into the interior

360:     Xface are the interpolation onto faces but not into the interior

362:     Xsurf are the interpolation onto the vertices and edges (the surfbasket)
363:                                       Xint
364:     Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
365:                                       Xsurf
366:   */
367:   N     = (m - istart)*(n - jstart)*(p - kstart);
368:   Nint  = (m-2-istart)*(n-2-jstart)*(p-2-kstart);
369:   Nface = 2*((m-2-istart)*(n-2-jstart) + (m-2-istart)*(p-2-kstart) + (n-2-jstart)*(p-2-kstart));
370:   Nwire = 4*((m-2-istart) + (n-2-jstart) + (p-2-kstart)) + 8;
371:   Nsurf = Nface + Nwire;
372:   MatCreateSeqDense(MPI_COMM_SELF,Nint,6,NULL,&Xint);
373:   MatCreateSeqDense(MPI_COMM_SELF,Nsurf,6,NULL,&Xsurf);
374:   MatDenseGetArray(Xsurf,&xsurf);

376:   /*
377:      Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
378:      Xsurf will be all zero (thus making the coarse matrix singular).
379:   */
380:   if (m-istart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in X direction must be at least 3");
381:   if (n-jstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Y direction must be at least 3");
382:   if (p-kstart < 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Number of grid points per process in Z direction must be at least 3");

384:   cnt = 0;
385:   for (j=1; j<n-1-jstart; j++) {
386:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 0*Nsurf] = 1;
387:   }

389:   for (k=1; k<p-1-kstart; k++) {
390:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 1*Nsurf] = 1;
391:     for (j=1; j<n-1-jstart; j++) {
392:       xsurf[cnt++ + 2*Nsurf] = 1;
393:       /* these are the interior nodes */
394:       xsurf[cnt++ + 3*Nsurf] = 1;
395:     }
396:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
397:   }
398:   for (j=1;j<n-1-jstart;j++) {
399:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 5*Nsurf] = 1;
400:   }

402: #if defined(PETSC_USE_DEBUG_foo)
403:   for (i=0; i<Nsurf; i++) {
404:     tmp = 0.0;
405:     for (j=0; j<6; j++) tmp += xsurf[i+j*Nsurf];

407:     if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xsurf interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
408:   }
409: #endif
410:   MatDenseRestoreArray(Xsurf,&xsurf);
411:   /* MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);*/

413:   /*
414:        I are the indices for all the needed vertices (in global numbering)
415:        Iint are the indices for the interior values, I surf for the surface values
416:             (This is just for the part of the global matrix obtained with MatCreateSubMatrix(), it
417:              is NOT the local DMDA ordering.)
418:        IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
419:   */
420: #define Endpoint(a,start,b) (a == 0 || a == (b-1-start))
421:   PetscMalloc3(N,&II,Nint,&Iint,Nsurf,&Isurf);
422:   PetscMalloc2(Nint,&IIint,Nsurf,&IIsurf);
423:   for (k=0; k<p-kstart; k++) {
424:     for (j=0; j<n-jstart; j++) {
425:       for (i=0; i<m-istart; i++) {
426:         II[c++] = i + j*mwidth + k*mwidth*nwidth;

428:         if (!Endpoint(i,istart,m) && !Endpoint(j,jstart,n) && !Endpoint(k,kstart,p)) {
429:           IIint[cint]  = i + j*mwidth + k*mwidth*nwidth;
430:           Iint[cint++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
431:         } else {
432:           IIsurf[csurf]  = i + j*mwidth + k*mwidth*nwidth;
433:           Isurf[csurf++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
434:         }
435:       }
436:     }
437:   }
438:   if (c != N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"c != N");
439:   if (cint != Nint) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"cint != Nint");
440:   if (csurf != Nsurf) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csurf != Nsurf");
441:   DMGetLocalToGlobalMapping(da,&ltg);
442:   ISLocalToGlobalMappingApply(ltg,N,II,II);
443:   ISLocalToGlobalMappingApply(ltg,Nint,IIint,IIint);
444:   ISLocalToGlobalMappingApply(ltg,Nsurf,IIsurf,IIsurf);
445:   PetscObjectGetComm((PetscObject)da,&comm);
446:   ISCreateGeneral(comm,N,II,PETSC_COPY_VALUES,&is);
447:   ISCreateGeneral(PETSC_COMM_SELF,Nint,Iint,PETSC_COPY_VALUES,&isint);
448:   ISCreateGeneral(PETSC_COMM_SELF,Nsurf,Isurf,PETSC_COPY_VALUES,&issurf);
449:   PetscFree3(II,Iint,Isurf);

451:   ISSort(is);
452:   MatCreateSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
453:   A    = *Aholder;
454:   PetscFree(Aholder);

456:   MatCreateSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
457:   MatCreateSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
458:   MatCreateSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);

460:   /*
461:      Solve for the interpolation onto the interior Xint
462:   */
463:   MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
464:   MatScale(Xint_tmp,-1.0);

466:   if (exotic->directSolve) {
467:     MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
468:     MatFactorInfoInitialize(&info);
469:     MatGetOrdering(Aii,MATORDERINGND,&row,&col);
470:     MatLUFactorSymbolic(iAii,Aii,row,col,&info);
471:     ISDestroy(&row);
472:     ISDestroy(&col);
473:     MatLUFactorNumeric(iAii,Aii,&info);
474:     MatMatSolve(iAii,Xint_tmp,Xint);
475:     MatDestroy(&iAii);
476:   } else {
477:     Vec         b,x;
478:     PetscScalar *xint_tmp;

480:     MatDenseGetArray(Xint,&xint);
481:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,NULL,&x);
482:     MatDenseGetArray(Xint_tmp,&xint_tmp);
483:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,NULL,&b);
484:     KSPSetOperators(exotic->ksp,Aii,Aii);
485:     for (i=0; i<6; i++) {
486:       VecPlaceArray(x,xint+i*Nint);
487:       VecPlaceArray(b,xint_tmp+i*Nint);
488:       KSPSolve(exotic->ksp,b,x);
489:       KSPCheckSolve(exotic->ksp,pc,x);
490:       VecResetArray(x);
491:       VecResetArray(b);
492:     }
493:     MatDenseRestoreArray(Xint,&xint);
494:     MatDenseRestoreArray(Xint_tmp,&xint_tmp);
495:     VecDestroy(&x);
496:     VecDestroy(&b);
497:   }
498:   MatDestroy(&Xint_tmp);

500: #if defined(PETSC_USE_DEBUG_foo)
501:   MatDenseGetArrayRead(Xint,&rxint);
502:   for (i=0; i<Nint; i++) {
503:     tmp = 0.0;
504:     for (j=0; j<6; j++) tmp += rxint[i+j*Nint];

506:     if (PetscAbsScalar(tmp-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong Xint interpolation at i %D value %g",i,(double)PetscAbsScalar(tmp));
507:   }
508:   MatDenseRestoreArrayRead(Xint,&rxint);
509:   /* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD); */
510: #endif

512:   /*         total faces    */
513:   Ntotal =  mp*np*(pp+1) + mp*pp*(np+1) + np*pp*(mp+1);

515:   /*
516:       For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
517:   */
518:   cnt = 0;
519:   { gl[cnt++] = mwidth+1;}
520:   {
521:     { gl[cnt++] = mwidth*nwidth+1;}
522:     { gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;}
523:     { gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1)+1;}
524:   }
525:   { gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth+1;}

527:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
528:   /* convert that to global numbering and get them on all processes */
529:   ISLocalToGlobalMappingApply(ltg,6,gl,gl);
530:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
531:   PetscMalloc1(6*mp*np*pp,&globals);
532:   MPI_Allgather(gl,6,MPIU_INT,globals,6,MPIU_INT,PetscObjectComm((PetscObject)da));

534:   /* Number the coarse grid points from 0 to Ntotal */
535:   MatGetSize(Aglobal,&Nt,NULL);
536:   PetscTableCreate(Ntotal/3,Nt+1,&ht);
537:   for (i=0; i<6*mp*np*pp; i++) {
538:     PetscTableAddCount(ht,globals[i]+1);
539:   }
540:   PetscTableGetCount(ht,&cnt);
541:   if (cnt != Ntotal) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Hash table size %D not equal to total number coarse grid points %D",cnt,Ntotal);
542:   PetscFree(globals);
543:   for (i=0; i<6; i++) {
544:     PetscTableFind(ht,gl[i]+1,&gl[i]);
545:     gl[i]--;
546:   }
547:   PetscTableDestroy(&ht);
548:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */

550:   /* construct global interpolation matrix */
551:   MatGetLocalSize(Aglobal,&Ng,NULL);
552:   if (reuse == MAT_INITIAL_MATRIX) {
553:     MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint,NULL,P);
554:   } else {
555:     MatZeroEntries(*P);
556:   }
557:   MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
558:   MatDenseGetArrayRead(Xint,&rxint);
559:   MatSetValues(*P,Nint,IIint,6,gl,rxint,INSERT_VALUES);
560:   MatDenseRestoreArrayRead(Xint,&rxint);
561:   MatDenseGetArrayRead(Xsurf,&rxint);
562:   MatSetValues(*P,Nsurf,IIsurf,6,gl,rxint,INSERT_VALUES);
563:   MatDenseRestoreArrayRead(Xsurf,&rxint);
564:   MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
565:   MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
566:   PetscFree2(IIint,IIsurf);

568: #if defined(PETSC_USE_DEBUG_foo)
569:   {
570:     Vec         x,y;
571:     PetscScalar *yy;
572:     VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
573:     VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
574:     VecSet(x,1.0);
575:     MatMult(*P,x,y);
576:     VecGetArray(y,&yy);
577:     for (i=0; i<Ng; i++) {
578:       if (PetscAbsScalar(yy[i]-1.0) > 1.e-10) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Wrong p interpolation at i %D value %g",i,(double)PetscAbsScalar(yy[i]));
579:     }
580:     VecRestoreArray(y,&yy);
581:     VecDestroy(x);
582:     VecDestroy(y);
583:   }
584: #endif

586:   MatDestroy(&Aii);
587:   MatDestroy(&Ais);
588:   MatDestroy(&Asi);
589:   MatDestroy(&A);
590:   ISDestroy(&is);
591:   ISDestroy(&isint);
592:   ISDestroy(&issurf);
593:   MatDestroy(&Xint);
594:   MatDestroy(&Xsurf);
595:   return(0);
596: }

598: /*@
599:    PCExoticSetType - Sets the type of coarse grid interpolation to use

601:    Logically Collective on PC

603:    Input Parameters:
604: +  pc - the preconditioner context
605: -  type - either PC_EXOTIC_FACE or PC_EXOTIC_WIREBASKET (defaults to face)

607:    Notes:
608:     The face based interpolation has 1 degree of freedom per face and ignores the
609:      edge and vertex values completely in the coarse problem. For any seven point
610:      stencil the interpolation of a constant on all faces into the interior is that constant.

612:      The wirebasket interpolation has 1 degree of freedom per vertex, per edge and
613:      per face. A constant on the subdomain boundary is interpolated as that constant
614:      in the interior of the domain.

616:      The coarse grid matrix is obtained via the Galerkin computation A_c = R A R^T, hence
617:      if A is nonsingular A_c is also nonsingular.

619:      Both interpolations are suitable for only scalar problems.

621:    Level: intermediate

623: .seealso: PCEXOTIC, PCExoticType()
624: @*/
625: PetscErrorCode  PCExoticSetType(PC pc,PCExoticType type)
626: {

632:   PetscTryMethod(pc,"PCExoticSetType_C",(PC,PCExoticType),(pc,type));
633:   return(0);
634: }

636: static PetscErrorCode  PCExoticSetType_Exotic(PC pc,PCExoticType type)
637: {
638:   PC_MG     *mg  = (PC_MG*)pc->data;
639:   PC_Exotic *ctx = (PC_Exotic*) mg->innerctx;

642:   ctx->type = type;
643:   return(0);
644: }

646: PetscErrorCode PCSetUp_Exotic(PC pc)
647: {
649:   Mat            A;
650:   PC_MG          *mg   = (PC_MG*)pc->data;
651:   PC_Exotic      *ex   = (PC_Exotic*) mg->innerctx;
652:   MatReuse       reuse = (ex->P) ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;

655:   if (!pc->dm) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Need to call PCSetDM() before using this PC");
656:   PCGetOperators(pc,NULL,&A);
657:   if (ex->type == PC_EXOTIC_FACE) {
658:     DMDAGetFaceInterpolation(pc,pc->dm,ex,A,reuse,&ex->P);
659:   } else if (ex->type == PC_EXOTIC_WIREBASKET) {
660:     DMDAGetWireBasketInterpolation(pc,pc->dm,ex,A,reuse,&ex->P);
661:   } else SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Unknown exotic coarse space %d",ex->type);
662:   PCMGSetInterpolation(pc,1,ex->P);
663:   /* if PC has attached DM we must remove it or the PCMG will use it to compute incorrect sized vectors and interpolations */
664:   PCSetDM(pc,NULL);
665:   PCSetUp_MG(pc);
666:   return(0);
667: }

669: PetscErrorCode PCDestroy_Exotic(PC pc)
670: {
672:   PC_MG          *mg  = (PC_MG*)pc->data;
673:   PC_Exotic      *ctx = (PC_Exotic*) mg->innerctx;

676:   MatDestroy(&ctx->P);
677:   KSPDestroy(&ctx->ksp);
678:   PetscFree(ctx);
679:   PCDestroy_MG(pc);
680:   return(0);
681: }

683: PetscErrorCode PCView_Exotic(PC pc,PetscViewer viewer)
684: {
685:   PC_MG          *mg = (PC_MG*)pc->data;
687:   PetscBool      iascii;
688:   PC_Exotic      *ctx = (PC_Exotic*) mg->innerctx;

691:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
692:   if (iascii) {
693:     PetscViewerASCIIPrintf(viewer,"    Exotic type = %s\n",PCExoticTypes[ctx->type]);
694:     if (ctx->directSolve) {
695:       PetscViewerASCIIPrintf(viewer,"      Using direct solver to construct interpolation\n");
696:     } else {
697:       PetscViewer sviewer;
698:       PetscMPIInt rank;

700:       PetscViewerASCIIPrintf(viewer,"      Using iterative solver to construct interpolation\n");
701:       PetscViewerASCIIPushTab(viewer);
702:       PetscViewerASCIIPushTab(viewer);  /* should not need to push this twice? */
703:       PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
704:       MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
705:       if (rank == 0) {
706:         KSPView(ctx->ksp,sviewer);
707:       }
708:       PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
709:       PetscViewerASCIIPopTab(viewer);
710:       PetscViewerASCIIPopTab(viewer);
711:     }
712:   }
713:   PCView_MG(pc,viewer);
714:   return(0);
715: }

717: PetscErrorCode PCSetFromOptions_Exotic(PetscOptionItems *PetscOptionsObject,PC pc)
718: {
720:   PetscBool      flg;
721:   PC_MG          *mg = (PC_MG*)pc->data;
722:   PCExoticType   mgctype;
723:   PC_Exotic      *ctx = (PC_Exotic*) mg->innerctx;

726:   PetscOptionsHead(PetscOptionsObject,"Exotic coarse space options");
727:   PetscOptionsEnum("-pc_exotic_type","face or wirebasket","PCExoticSetType",PCExoticTypes,(PetscEnum)ctx->type,(PetscEnum*)&mgctype,&flg);
728:   if (flg) {
729:     PCExoticSetType(pc,mgctype);
730:   }
731:   PetscOptionsBool("-pc_exotic_direct_solver","use direct solver to construct interpolation","None",ctx->directSolve,&ctx->directSolve,NULL);
732:   if (!ctx->directSolve) {
733:     if (!ctx->ksp) {
734:       const char *prefix;
735:       KSPCreate(PETSC_COMM_SELF,&ctx->ksp);
736:       KSPSetErrorIfNotConverged(ctx->ksp,pc->erroriffailure);
737:       PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)pc,1);
738:       PetscLogObjectParent((PetscObject)pc,(PetscObject)ctx->ksp);
739:       PCGetOptionsPrefix(pc,&prefix);
740:       KSPSetOptionsPrefix(ctx->ksp,prefix);
741:       KSPAppendOptionsPrefix(ctx->ksp,"exotic_");
742:     }
743:     KSPSetFromOptions(ctx->ksp);
744:   }
745:   PetscOptionsTail();
746:   return(0);
747: }

749: /*MC
750:      PCEXOTIC - Two level overlapping Schwarz preconditioner with exotic (non-standard) coarse grid spaces

752:      This uses the PCMG infrastructure restricted to two levels and the face and wirebasket based coarse
753:    grid spaces.

755:    Notes:
756:     By default this uses GMRES on the fine grid smoother so this should be used with KSPFGMRES or the smoother changed to not use GMRES

758:    References:
759: +  1. - These coarse grid spaces originate in the work of Bramble, Pasciak  and Schatz, "The Construction
760:    of Preconditioners for Elliptic Problems by Substructing IV", Mathematics of Computation, volume 53, 1989.
761: .  2. - They were generalized slightly in "Domain Decomposition Method for Linear Elasticity", Ph. D. thesis, Barry Smith,
762:    New York University, 1990.
763: .  3. - They were then explored in great detail in Dryja, Smith, Widlund, "Schwarz Analysis
764:    of Iterative Substructuring Methods for Elliptic Problems in Three Dimensions, SIAM Journal on Numerical
765:    Analysis, volume 31. 1994. These were developed in the context of iterative substructuring preconditioners.
766: .  4. - They were then ingeniously applied as coarse grid spaces for overlapping Schwarz methods by Dohrmann and Widlund.
767:    They refer to them as GDSW (generalized Dryja, Smith, Widlund preconditioners). See, for example,
768:    Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Extending theory for domain decomposition algorithms to irregular subdomains. In Ulrich Langer, Marco
769:    Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings
770:    of the 17th International Conference on Domain Decomposition Methods in
771:    Science and Engineering, held in Strobl, Austria, 2006, number 60 in
772:    Springer Verlag, Lecture Notes in Computational Science and Engineering, 2007.
773: .  5. -  Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. A family of energy minimizing coarse spaces for overlapping Schwarz preconditioners. In Ulrich Langer,
774:    Marco Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings
775:    of the 17th International Conference on Domain Decomposition Methods
776:    in Science and Engineering, held in Strobl, Austria, 2006, number 60 in
777:    Springer Verlag, Lecture Notes in Computational Science and Engineering, 2007
778: .  6. - Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Domain decomposition
779:    for less regular subdomains: Overlapping Schwarz in two dimensions. SIAM J.
780:    Numer. Anal., 46(4), 2008.
781: -  7. - Clark R. Dohrmann and Olof B. Widlund. An overlapping Schwarz
782:    algorithm for almost incompressible elasticity. Technical Report
783:    TR2008 912, Department of Computer Science, Courant Institute
784:    of Mathematical Sciences, New York University, May 2008. URL:

786:    Options Database: The usual PCMG options are supported, such as -mg_levels_pc_type <type> -mg_coarse_pc_type <type>
787:       -pc_mg_type <type>

789:    Level: advanced

791: .seealso:  PCMG, PCSetDM(), PCExoticType, PCExoticSetType()
792: M*/

794: PETSC_EXTERN PetscErrorCode PCCreate_Exotic(PC pc)
795: {
797:   PC_Exotic      *ex;
798:   PC_MG          *mg;

801:   /* if type was previously mg; must manually destroy it because call to PCSetType(pc,PCMG) will not destroy it */
802:   if (pc->ops->destroy) {
803:      (*pc->ops->destroy)(pc);
804:     pc->data = NULL;
805:   }
806:   PetscFree(((PetscObject)pc)->type_name);
807:   ((PetscObject)pc)->type_name = NULL;

809:   PCSetType(pc,PCMG);
810:   PCMGSetLevels(pc,2,NULL);
811:   PCMGSetGalerkin(pc,PC_MG_GALERKIN_PMAT);
812:   PetscNew(&ex); \
813:   ex->type     = PC_EXOTIC_FACE;
814:   mg           = (PC_MG*) pc->data;
815:   mg->innerctx = ex;

817:   pc->ops->setfromoptions = PCSetFromOptions_Exotic;
818:   pc->ops->view           = PCView_Exotic;
819:   pc->ops->destroy        = PCDestroy_Exotic;
820:   pc->ops->setup          = PCSetUp_Exotic;

822:   PetscObjectComposeFunction((PetscObject)pc,"PCExoticSetType_C",PCExoticSetType_Exotic);
823:   return(0);
824: }