Actual source code: wb.c

petsc-3.5.2 2014-09-08
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  2: #include <petscdmda.h>   /*I "petscdmda.h" I*/
  3: #include <../src/ksp/pc/impls/mg/mgimpl.h>   /*I "petscksp.h" I*/
  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",0};


 18: /*
 19:       DMDAGetWireBasketInterpolation - Gets the interpolation for a wirebasket based coarse space

 21: */
 22: PetscErrorCode DMDAGetWireBasketInterpolation(DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
 23: {
 24:   PetscErrorCode         ierr;
 25:   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;
 26:   PetscInt               mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[26],*globals,Ng,*IIint,*IIsurf,Nt;
 27:   Mat                    Xint, Xsurf,Xint_tmp;
 28:   IS                     isint,issurf,is,row,col;
 29:   ISLocalToGlobalMapping ltg;
 30:   MPI_Comm               comm;
 31:   Mat                    A,Aii,Ais,Asi,*Aholder,iAii;
 32:   MatFactorInfo          info;
 33:   PetscScalar            *xsurf,*xint;
 34: #if defined(PETSC_USE_DEBUG_foo)
 35:   PetscScalar            tmp;
 36: #endif
 37:   PetscTable             ht;

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

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

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

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

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

 71:   /*
 72:      Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
 73:      Xsurf will be all zero (thus making the coarse matrix singular).
 74:   */
 75:   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");
 76:   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");
 77:   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");

 79:   cnt = 0;

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

 85:   for (j=1; j<n-1-jstart; j++) {
 86:     xsurf[cnt++ + 3*Nsurf] = 1;
 87:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
 88:     xsurf[cnt++ + 5*Nsurf] = 1;
 89:   }

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

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

100:     for (j=1; j<n-1-jstart; j++) {
101:       xsurf[cnt++ + 12*Nsurf] = 1;
102:       /* these are the interior nodes */
103:       xsurf[cnt++ + 13*Nsurf] = 1;
104:     }

106:     xsurf[cnt++ + 14*Nsurf] = 1;
107:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 15*Nsurf] = 1;
108:     xsurf[cnt++ + 16*Nsurf] = 1;
109:   }

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

115:   for (j=1;j<n-1-jstart;j++) {
116:     xsurf[cnt++ + 20*Nsurf] = 1;
117:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 21*Nsurf] = 1;
118:     xsurf[cnt++ + 22*Nsurf] = 1;
119:   }

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


126:   /* interpolations only sum to 1 when using direct solver */
127: #if defined(PETSC_USE_DEBUG_foo)
128:   for (i=0; i<Nsurf; i++) {
129:     tmp = 0.0;
130:     for (j=0; j<26; j++) tmp += xsurf[i+j*Nsurf];
131:     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));
132:   }
133: #endif
134:   MatDenseRestoreArray(Xsurf,&xsurf);
135:   /* MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);*/


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

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

176:   MatGetSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
177:   A    = *Aholder;
178:   PetscFree(Aholder);

180:   MatGetSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
181:   MatGetSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
182:   MatGetSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);

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

203:     MatDenseGetArray(Xint,&xint);
204:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&x);
205:     MatDenseGetArray(Xint_tmp,&xint_tmp);
206:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&b);
207:     KSPSetOperators(exotic->ksp,Aii,Aii);
208:     for (i=0; i<26; i++) {
209:       VecPlaceArray(x,xint+i*Nint);
210:       VecPlaceArray(b,xint_tmp+i*Nint);
211:       KSPSolve(exotic->ksp,b,x);
212:       VecResetArray(x);
213:       VecResetArray(b);
214:     }
215:     MatDenseRestoreArray(Xint,&xint);
216:     MatDenseRestoreArray(Xint_tmp,&xint_tmp);
217:     VecDestroy(&x);
218:     VecDestroy(&b);
219:   }
220:   MatDestroy(&Xint_tmp);

222: #if defined(PETSC_USE_DEBUG_foo)
223:   MatDenseGetArray(Xint,&xint);
224:   for (i=0; i<Nint; i++) {
225:     tmp = 0.0;
226:     for (j=0; j<26; j++) tmp += xint[i+j*Nint];

228:     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));
229:   }
230:   MatDenseRestoreArray(Xint,&xint);
231:   /* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD); */
232: #endif


235:   /*         total vertices             total faces                                  total edges */
236:   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);

238:   /*
239:       For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
240:   */
241:   cnt = 0;

243:   gl[cnt++] = 0;  { gl[cnt++] = 1;} gl[cnt++] = m-istart-1;
244:   { gl[cnt++] = mwidth;  { gl[cnt++] = mwidth+1;} gl[cnt++] = mwidth + m-istart-1;}
245:   gl[cnt++] = mwidth*(n-jstart-1);  { gl[cnt++] = mwidth*(n-jstart-1)+1;} gl[cnt++] = mwidth*(n-jstart-1) + m-istart-1;
246:   {
247:     gl[cnt++] = mwidth*nwidth;  { gl[cnt++] = mwidth*nwidth+1;}  gl[cnt++] = mwidth*nwidth+ m-istart-1;
248:     { gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;}
249:     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;
250:   }
251:   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;
252:   { 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;}
253:   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;

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

262:   /* Number the coarse grid points from 0 to Ntotal */
263:   MatGetSize(Aglobal,&Nt,NULL);
264:   PetscTableCreate(Ntotal/3,Nt+1,&ht);
265:   for (i=0; i<26*mp*np*pp; i++) {
266:     PetscTableAddCount(ht,globals[i]+1);
267:   }
268:   PetscTableGetCount(ht,&cnt);
269:   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);
270:   PetscFree(globals);
271:   for (i=0; i<26; i++) {
272:     PetscTableFind(ht,gl[i]+1,&gl[i]);
273:     gl[i]--;
274:   }
275:   PetscTableDestroy(&ht);
276:   /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */

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

296: #if defined(PETSC_USE_DEBUG_foo)
297:   {
298:     Vec         x,y;
299:     PetscScalar *yy;
300:     VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
301:     VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
302:     VecSet(x,1.0);
303:     MatMult(*P,x,y);
304:     VecGetArray(y,&yy);
305:     for (i=0; i<Ng; i++) {
306:       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]));
307:     }
308:     VecRestoreArray(y,&yy);
309:     VecDestroy(x);
310:     VecDestroy(y);
311:   }
312: #endif

314:   MatDestroy(&Aii);
315:   MatDestroy(&Ais);
316:   MatDestroy(&Asi);
317:   MatDestroy(&A);
318:   ISDestroy(&is);
319:   ISDestroy(&isint);
320:   ISDestroy(&issurf);
321:   MatDestroy(&Xint);
322:   MatDestroy(&Xsurf);
323:   return(0);
324: }

328: /*
329:       DMDAGetFaceInterpolation - Gets the interpolation for a face based coarse space

331: */
332: PetscErrorCode DMDAGetFaceInterpolation(DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
333: {
334:   PetscErrorCode         ierr;
335:   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;
336:   PetscInt               mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[6],*globals,Ng,*IIint,*IIsurf,Nt;
337:   Mat                    Xint, Xsurf,Xint_tmp;
338:   IS                     isint,issurf,is,row,col;
339:   ISLocalToGlobalMapping ltg;
340:   MPI_Comm               comm;
341:   Mat                    A,Aii,Ais,Asi,*Aholder,iAii;
342:   MatFactorInfo          info;
343:   PetscScalar            *xsurf,*xint;
344: #if defined(PETSC_USE_DEBUG_foo)
345:   PetscScalar            tmp;
346: #endif
347:   PetscTable             ht;

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

359:   /*
360:     the columns of P are the interpolation of each coarse grid point (one for each vertex and edge)
361:     to all the local degrees of freedom (this includes the vertices, edges and faces).

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

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

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

381:   /*
382:      Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
383:      Xsurf will be all zero (thus making the coarse matrix singular).
384:   */
385:   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");
386:   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");
387:   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");

389:   cnt = 0;
390:   for (j=1; j<n-1-jstart; j++) {
391:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 0*Nsurf] = 1;
392:   }

394:   for (k=1; k<p-1-kstart; k++) {
395:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 1*Nsurf] = 1;
396:     for (j=1; j<n-1-jstart; j++) {
397:       xsurf[cnt++ + 2*Nsurf] = 1;
398:       /* these are the interior nodes */
399:       xsurf[cnt++ + 3*Nsurf] = 1;
400:     }
401:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
402:   }
403:   for (j=1;j<n-1-jstart;j++) {
404:     for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 5*Nsurf] = 1;
405:   }

407: #if defined(PETSC_USE_DEBUG_foo)
408:   for (i=0; i<Nsurf; i++) {
409:     tmp = 0.0;
410:     for (j=0; j<6; j++) tmp += xsurf[i+j*Nsurf];

412:     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));
413:   }
414: #endif
415:   MatDenseRestoreArray(Xsurf,&xsurf);
416:   /* MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);*/


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

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

457:   ISSort(is);
458:   MatGetSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
459:   A    = *Aholder;
460:   PetscFree(Aholder);

462:   MatGetSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
463:   MatGetSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
464:   MatGetSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);

466:   /*
467:      Solve for the interpolation onto the interior Xint
468:   */
469:   MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
470:   MatScale(Xint_tmp,-1.0);

472:   if (exotic->directSolve) {
473:     MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
474:     MatFactorInfoInitialize(&info);
475:     MatGetOrdering(Aii,MATORDERINGND,&row,&col);
476:     MatLUFactorSymbolic(iAii,Aii,row,col,&info);
477:     ISDestroy(&row);
478:     ISDestroy(&col);
479:     MatLUFactorNumeric(iAii,Aii,&info);
480:     MatMatSolve(iAii,Xint_tmp,Xint);
481:     MatDestroy(&iAii);
482:   } else {
483:     Vec         b,x;
484:     PetscScalar *xint_tmp;

486:     MatDenseGetArray(Xint,&xint);
487:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&x);
488:     MatDenseGetArray(Xint_tmp,&xint_tmp);
489:     VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&b);
490:     KSPSetOperators(exotic->ksp,Aii,Aii);
491:     for (i=0; i<6; i++) {
492:       VecPlaceArray(x,xint+i*Nint);
493:       VecPlaceArray(b,xint_tmp+i*Nint);
494:       KSPSolve(exotic->ksp,b,x);
495:       VecResetArray(x);
496:       VecResetArray(b);
497:     }
498:     MatDenseRestoreArray(Xint,&xint);
499:     MatDenseRestoreArray(Xint_tmp,&xint_tmp);
500:     VecDestroy(&x);
501:     VecDestroy(&b);
502:   }
503:   MatDestroy(&Xint_tmp);

505: #if defined(PETSC_USE_DEBUG_foo)
506:   MatDenseGetArray(Xint,&xint);
507:   for (i=0; i<Nint; i++) {
508:     tmp = 0.0;
509:     for (j=0; j<6; j++) tmp += xint[i+j*Nint];

511:     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));
512:   }
513:   MatDenseRestoreArray(Xint,&xint);
514:   /* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD); */
515: #endif


518:   /*         total faces    */
519:   Ntotal =  mp*np*(pp+1) + mp*pp*(np+1) + np*pp*(mp+1);

521:   /*
522:       For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
523:   */
524:   cnt = 0;
525:   { gl[cnt++] = mwidth+1;}
526:   {
527:     { gl[cnt++] = mwidth*nwidth+1;}
528:     { gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;}
529:     { gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1)+1;}
530:   }
531:   { gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth+1;}

533:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
534:   /* convert that to global numbering and get them on all processes */
535:   ISLocalToGlobalMappingApply(ltg,6,gl,gl);
536:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
537:   PetscMalloc1(6*mp*np*pp,&globals);
538:   MPI_Allgather(gl,6,MPIU_INT,globals,6,MPIU_INT,PetscObjectComm((PetscObject)da));

540:   /* Number the coarse grid points from 0 to Ntotal */
541:   MatGetSize(Aglobal,&Nt,NULL);
542:   PetscTableCreate(Ntotal/3,Nt+1,&ht);
543:   for (i=0; i<6*mp*np*pp; i++) {
544:     PetscTableAddCount(ht,globals[i]+1);
545:   }
546:   PetscTableGetCount(ht,&cnt);
547:   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);
548:   PetscFree(globals);
549:   for (i=0; i<6; i++) {
550:     PetscTableFind(ht,gl[i]+1,&gl[i]);
551:     gl[i]--;
552:   }
553:   PetscTableDestroy(&ht);
554:   /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */

556:   /* construct global interpolation matrix */
557:   MatGetLocalSize(Aglobal,&Ng,NULL);
558:   if (reuse == MAT_INITIAL_MATRIX) {
559:     MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint,NULL,P);
560:   } else {
561:     MatZeroEntries(*P);
562:   }
563:   MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
564:   MatDenseGetArray(Xint,&xint);
565:   MatSetValues(*P,Nint,IIint,6,gl,xint,INSERT_VALUES);
566:   MatDenseRestoreArray(Xint,&xint);
567:   MatDenseGetArray(Xsurf,&xsurf);
568:   MatSetValues(*P,Nsurf,IIsurf,6,gl,xsurf,INSERT_VALUES);
569:   MatDenseRestoreArray(Xsurf,&xsurf);
570:   MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
571:   MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
572:   PetscFree2(IIint,IIsurf);


575: #if defined(PETSC_USE_DEBUG_foo)
576:   {
577:     Vec         x,y;
578:     PetscScalar *yy;
579:     VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
580:     VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
581:     VecSet(x,1.0);
582:     MatMult(*P,x,y);
583:     VecGetArray(y,&yy);
584:     for (i=0; i<Ng; i++) {
585:       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]));
586:     }
587:     VecRestoreArray(y,&yy);
588:     VecDestroy(x);
589:     VecDestroy(y);
590:   }
591: #endif

593:   MatDestroy(&Aii);
594:   MatDestroy(&Ais);
595:   MatDestroy(&Asi);
596:   MatDestroy(&A);
597:   ISDestroy(&is);
598:   ISDestroy(&isint);
599:   ISDestroy(&issurf);
600:   MatDestroy(&Xint);
601:   MatDestroy(&Xsurf);
602:   return(0);
603: }


608: /*@
609:    PCExoticSetType - Sets the type of coarse grid interpolation to use

611:    Logically Collective on PC

613:    Input Parameters:
614: +  pc - the preconditioner context
615: -  type - either PC_EXOTIC_FACE or PC_EXOTIC_WIREBASKET (defaults to face)

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

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

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

628:      Both interpolations are suitable for only scalar problems.

630:    Level: intermediate


633: .seealso: PCEXOTIC, PCExoticType()
634: @*/
635: PetscErrorCode  PCExoticSetType(PC pc,PCExoticType type)
636: {

642:   PetscTryMethod(pc,"PCExoticSetType_C",(PC,PCExoticType),(pc,type));
643:   return(0);
644: }

648: static PetscErrorCode  PCExoticSetType_Exotic(PC pc,PCExoticType type)
649: {
650:   PC_MG     *mg  = (PC_MG*)pc->data;
651:   PC_Exotic *ctx = (PC_Exotic*) mg->innerctx;

654:   ctx->type = type;
655:   return(0);
656: }

660: PetscErrorCode PCSetUp_Exotic(PC pc)
661: {
663:   Mat            A;
664:   PC_MG          *mg   = (PC_MG*)pc->data;
665:   PC_Exotic      *ex   = (PC_Exotic*) mg->innerctx;
666:   MatReuse       reuse = (ex->P) ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;

669:   if (!pc->dm) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Need to call PCSetDM() before using this PC");
670:   PCGetOperators(pc,NULL,&A);
671:   if (ex->type == PC_EXOTIC_FACE) {
672:     DMDAGetFaceInterpolation(pc->dm,ex,A,reuse,&ex->P);
673:   } else if (ex->type == PC_EXOTIC_WIREBASKET) {
674:     DMDAGetWireBasketInterpolation(pc->dm,ex,A,reuse,&ex->P);
675:   } else SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Unknown exotic coarse space %d",ex->type);
676:   PCMGSetInterpolation(pc,1,ex->P);
677:   /* if PC has attached DM we must remove it or the PCMG will use it to compute incorrect sized vectors and interpolations */
678:   PCSetDM(pc,NULL);
679:   PCSetUp_MG(pc);
680:   return(0);
681: }

685: PetscErrorCode PCDestroy_Exotic(PC pc)
686: {
688:   PC_MG          *mg  = (PC_MG*)pc->data;
689:   PC_Exotic      *ctx = (PC_Exotic*) mg->innerctx;

692:   MatDestroy(&ctx->P);
693:   KSPDestroy(&ctx->ksp);
694:   PetscFree(ctx);
695:   PCDestroy_MG(pc);
696:   return(0);
697: }

701: PetscErrorCode PCView_Exotic(PC pc,PetscViewer viewer)
702: {
703:   PC_MG          *mg = (PC_MG*)pc->data;
705:   PetscBool      iascii;
706:   PC_Exotic      *ctx = (PC_Exotic*) mg->innerctx;

709:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
710:   if (iascii) {
711:     PetscViewerASCIIPrintf(viewer,"    Exotic type = %s\n",PCExoticTypes[ctx->type]);
712:     if (ctx->directSolve) {
713:       PetscViewerASCIIPrintf(viewer,"      Using direct solver to construct interpolation\n");
714:     } else {
715:       PetscViewer sviewer;
716:       PetscMPIInt rank;

718:       PetscViewerASCIIPrintf(viewer,"      Using iterative solver to construct interpolation\n");
719:       PetscViewerASCIIPushTab(viewer);
720:       PetscViewerASCIIPushTab(viewer);  /* should not need to push this twice? */
721:       PetscViewerGetSingleton(viewer,&sviewer);
722:       MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
723:       if (!rank) {
724:         KSPView(ctx->ksp,sviewer);
725:       }
726:       PetscViewerRestoreSingleton(viewer,&sviewer);
727:       PetscViewerASCIIPopTab(viewer);
728:       PetscViewerASCIIPopTab(viewer);
729:     }
730:   }
731:   PCView_MG(pc,viewer);
732:   return(0);
733: }

737: PetscErrorCode PCSetFromOptions_Exotic(PC pc)
738: {
740:   PetscBool      flg;
741:   PC_MG          *mg = (PC_MG*)pc->data;
742:   PCExoticType   mgctype;
743:   PC_Exotic      *ctx = (PC_Exotic*) mg->innerctx;

746:   PetscOptionsHead("Exotic coarse space options");
747:   PetscOptionsEnum("-pc_exotic_type","face or wirebasket","PCExoticSetType",PCExoticTypes,(PetscEnum)ctx->type,(PetscEnum*)&mgctype,&flg);
748:   if (flg) {
749:     PCExoticSetType(pc,mgctype);
750:   }
751:   PetscOptionsBool("-pc_exotic_direct_solver","use direct solver to construct interpolation","None",ctx->directSolve,&ctx->directSolve,NULL);
752:   if (!ctx->directSolve) {
753:     if (!ctx->ksp) {
754:       const char *prefix;
755:       KSPCreate(PETSC_COMM_SELF,&ctx->ksp);
756:       PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)pc,1);
757:       PetscLogObjectParent((PetscObject)pc,(PetscObject)ctx->ksp);
758:       PCGetOptionsPrefix(pc,&prefix);
759:       KSPSetOptionsPrefix(ctx->ksp,prefix);
760:       KSPAppendOptionsPrefix(ctx->ksp,"exotic_");
761:     }
762:     KSPSetFromOptions(ctx->ksp);
763:   }
764:   PetscOptionsTail();
765:   return(0);
766: }


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

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

775:    Notes: 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

777:    References: These coarse grid spaces originate in the work of Bramble, Pasciak  and Schatz, "The Construction
778:    of Preconditioners for Elliptic Problems by Substructing IV", Mathematics of Computation, volume 53 pages 1--24, 1989.
779:    They were generalized slightly in "Domain Decomposition Method for Linear Elasticity", Ph. D. thesis, Barry Smith,
780:    New York University, 1990. They were then explored in great detail in Dryja, Smith, Widlund, "Schwarz Analysis
781:    of Iterative Substructuring Methods for Elliptic Problems in Three Dimensions, SIAM Journal on Numerical
782:    Analysis, volume 31. pages 1662-1694, 1994. These were developed in the context of iterative substructuring preconditioners.
783:    They were then ingeniously applied as coarse grid spaces for overlapping Schwarz methods by Dohrmann and Widlund.
784:    They refer to them as GDSW (generalized Dryja, Smith, Widlund preconditioners). See, for example,
785:    Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Extending theory for domain decomposition algorithms to irregular subdomains. In Ulrich Langer, Marco
786:    Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings
787:    of the 17th International Conference on Domain Decomposition Methods in
788:    Science and Engineering, held in Strobl, Austria, July 3-7, 2006, number 60 in
789:    Springer-Verlag, Lecture Notes in Computational Science and Engineering, pages 255-261, 2007.
790:    Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. A family of energy min-
791:    imizing coarse spaces for overlapping Schwarz preconditioners. In Ulrich Langer,
792:    Marco Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings
793:    of the 17th International Conference on Domain Decomposition Methods
794:    in Science and Engineering, held in Strobl, Austria, July 3-7, 2006, number 60 in
795:    Springer-Verlag, Lecture Notes in Computational Science and Engineering, pages 247-254, 2007
796:    Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Domain decomposition
797:    for less regular subdomains: Overlapping Schwarz in two dimensions. SIAM J.
798:    Numer. Anal., 46(4):2153-2168, 2008.
799:    Clark R. Dohrmann and Olof B. Widlund. An overlapping Schwarz
800:    algorithm for almost incompressible elasticity. Technical Report
801:    TR2008-912, Department of Computer Science, Courant Institute
802:    of Mathematical Sciences, New York University, May 2008. URL:
803:    http://cs.nyu.edu/csweb/Research/TechReports/TR2008-912/TR2008-912.pdf

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

808:    Level: advanced

810: .seealso:  PCMG, PCSetDM(), PCExoticType, PCExoticSetType()
811: M*/

815: PETSC_EXTERN PetscErrorCode PCCreate_Exotic(PC pc)
816: {
818:   PC_Exotic      *ex;
819:   PC_MG          *mg;

822:   /* if type was previously mg; must manually destroy it because call to PCSetType(pc,PCMG) will not destroy it */
823:   if (pc->ops->destroy) {
824:      (*pc->ops->destroy)(pc);
825:     pc->data = 0;
826:   }
827:   PetscFree(((PetscObject)pc)->type_name);
828:   ((PetscObject)pc)->type_name = 0;

830:   PCSetType(pc,PCMG);
831:   PCMGSetLevels(pc,2,NULL);
832:   PCMGSetGalerkin(pc,PETSC_TRUE);
833:   PetscNew(&ex); \
834:   ex->type     = PC_EXOTIC_FACE;
835:   mg           = (PC_MG*) pc->data;
836:   mg->innerctx = ex;


839:   pc->ops->setfromoptions = PCSetFromOptions_Exotic;
840:   pc->ops->view           = PCView_Exotic;
841:   pc->ops->destroy        = PCDestroy_Exotic;
842:   pc->ops->setup          = PCSetUp_Exotic;

844:   PetscObjectComposeFunction((PetscObject)pc,"PCExoticSetType_C",PCExoticSetType_Exotic);
845:   return(0);
846: }