Actual source code: wb.c
petsc-3.8.4 2018-03-24
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",0};
16: /*
17: DMDAGetWireBasketInterpolation - Gets the interpolation for a wirebasket based coarse space
19: */
20: PetscErrorCode DMDAGetWireBasketInterpolation(DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
21: {
22: PetscErrorCode ierr;
23: 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;
24: PetscInt mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[26],*globals,Ng,*IIint,*IIsurf,Nt;
25: Mat Xint, Xsurf,Xint_tmp;
26: IS isint,issurf,is,row,col;
27: ISLocalToGlobalMapping ltg;
28: MPI_Comm comm;
29: Mat A,Aii,Ais,Asi,*Aholder,iAii;
30: MatFactorInfo info;
31: PetscScalar *xsurf,*xint;
32: #if defined(PETSC_USE_DEBUG_foo)
33: PetscScalar tmp;
34: #endif
35: PetscTable ht;
38: DMDAGetInfo(da,&dim,0,0,0,&mp,&np,&pp,&dof,0,0,0,0,0);
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,0,0,0,&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;
124: /* interpolations only sum to 1 when using direct solver */
125: #if defined(PETSC_USE_DEBUG_foo)
126: for (i=0; i<Nsurf; i++) {
127: tmp = 0.0;
128: for (j=0; j<26; j++) tmp += xsurf[i+j*Nsurf];
129: 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));
130: }
131: #endif
132: MatDenseRestoreArray(Xsurf,&xsurf);
133: /* MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);*/
136: /*
137: I are the indices for all the needed vertices (in global numbering)
138: Iint are the indices for the interior values, I surf for the surface values
139: (This is just for the part of the global matrix obtained with MatCreateSubMatrix(), it
140: is NOT the local DMDA ordering.)
141: IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
142: */
143: #define Endpoint(a,start,b) (a == 0 || a == (b-1-start))
144: PetscMalloc3(N,&II,Nint,&Iint,Nsurf,&Isurf);
145: PetscMalloc2(Nint,&IIint,Nsurf,&IIsurf);
146: for (k=0; k<p-kstart; k++) {
147: for (j=0; j<n-jstart; j++) {
148: for (i=0; i<m-istart; i++) {
149: II[c++] = i + j*mwidth + k*mwidth*nwidth;
151: if (!Endpoint(i,istart,m) && !Endpoint(j,jstart,n) && !Endpoint(k,kstart,p)) {
152: IIint[cint] = i + j*mwidth + k*mwidth*nwidth;
153: Iint[cint++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
154: } else {
155: IIsurf[csurf] = i + j*mwidth + k*mwidth*nwidth;
156: Isurf[csurf++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
157: }
158: }
159: }
160: }
161: if (c != N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"c != N");
162: if (cint != Nint) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"cint != Nint");
163: if (csurf != Nsurf) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csurf != Nsurf");
164: DMGetLocalToGlobalMapping(da,<g);
165: ISLocalToGlobalMappingApply(ltg,N,II,II);
166: ISLocalToGlobalMappingApply(ltg,Nint,IIint,IIint);
167: ISLocalToGlobalMappingApply(ltg,Nsurf,IIsurf,IIsurf);
168: PetscObjectGetComm((PetscObject)da,&comm);
169: ISCreateGeneral(comm,N,II,PETSC_COPY_VALUES,&is);
170: ISCreateGeneral(PETSC_COMM_SELF,Nint,Iint,PETSC_COPY_VALUES,&isint);
171: ISCreateGeneral(PETSC_COMM_SELF,Nsurf,Isurf,PETSC_COPY_VALUES,&issurf);
172: PetscFree3(II,Iint,Isurf);
174: MatCreateSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
175: A = *Aholder;
176: PetscFree(Aholder);
178: MatCreateSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
179: MatCreateSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
180: MatCreateSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);
182: /*
183: Solve for the interpolation onto the interior Xint
184: */
185: MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
186: MatScale(Xint_tmp,-1.0);
187: if (exotic->directSolve) {
188: MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
189: MatFactorInfoInitialize(&info);
190: MatGetOrdering(Aii,MATORDERINGND,&row,&col);
191: MatLUFactorSymbolic(iAii,Aii,row,col,&info);
192: ISDestroy(&row);
193: ISDestroy(&col);
194: MatLUFactorNumeric(iAii,Aii,&info);
195: MatMatSolve(iAii,Xint_tmp,Xint);
196: MatDestroy(&iAii);
197: } else {
198: Vec b,x;
199: PetscScalar *xint_tmp;
201: MatDenseGetArray(Xint,&xint);
202: VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&x);
203: MatDenseGetArray(Xint_tmp,&xint_tmp);
204: VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&b);
205: KSPSetOperators(exotic->ksp,Aii,Aii);
206: for (i=0; i<26; i++) {
207: VecPlaceArray(x,xint+i*Nint);
208: VecPlaceArray(b,xint_tmp+i*Nint);
209: KSPSolve(exotic->ksp,b,x);
210: VecResetArray(x);
211: VecResetArray(b);
212: }
213: MatDenseRestoreArray(Xint,&xint);
214: MatDenseRestoreArray(Xint_tmp,&xint_tmp);
215: VecDestroy(&x);
216: VecDestroy(&b);
217: }
218: MatDestroy(&Xint_tmp);
220: #if defined(PETSC_USE_DEBUG_foo)
221: MatDenseGetArray(Xint,&xint);
222: for (i=0; i<Nint; i++) {
223: tmp = 0.0;
224: for (j=0; j<26; j++) tmp += xint[i+j*Nint];
226: 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));
227: }
228: MatDenseRestoreArray(Xint,&xint);
229: /* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD); */
230: #endif
233: /* total vertices total faces total edges */
234: 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);
236: /*
237: For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
238: */
239: cnt = 0;
241: gl[cnt++] = 0; { gl[cnt++] = 1;} gl[cnt++] = m-istart-1;
242: { gl[cnt++] = mwidth; { gl[cnt++] = mwidth+1;} gl[cnt++] = mwidth + m-istart-1;}
243: gl[cnt++] = mwidth*(n-jstart-1); { gl[cnt++] = mwidth*(n-jstart-1)+1;} gl[cnt++] = mwidth*(n-jstart-1) + m-istart-1;
244: {
245: gl[cnt++] = mwidth*nwidth; { gl[cnt++] = mwidth*nwidth+1;} gl[cnt++] = mwidth*nwidth+ m-istart-1;
246: { gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;}
247: 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;
248: }
249: 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;
250: { 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;}
251: 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;
253: /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
254: /* convert that to global numbering and get them on all processes */
255: ISLocalToGlobalMappingApply(ltg,26,gl,gl);
256: /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
257: PetscMalloc1(26*mp*np*pp,&globals);
258: MPI_Allgather(gl,26,MPIU_INT,globals,26,MPIU_INT,PetscObjectComm((PetscObject)da));
260: /* Number the coarse grid points from 0 to Ntotal */
261: MatGetSize(Aglobal,&Nt,NULL);
262: PetscTableCreate(Ntotal/3,Nt+1,&ht);
263: for (i=0; i<26*mp*np*pp; i++) {
264: PetscTableAddCount(ht,globals[i]+1);
265: }
266: PetscTableGetCount(ht,&cnt);
267: 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);
268: PetscFree(globals);
269: for (i=0; i<26; i++) {
270: PetscTableFind(ht,gl[i]+1,&gl[i]);
271: gl[i]--;
272: }
273: PetscTableDestroy(&ht);
274: /* PetscIntView(26,gl,PETSC_VIEWER_STDOUT_WORLD); */
276: /* construct global interpolation matrix */
277: MatGetLocalSize(Aglobal,&Ng,NULL);
278: if (reuse == MAT_INITIAL_MATRIX) {
279: MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint+Nsurf,NULL,P);
280: } else {
281: MatZeroEntries(*P);
282: }
283: MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
284: MatDenseGetArray(Xint,&xint);
285: MatSetValues(*P,Nint,IIint,26,gl,xint,INSERT_VALUES);
286: MatDenseRestoreArray(Xint,&xint);
287: MatDenseGetArray(Xsurf,&xsurf);
288: MatSetValues(*P,Nsurf,IIsurf,26,gl,xsurf,INSERT_VALUES);
289: MatDenseRestoreArray(Xsurf,&xsurf);
290: MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
291: MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
292: PetscFree2(IIint,IIsurf);
294: #if defined(PETSC_USE_DEBUG_foo)
295: {
296: Vec x,y;
297: PetscScalar *yy;
298: VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
299: VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
300: VecSet(x,1.0);
301: MatMult(*P,x,y);
302: VecGetArray(y,&yy);
303: for (i=0; i<Ng; i++) {
304: 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]));
305: }
306: VecRestoreArray(y,&yy);
307: VecDestroy(x);
308: VecDestroy(y);
309: }
310: #endif
312: MatDestroy(&Aii);
313: MatDestroy(&Ais);
314: MatDestroy(&Asi);
315: MatDestroy(&A);
316: ISDestroy(&is);
317: ISDestroy(&isint);
318: ISDestroy(&issurf);
319: MatDestroy(&Xint);
320: MatDestroy(&Xsurf);
321: return(0);
322: }
324: /*
325: DMDAGetFaceInterpolation - Gets the interpolation for a face based coarse space
327: */
328: PetscErrorCode DMDAGetFaceInterpolation(DM da,PC_Exotic *exotic,Mat Aglobal,MatReuse reuse,Mat *P)
329: {
330: PetscErrorCode ierr;
331: 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;
332: PetscInt mwidth,nwidth,pwidth,cnt,mp,np,pp,Ntotal,gl[6],*globals,Ng,*IIint,*IIsurf,Nt;
333: Mat Xint, Xsurf,Xint_tmp;
334: IS isint,issurf,is,row,col;
335: ISLocalToGlobalMapping ltg;
336: MPI_Comm comm;
337: Mat A,Aii,Ais,Asi,*Aholder,iAii;
338: MatFactorInfo info;
339: PetscScalar *xsurf,*xint;
340: #if defined(PETSC_USE_DEBUG_foo)
341: PetscScalar tmp;
342: #endif
343: PetscTable ht;
346: DMDAGetInfo(da,&dim,0,0,0,&mp,&np,&pp,&dof,0,0,0,0,0);
347: if (dof != 1) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only for single field problems");
348: if (dim != 3) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Only coded for 3d problems");
349: DMDAGetCorners(da,0,0,0,&m,&n,&p);
350: DMDAGetGhostCorners(da,&istart,&jstart,&kstart,&mwidth,&nwidth,&pwidth);
351: istart = istart ? -1 : 0;
352: jstart = jstart ? -1 : 0;
353: kstart = kstart ? -1 : 0;
355: /*
356: the columns of P are the interpolation of each coarse grid point (one for each vertex and edge)
357: to all the local degrees of freedom (this includes the vertices, edges and faces).
359: Xint are the subset of the interpolation into the interior
361: Xface are the interpolation onto faces but not into the interior
363: Xsurf are the interpolation onto the vertices and edges (the surfbasket)
364: Xint
365: Symbolically one could write P = (Xface) after interchanging the rows to match the natural ordering on the domain
366: Xsurf
367: */
368: N = (m - istart)*(n - jstart)*(p - kstart);
369: Nint = (m-2-istart)*(n-2-jstart)*(p-2-kstart);
370: Nface = 2*((m-2-istart)*(n-2-jstart) + (m-2-istart)*(p-2-kstart) + (n-2-jstart)*(p-2-kstart));
371: Nwire = 4*((m-2-istart) + (n-2-jstart) + (p-2-kstart)) + 8;
372: Nsurf = Nface + Nwire;
373: MatCreateSeqDense(MPI_COMM_SELF,Nint,6,NULL,&Xint);
374: MatCreateSeqDense(MPI_COMM_SELF,Nsurf,6,NULL,&Xsurf);
375: MatDenseGetArray(Xsurf,&xsurf);
377: /*
378: Require that all 12 edges and 6 faces have at least one grid point. Otherwise some of the columns of
379: Xsurf will be all zero (thus making the coarse matrix singular).
380: */
381: 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");
382: 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");
383: 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");
385: cnt = 0;
386: for (j=1; j<n-1-jstart; j++) {
387: for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 0*Nsurf] = 1;
388: }
390: for (k=1; k<p-1-kstart; k++) {
391: for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 1*Nsurf] = 1;
392: for (j=1; j<n-1-jstart; j++) {
393: xsurf[cnt++ + 2*Nsurf] = 1;
394: /* these are the interior nodes */
395: xsurf[cnt++ + 3*Nsurf] = 1;
396: }
397: for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 4*Nsurf] = 1;
398: }
399: for (j=1;j<n-1-jstart;j++) {
400: for (i=1; i<m-istart-1; i++) xsurf[cnt++ + 5*Nsurf] = 1;
401: }
403: #if defined(PETSC_USE_DEBUG_foo)
404: for (i=0; i<Nsurf; i++) {
405: tmp = 0.0;
406: for (j=0; j<6; j++) tmp += xsurf[i+j*Nsurf];
408: 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));
409: }
410: #endif
411: MatDenseRestoreArray(Xsurf,&xsurf);
412: /* MatView(Xsurf,PETSC_VIEWER_STDOUT_WORLD);*/
415: /*
416: I are the indices for all the needed vertices (in global numbering)
417: Iint are the indices for the interior values, I surf for the surface values
418: (This is just for the part of the global matrix obtained with MatCreateSubMatrix(), it
419: is NOT the local DMDA ordering.)
420: IIint and IIsurf are the same as the Iint, Isurf except they are in the global numbering
421: */
422: #define Endpoint(a,start,b) (a == 0 || a == (b-1-start))
423: PetscMalloc3(N,&II,Nint,&Iint,Nsurf,&Isurf);
424: PetscMalloc2(Nint,&IIint,Nsurf,&IIsurf);
425: for (k=0; k<p-kstart; k++) {
426: for (j=0; j<n-jstart; j++) {
427: for (i=0; i<m-istart; i++) {
428: II[c++] = i + j*mwidth + k*mwidth*nwidth;
430: if (!Endpoint(i,istart,m) && !Endpoint(j,jstart,n) && !Endpoint(k,kstart,p)) {
431: IIint[cint] = i + j*mwidth + k*mwidth*nwidth;
432: Iint[cint++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
433: } else {
434: IIsurf[csurf] = i + j*mwidth + k*mwidth*nwidth;
435: Isurf[csurf++] = i + j*(m-istart) + k*(m-istart)*(n-jstart);
436: }
437: }
438: }
439: }
440: if (c != N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"c != N");
441: if (cint != Nint) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"cint != Nint");
442: if (csurf != Nsurf) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"csurf != Nsurf");
443: DMGetLocalToGlobalMapping(da,<g);
444: ISLocalToGlobalMappingApply(ltg,N,II,II);
445: ISLocalToGlobalMappingApply(ltg,Nint,IIint,IIint);
446: ISLocalToGlobalMappingApply(ltg,Nsurf,IIsurf,IIsurf);
447: PetscObjectGetComm((PetscObject)da,&comm);
448: ISCreateGeneral(comm,N,II,PETSC_COPY_VALUES,&is);
449: ISCreateGeneral(PETSC_COMM_SELF,Nint,Iint,PETSC_COPY_VALUES,&isint);
450: ISCreateGeneral(PETSC_COMM_SELF,Nsurf,Isurf,PETSC_COPY_VALUES,&issurf);
451: PetscFree3(II,Iint,Isurf);
453: ISSort(is);
454: MatCreateSubMatrices(Aglobal,1,&is,&is,MAT_INITIAL_MATRIX,&Aholder);
455: A = *Aholder;
456: PetscFree(Aholder);
458: MatCreateSubMatrix(A,isint,isint,MAT_INITIAL_MATRIX,&Aii);
459: MatCreateSubMatrix(A,isint,issurf,MAT_INITIAL_MATRIX,&Ais);
460: MatCreateSubMatrix(A,issurf,isint,MAT_INITIAL_MATRIX,&Asi);
462: /*
463: Solve for the interpolation onto the interior Xint
464: */
465: MatMatMult(Ais,Xsurf,MAT_INITIAL_MATRIX,PETSC_DETERMINE,&Xint_tmp);
466: MatScale(Xint_tmp,-1.0);
468: if (exotic->directSolve) {
469: MatGetFactor(Aii,MATSOLVERPETSC,MAT_FACTOR_LU,&iAii);
470: MatFactorInfoInitialize(&info);
471: MatGetOrdering(Aii,MATORDERINGND,&row,&col);
472: MatLUFactorSymbolic(iAii,Aii,row,col,&info);
473: ISDestroy(&row);
474: ISDestroy(&col);
475: MatLUFactorNumeric(iAii,Aii,&info);
476: MatMatSolve(iAii,Xint_tmp,Xint);
477: MatDestroy(&iAii);
478: } else {
479: Vec b,x;
480: PetscScalar *xint_tmp;
482: MatDenseGetArray(Xint,&xint);
483: VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&x);
484: MatDenseGetArray(Xint_tmp,&xint_tmp);
485: VecCreateSeqWithArray(PETSC_COMM_SELF,1,Nint,0,&b);
486: KSPSetOperators(exotic->ksp,Aii,Aii);
487: for (i=0; i<6; i++) {
488: VecPlaceArray(x,xint+i*Nint);
489: VecPlaceArray(b,xint_tmp+i*Nint);
490: KSPSolve(exotic->ksp,b,x);
491: VecResetArray(x);
492: VecResetArray(b);
493: }
494: MatDenseRestoreArray(Xint,&xint);
495: MatDenseRestoreArray(Xint_tmp,&xint_tmp);
496: VecDestroy(&x);
497: VecDestroy(&b);
498: }
499: MatDestroy(&Xint_tmp);
501: #if defined(PETSC_USE_DEBUG_foo)
502: MatDenseGetArray(Xint,&xint);
503: for (i=0; i<Nint; i++) {
504: tmp = 0.0;
505: for (j=0; j<6; j++) tmp += xint[i+j*Nint];
507: 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));
508: }
509: MatDenseRestoreArray(Xint,&xint);
510: /* ierr =MatView(Xint,PETSC_VIEWER_STDOUT_WORLD); */
511: #endif
514: /* total faces */
515: Ntotal = mp*np*(pp+1) + mp*pp*(np+1) + np*pp*(mp+1);
517: /*
518: For each vertex, edge, face on process (in the same orderings as used above) determine its local number including ghost points
519: */
520: cnt = 0;
521: { gl[cnt++] = mwidth+1;}
522: {
523: { gl[cnt++] = mwidth*nwidth+1;}
524: { gl[cnt++] = mwidth*nwidth + mwidth; /* these are the interior nodes */ gl[cnt++] = mwidth*nwidth + mwidth+m-istart-1;}
525: { gl[cnt++] = mwidth*nwidth+mwidth*(n-jstart-1)+1;}
526: }
527: { gl[cnt++] = mwidth*nwidth*(p-kstart-1) + mwidth+1;}
529: /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
530: /* convert that to global numbering and get them on all processes */
531: ISLocalToGlobalMappingApply(ltg,6,gl,gl);
532: /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
533: PetscMalloc1(6*mp*np*pp,&globals);
534: MPI_Allgather(gl,6,MPIU_INT,globals,6,MPIU_INT,PetscObjectComm((PetscObject)da));
536: /* Number the coarse grid points from 0 to Ntotal */
537: MatGetSize(Aglobal,&Nt,NULL);
538: PetscTableCreate(Ntotal/3,Nt+1,&ht);
539: for (i=0; i<6*mp*np*pp; i++) {
540: PetscTableAddCount(ht,globals[i]+1);
541: }
542: PetscTableGetCount(ht,&cnt);
543: 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);
544: PetscFree(globals);
545: for (i=0; i<6; i++) {
546: PetscTableFind(ht,gl[i]+1,&gl[i]);
547: gl[i]--;
548: }
549: PetscTableDestroy(&ht);
550: /* PetscIntView(6,gl,PETSC_VIEWER_STDOUT_WORLD); */
552: /* construct global interpolation matrix */
553: MatGetLocalSize(Aglobal,&Ng,NULL);
554: if (reuse == MAT_INITIAL_MATRIX) {
555: MatCreateAIJ(PetscObjectComm((PetscObject)da),Ng,PETSC_DECIDE,PETSC_DECIDE,Ntotal,Nint+Nsurf,NULL,Nint,NULL,P);
556: } else {
557: MatZeroEntries(*P);
558: }
559: MatSetOption(*P,MAT_ROW_ORIENTED,PETSC_FALSE);
560: MatDenseGetArray(Xint,&xint);
561: MatSetValues(*P,Nint,IIint,6,gl,xint,INSERT_VALUES);
562: MatDenseRestoreArray(Xint,&xint);
563: MatDenseGetArray(Xsurf,&xsurf);
564: MatSetValues(*P,Nsurf,IIsurf,6,gl,xsurf,INSERT_VALUES);
565: MatDenseRestoreArray(Xsurf,&xsurf);
566: MatAssemblyBegin(*P,MAT_FINAL_ASSEMBLY);
567: MatAssemblyEnd(*P,MAT_FINAL_ASSEMBLY);
568: PetscFree2(IIint,IIsurf);
571: #if defined(PETSC_USE_DEBUG_foo)
572: {
573: Vec x,y;
574: PetscScalar *yy;
575: VecCreateMPI(PetscObjectComm((PetscObject)da),Ng,PETSC_DETERMINE,&y);
576: VecCreateMPI(PetscObjectComm((PetscObject)da),PETSC_DETERMINE,Ntotal,&x);
577: VecSet(x,1.0);
578: MatMult(*P,x,y);
579: VecGetArray(y,&yy);
580: for (i=0; i<Ng; i++) {
581: 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]));
582: }
583: VecRestoreArray(y,&yy);
584: VecDestroy(x);
585: VecDestroy(y);
586: }
587: #endif
589: MatDestroy(&Aii);
590: MatDestroy(&Ais);
591: MatDestroy(&Asi);
592: MatDestroy(&A);
593: ISDestroy(&is);
594: ISDestroy(&isint);
595: ISDestroy(&issurf);
596: MatDestroy(&Xint);
597: MatDestroy(&Xsurf);
598: return(0);
599: }
602: /*@
603: PCExoticSetType - Sets the type of coarse grid interpolation to use
605: Logically Collective on PC
607: Input Parameters:
608: + pc - the preconditioner context
609: - type - either PC_EXOTIC_FACE or PC_EXOTIC_WIREBASKET (defaults to face)
611: Notes: The face based interpolation has 1 degree of freedom per face and ignores the
612: edge and vertex values completely in the coarse problem. For any seven point
613: stencil the interpolation of a constant on all faces into the interior is that constant.
615: The wirebasket interpolation has 1 degree of freedom per vertex, per edge and
616: per face. A constant on the subdomain boundary is interpolated as that constant
617: in the interior of the domain.
619: The coarse grid matrix is obtained via the Galerkin computation A_c = R A R^T, hence
620: if A is nonsingular A_c is also nonsingular.
622: Both interpolations are suitable for only scalar problems.
624: Level: intermediate
627: .seealso: PCEXOTIC, PCExoticType()
628: @*/
629: PetscErrorCode PCExoticSetType(PC pc,PCExoticType type)
630: {
636: PetscTryMethod(pc,"PCExoticSetType_C",(PC,PCExoticType),(pc,type));
637: return(0);
638: }
640: static PetscErrorCode PCExoticSetType_Exotic(PC pc,PCExoticType type)
641: {
642: PC_MG *mg = (PC_MG*)pc->data;
643: PC_Exotic *ctx = (PC_Exotic*) mg->innerctx;
646: ctx->type = type;
647: return(0);
648: }
650: PetscErrorCode PCSetUp_Exotic(PC pc)
651: {
653: Mat A;
654: PC_MG *mg = (PC_MG*)pc->data;
655: PC_Exotic *ex = (PC_Exotic*) mg->innerctx;
656: MatReuse reuse = (ex->P) ? MAT_REUSE_MATRIX : MAT_INITIAL_MATRIX;
659: if (!pc->dm) SETERRQ(PetscObjectComm((PetscObject)pc),PETSC_ERR_ARG_WRONGSTATE,"Need to call PCSetDM() before using this PC");
660: PCGetOperators(pc,NULL,&A);
661: if (ex->type == PC_EXOTIC_FACE) {
662: DMDAGetFaceInterpolation(pc->dm,ex,A,reuse,&ex->P);
663: } else if (ex->type == PC_EXOTIC_WIREBASKET) {
664: DMDAGetWireBasketInterpolation(pc->dm,ex,A,reuse,&ex->P);
665: } else SETERRQ1(PetscObjectComm((PetscObject)pc),PETSC_ERR_PLIB,"Unknown exotic coarse space %d",ex->type);
666: PCMGSetInterpolation(pc,1,ex->P);
667: /* if PC has attached DM we must remove it or the PCMG will use it to compute incorrect sized vectors and interpolations */
668: PCSetDM(pc,NULL);
669: PCSetUp_MG(pc);
670: return(0);
671: }
673: PetscErrorCode PCDestroy_Exotic(PC pc)
674: {
676: PC_MG *mg = (PC_MG*)pc->data;
677: PC_Exotic *ctx = (PC_Exotic*) mg->innerctx;
680: MatDestroy(&ctx->P);
681: KSPDestroy(&ctx->ksp);
682: PetscFree(ctx);
683: PCDestroy_MG(pc);
684: return(0);
685: }
687: PetscErrorCode PCView_Exotic(PC pc,PetscViewer viewer)
688: {
689: PC_MG *mg = (PC_MG*)pc->data;
691: PetscBool iascii;
692: PC_Exotic *ctx = (PC_Exotic*) mg->innerctx;
695: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
696: if (iascii) {
697: PetscViewerASCIIPrintf(viewer," Exotic type = %s\n",PCExoticTypes[ctx->type]);
698: if (ctx->directSolve) {
699: PetscViewerASCIIPrintf(viewer," Using direct solver to construct interpolation\n");
700: } else {
701: PetscViewer sviewer;
702: PetscMPIInt rank;
704: PetscViewerASCIIPrintf(viewer," Using iterative solver to construct interpolation\n");
705: PetscViewerASCIIPushTab(viewer);
706: PetscViewerASCIIPushTab(viewer); /* should not need to push this twice? */
707: PetscViewerGetSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
708: MPI_Comm_rank(PetscObjectComm((PetscObject)pc),&rank);
709: if (!rank) {
710: KSPView(ctx->ksp,sviewer);
711: }
712: PetscViewerRestoreSubViewer(viewer,PETSC_COMM_SELF,&sviewer);
713: PetscViewerASCIIPopTab(viewer);
714: PetscViewerASCIIPopTab(viewer);
715: }
716: }
717: PCView_MG(pc,viewer);
718: return(0);
719: }
721: PetscErrorCode PCSetFromOptions_Exotic(PetscOptionItems *PetscOptionsObject,PC pc)
722: {
724: PetscBool flg;
725: PC_MG *mg = (PC_MG*)pc->data;
726: PCExoticType mgctype;
727: PC_Exotic *ctx = (PC_Exotic*) mg->innerctx;
730: PetscOptionsHead(PetscOptionsObject,"Exotic coarse space options");
731: PetscOptionsEnum("-pc_exotic_type","face or wirebasket","PCExoticSetType",PCExoticTypes,(PetscEnum)ctx->type,(PetscEnum*)&mgctype,&flg);
732: if (flg) {
733: PCExoticSetType(pc,mgctype);
734: }
735: PetscOptionsBool("-pc_exotic_direct_solver","use direct solver to construct interpolation","None",ctx->directSolve,&ctx->directSolve,NULL);
736: if (!ctx->directSolve) {
737: if (!ctx->ksp) {
738: const char *prefix;
739: KSPCreate(PETSC_COMM_SELF,&ctx->ksp);
740: KSPSetErrorIfNotConverged(ctx->ksp,pc->erroriffailure);
741: PetscObjectIncrementTabLevel((PetscObject)ctx->ksp,(PetscObject)pc,1);
742: PetscLogObjectParent((PetscObject)pc,(PetscObject)ctx->ksp);
743: PCGetOptionsPrefix(pc,&prefix);
744: KSPSetOptionsPrefix(ctx->ksp,prefix);
745: KSPAppendOptionsPrefix(ctx->ksp,"exotic_");
746: }
747: KSPSetFromOptions(ctx->ksp);
748: }
749: PetscOptionsTail();
750: return(0);
751: }
754: /*MC
755: PCEXOTIC - Two level overlapping Schwarz preconditioner with exotic (non-standard) coarse grid spaces
757: This uses the PCMG infrastructure restricted to two levels and the face and wirebasket based coarse
758: grid spaces.
760: 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
762: References:
763: + 1. - These coarse grid spaces originate in the work of Bramble, Pasciak and Schatz, "The Construction
764: of Preconditioners for Elliptic Problems by Substructing IV", Mathematics of Computation, volume 53, 1989.
765: . 2. - They were generalized slightly in "Domain Decomposition Method for Linear Elasticity", Ph. D. thesis, Barry Smith,
766: New York University, 1990.
767: . 3. - They were then explored in great detail in Dryja, Smith, Widlund, "Schwarz Analysis
768: of Iterative Substructuring Methods for Elliptic Problems in Three Dimensions, SIAM Journal on Numerical
769: Analysis, volume 31. 1994. These were developed in the context of iterative substructuring preconditioners.
770: . 4. - They were then ingeniously applied as coarse grid spaces for overlapping Schwarz methods by Dohrmann and Widlund.
771: They refer to them as GDSW (generalized Dryja, Smith, Widlund preconditioners). See, for example,
772: Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Extending theory for domain decomposition algorithms to irregular subdomains. In Ulrich Langer, Marco
773: Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings
774: of the 17th International Conference on Domain Decomposition Methods in
775: Science and Engineering, held in Strobl, Austria, 2006, number 60 in
776: Springer Verlag, Lecture Notes in Computational Science and Engineering, 2007.
777: . 5. - Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. A family of energy minimizing coarse spaces for overlapping Schwarz preconditioners. In Ulrich Langer,
778: Marco Discacciati, David Keyes, Olof Widlund, and Walter Zulehner, editors, Proceedings
779: of the 17th International Conference on Domain Decomposition Methods
780: in Science and Engineering, held in Strobl, Austria, 2006, number 60 in
781: Springer Verlag, Lecture Notes in Computational Science and Engineering, 2007
782: . 6. - Clark R. Dohrmann, Axel Klawonn, and Olof B. Widlund. Domain decomposition
783: for less regular subdomains: Overlapping Schwarz in two dimensions. SIAM J.
784: Numer. Anal., 46(4), 2008.
785: - 7. - Clark R. Dohrmann and Olof B. Widlund. An overlapping Schwarz
786: algorithm for almost incompressible elasticity. Technical Report
787: TR2008 912, Department of Computer Science, Courant Institute
788: of Mathematical Sciences, New York University, May 2008. URL:
790: Options Database: The usual PCMG options are supported, such as -mg_levels_pc_type <type> -mg_coarse_pc_type <type>
791: -pc_mg_type <type>
793: Level: advanced
795: .seealso: PCMG, PCSetDM(), PCExoticType, PCExoticSetType()
796: M*/
798: PETSC_EXTERN PetscErrorCode PCCreate_Exotic(PC pc)
799: {
801: PC_Exotic *ex;
802: PC_MG *mg;
805: /* if type was previously mg; must manually destroy it because call to PCSetType(pc,PCMG) will not destroy it */
806: if (pc->ops->destroy) {
807: (*pc->ops->destroy)(pc);
808: pc->data = 0;
809: }
810: PetscFree(((PetscObject)pc)->type_name);
811: ((PetscObject)pc)->type_name = 0;
813: PCSetType(pc,PCMG);
814: PCMGSetLevels(pc,2,NULL);
815: PCMGSetGalerkin(pc,PC_MG_GALERKIN_PMAT);
816: PetscNew(&ex); \
817: ex->type = PC_EXOTIC_FACE;
818: mg = (PC_MG*) pc->data;
819: mg->innerctx = ex;
822: pc->ops->setfromoptions = PCSetFromOptions_Exotic;
823: pc->ops->view = PCView_Exotic;
824: pc->ops->destroy = PCDestroy_Exotic;
825: pc->ops->setup = PCSetUp_Exotic;
827: PetscObjectComposeFunction((PetscObject)pc,"PCExoticSetType_C",PCExoticSetType_Exotic);
828: return(0);
829: }