xref: /petsc/src/dm/impls/da/dainterp.c (revision 3564f093082c4e39e657fbd7ab2e39df4067bb32)
1 
2 /*
3   Code for interpolating between grids represented by DMDAs
4 */
5 
6 #include <private/daimpl.h>    /*I   "petscdmda.h"   I*/
7 #include <petscpcmg.h>
8 
9 #undef __FUNCT__
10 #define __FUNCT__ "DMGetInterpolationScale"
11 /*@
12     DMGetInterpolationScale - Forms L = R*1/diag(R*1) - L.*v is like a coarse grid average of the
13       nearby fine grid points.
14 
15   Input Parameters:
16 +      dac - DM that defines a coarse mesh
17 .      daf - DM that defines a fine mesh
18 -      mat - the restriction (or interpolation operator) from fine to coarse
19 
20   Output Parameter:
21 .    scale - the scaled vector
22 
23   Level: developer
24 
25 .seealso: DMGetInterpolation()
26 
27 @*/
28 PetscErrorCode  DMGetInterpolationScale(DM dac,DM daf,Mat mat,Vec *scale)
29 {
30   PetscErrorCode ierr;
31   Vec            fine;
32   PetscScalar    one = 1.0;
33 
34   PetscFunctionBegin;
35   ierr = DMCreateGlobalVector(daf,&fine);CHKERRQ(ierr);
36   ierr = DMCreateGlobalVector(dac,scale);CHKERRQ(ierr);
37   ierr = VecSet(fine,one);CHKERRQ(ierr);
38   ierr = MatRestrict(mat,fine,*scale);CHKERRQ(ierr);
39   ierr = VecDestroy(&fine);CHKERRQ(ierr);
40   ierr = VecReciprocal(*scale);CHKERRQ(ierr);
41   PetscFunctionReturn(0);
42 }
43 
44 #undef __FUNCT__
45 #define __FUNCT__ "DMGetInterpolation_DA_1D_Q1"
46 PetscErrorCode DMGetInterpolation_DA_1D_Q1(DM dac,DM daf,Mat *A)
47 {
48   PetscErrorCode   ierr;
49   PetscInt         i,i_start,m_f,Mx,*idx_f;
50   PetscInt         m_ghost,*idx_c,m_ghost_c;
51   PetscInt         row,col,i_start_ghost,mx,m_c,nc,ratio;
52   PetscInt         i_c,i_start_c,i_start_ghost_c,cols[2],dof;
53   PetscScalar      v[2],x,*coors = 0,*ccoors;
54   Mat              mat;
55   DMDABoundaryType bx;
56   Vec              vcoors,cvcoors;
57   DM_DA            *ddc = (DM_DA*)dac->data, *ddf = (DM_DA*)daf->data;
58 
59   PetscFunctionBegin;
60   ierr = DMDAGetInfo(dac,0,&Mx,0,0,0,0,0,0,0,&bx,0,0,0);CHKERRQ(ierr);
61   ierr = DMDAGetInfo(daf,0,&mx,0,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
62   if (bx == DMDA_BOUNDARY_PERIODIC){
63     ratio = mx/Mx;
64     if (ratio*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
65   } else {
66     ratio = (mx-1)/(Mx-1);
67     if (ratio*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
68   }
69 
70   ierr = DMDAGetCorners(daf,&i_start,0,0,&m_f,0,0);CHKERRQ(ierr);
71   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,0,0,&m_ghost,0,0);CHKERRQ(ierr);
72   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
73 
74   ierr = DMDAGetCorners(dac,&i_start_c,0,0,&m_c,0,0);CHKERRQ(ierr);
75   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,0,0,&m_ghost_c,0,0);CHKERRQ(ierr);
76   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
77 
78   /* create interpolation matrix */
79   ierr = MatCreate(((PetscObject)dac)->comm,&mat);CHKERRQ(ierr);
80   ierr = MatSetSizes(mat,m_f,m_c,mx,Mx);CHKERRQ(ierr);
81   ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
82   ierr = MatSeqAIJSetPreallocation(mat,2,PETSC_NULL);CHKERRQ(ierr);
83   ierr = MatMPIAIJSetPreallocation(mat,2,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
84 
85   ierr = DMDAGetCoordinates(daf,&vcoors);CHKERRQ(ierr);
86   if (vcoors) {
87     ierr = DMDAGetGhostedCoordinates(dac,&cvcoors);CHKERRQ(ierr);
88     ierr = DMDAVecGetArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
89     ierr = DMDAVecGetArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
90   }
91   /* loop over local fine grid nodes setting interpolation for those*/
92   if (!vcoors) {
93 
94     for (i=i_start; i<i_start+m_f; i++) {
95       /* convert to local "natural" numbering and then to PETSc global numbering */
96       row    = idx_f[dof*(i-i_start_ghost)]/dof;
97 
98       i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
99       if (i_c < i_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
100                                           i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
101 
102       /*
103        Only include those interpolation points that are truly
104        nonzero. Note this is very important for final grid lines
105        in x direction; since they have no right neighbor
106        */
107       x  = ((double)(i - i_c*ratio))/((double)ratio);
108       nc = 0;
109       /* one left and below; or we are right on it */
110       col      = dof*(i_c-i_start_ghost_c);
111       cols[nc] = idx_c[col]/dof;
112       v[nc++]  = - x + 1.0;
113       /* one right? */
114       if (i_c*ratio != i) {
115         cols[nc] = idx_c[col+dof]/dof;
116         v[nc++]  = x;
117       }
118       ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr);
119     }
120 
121   } else {
122     PetscScalar    *xi;
123     PetscInt       li,nxi,n;
124     PetscScalar    Ni[2];
125 
126     /* compute local coordinate arrays */
127     nxi   = ratio + 1;
128     ierr = PetscMalloc(sizeof(PetscScalar)*nxi,&xi);CHKERRQ(ierr);
129     for (li=0; li<nxi; li++) {
130       xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
131     }
132 
133     for (i=i_start; i<i_start+m_f; i++) {
134       /* convert to local "natural" numbering and then to PETSc global numbering */
135       row    = idx_f[dof*(i-i_start_ghost)]/dof;
136 
137       i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
138       if (i_c < i_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
139                                           i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
140 
141       /* remainders */
142       li = i - ratio * (i/ratio);
143       if (i==mx-1){ li = nxi-1; }
144 
145       /* corners */
146       col     = dof*(i_c-i_start_ghost_c);
147       cols[0] = idx_c[col]/dof;
148       Ni[0]   = 1.0;
149       if ( (li==0) || (li==nxi-1) ) {
150         ierr = MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);CHKERRQ(ierr);
151         continue;
152       }
153 
154       /* edges + interior */
155       /* remainders */
156       if (i==mx-1){ i_c--; }
157 
158       col     = dof*(i_c-i_start_ghost_c);
159       cols[0] = idx_c[col]/dof; /* one left and below; or we are right on it */
160       cols[1] = idx_c[col+dof]/dof;
161 
162       Ni[0] = 0.5*(1.0-xi[li]);
163       Ni[1] = 0.5*(1.0+xi[li]);
164       for (n=0; n<2; n++) {
165         if( PetscAbsScalar(Ni[n])<1.0e-32) { cols[n]=-1; }
166       }
167       ierr = MatSetValues(mat,1,&row,2,cols,Ni,INSERT_VALUES);CHKERRQ(ierr);
168     }
169     ierr = PetscFree(xi);CHKERRQ(ierr);
170   }
171   if (vcoors) {
172     ierr = DMDAVecRestoreArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
173     ierr = DMDAVecRestoreArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
174   }
175   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
176   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
177   ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
178   ierr = MatDestroy(&mat);CHKERRQ(ierr);
179   PetscFunctionReturn(0);
180 }
181 
182 #undef __FUNCT__
183 #define __FUNCT__ "DMGetInterpolation_DA_1D_Q0"
184 PetscErrorCode DMGetInterpolation_DA_1D_Q0(DM dac,DM daf,Mat *A)
185 {
186   PetscErrorCode   ierr;
187   PetscInt         i,i_start,m_f,Mx,*idx_f;
188   PetscInt         m_ghost,*idx_c,m_ghost_c;
189   PetscInt         row,col,i_start_ghost,mx,m_c,nc,ratio;
190   PetscInt         i_c,i_start_c,i_start_ghost_c,cols[2],dof;
191   PetscScalar      v[2],x;
192   Mat              mat;
193   DMDABoundaryType bx;
194 
195   PetscFunctionBegin;
196   ierr = DMDAGetInfo(dac,0,&Mx,0,0,0,0,0,0,0,&bx,0,0,0);CHKERRQ(ierr);
197   ierr = DMDAGetInfo(daf,0,&mx,0,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
198   if (bx == DMDA_BOUNDARY_PERIODIC){
199     ratio = mx/Mx;
200     if (ratio*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
201   } else {
202     ratio = (mx-1)/(Mx-1);
203     if (ratio*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
204   }
205 
206   ierr = DMDAGetCorners(daf,&i_start,0,0,&m_f,0,0);CHKERRQ(ierr);
207   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,0,0,&m_ghost,0,0);CHKERRQ(ierr);
208   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
209 
210   ierr = DMDAGetCorners(dac,&i_start_c,0,0,&m_c,0,0);CHKERRQ(ierr);
211   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,0,0,&m_ghost_c,0,0);CHKERRQ(ierr);
212   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
213 
214   /* create interpolation matrix */
215   ierr = MatCreate(((PetscObject)dac)->comm,&mat);CHKERRQ(ierr);
216   ierr = MatSetSizes(mat,m_f,m_c,mx,Mx);CHKERRQ(ierr);
217   ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
218   ierr = MatSeqAIJSetPreallocation(mat,2,PETSC_NULL);CHKERRQ(ierr);
219   ierr = MatMPIAIJSetPreallocation(mat,2,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
220 
221   /* loop over local fine grid nodes setting interpolation for those*/
222   for (i=i_start; i<i_start+m_f; i++) {
223     /* convert to local "natural" numbering and then to PETSc global numbering */
224     row    = idx_f[dof*(i-i_start_ghost)]/dof;
225 
226     i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
227 
228     /*
229          Only include those interpolation points that are truly
230          nonzero. Note this is very important for final grid lines
231          in x direction; since they have no right neighbor
232     */
233     x  = ((double)(i - i_c*ratio))/((double)ratio);
234     nc = 0;
235       /* one left and below; or we are right on it */
236     col      = dof*(i_c-i_start_ghost_c);
237     cols[nc] = idx_c[col]/dof;
238     v[nc++]  = - x + 1.0;
239     /* one right? */
240     if (i_c*ratio != i) {
241       cols[nc] = idx_c[col+dof]/dof;
242       v[nc++]  = x;
243     }
244     ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr);
245   }
246   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
247   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
248   ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
249   ierr = MatDestroy(&mat);CHKERRQ(ierr);
250   ierr = PetscLogFlops(5.0*m_f);CHKERRQ(ierr);
251   PetscFunctionReturn(0);
252 }
253 
254 #undef __FUNCT__
255 #define __FUNCT__ "DMGetInterpolation_DA_2D_Q1"
256 PetscErrorCode DMGetInterpolation_DA_2D_Q1(DM dac,DM daf,Mat *A)
257 {
258   PetscErrorCode   ierr;
259   PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof;
260   PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,*dnz,*onz;
261   PetscInt         row,col,i_start_ghost,j_start_ghost,cols[4],mx,m_c,my,nc,ratioi,ratioj;
262   PetscInt         i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c,col_shift,col_scale;
263   PetscMPIInt      size_c,size_f,rank_f;
264   PetscScalar      v[4],x,y;
265   Mat              mat;
266   DMDABoundaryType bx,by;
267   DMDACoor2d       **coors = 0,**ccoors;
268   Vec              vcoors,cvcoors;
269   DM_DA            *ddc = (DM_DA*)dac->data, *ddf = (DM_DA*)daf->data;
270 
271   PetscFunctionBegin;
272   ierr = DMDAGetInfo(dac,0,&Mx,&My,0,0,0,0,0,0,&bx,&by,0,0);CHKERRQ(ierr);
273   ierr = DMDAGetInfo(daf,0,&mx,&my,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
274   if (bx == DMDA_BOUNDARY_PERIODIC){
275     ratioi = mx/Mx;
276     if (ratioi*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
277   } else {
278     ratioi = (mx-1)/(Mx-1);
279     if (ratioi*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
280   }
281   if (by == DMDA_BOUNDARY_PERIODIC){
282     ratioj = my/My;
283     if (ratioj*My != my) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: my/My  must be integer: my %D My %D",my,My);
284   } else {
285     ratioj = (my-1)/(My-1);
286     if (ratioj*(My-1) != my-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (my - 1)/(My - 1) must be integer: my %D My %D",my,My);
287   }
288 
289 
290   ierr = DMDAGetCorners(daf,&i_start,&j_start,0,&m_f,&n_f,0);CHKERRQ(ierr);
291   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);CHKERRQ(ierr);
292   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
293 
294   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,0,&m_c,&n_c,0);CHKERRQ(ierr);
295   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);CHKERRQ(ierr);
296   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
297 
298   /*
299    Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
300    The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the
301    processors). It's effective length is hence 4 times its normal length, this is
302    why the col_scale is multiplied by the interpolation matrix column sizes.
303    sol_shift allows each set of 1/4 processors do its own interpolation using ITS
304    copy of the coarse vector. A bit of a hack but you do better.
305 
306    In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
307    */
308   ierr = MPI_Comm_size(((PetscObject)dac)->comm,&size_c);CHKERRQ(ierr);
309   ierr = MPI_Comm_size(((PetscObject)daf)->comm,&size_f);CHKERRQ(ierr);
310   ierr = MPI_Comm_rank(((PetscObject)daf)->comm,&rank_f);CHKERRQ(ierr);
311   col_scale = size_f/size_c;
312   col_shift = Mx*My*(rank_f/size_c);
313 
314   ierr = MatPreallocateInitialize(((PetscObject)daf)->comm,m_f*n_f,col_scale*m_c*n_c,dnz,onz);CHKERRQ(ierr);
315   for (j=j_start; j<j_start+n_f; j++) {
316     for (i=i_start; i<i_start+m_f; i++) {
317       /* convert to local "natural" numbering and then to PETSc global numbering */
318       row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
319 
320       i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
321       j_c = (j/ratioj);    /* coarse grid node below fine grid node */
322 
323       if (j_c < j_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
324                                           j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
325       if (i_c < i_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
326                                           i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
327 
328       /*
329        Only include those interpolation points that are truly
330        nonzero. Note this is very important for final grid lines
331        in x and y directions; since they have no right/top neighbors
332        */
333       nc = 0;
334       /* one left and below; or we are right on it */
335       col        = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
336       cols[nc++] = col_shift + idx_c[col]/dof;
337       /* one right and below */
338       if (i_c*ratioi != i) {
339         cols[nc++] = col_shift + idx_c[col+dof]/dof;
340       }
341       /* one left and above */
342       if (j_c*ratioj != j) {
343         cols[nc++] = col_shift + idx_c[col+m_ghost_c*dof]/dof;
344       }
345       /* one right and above */
346       if (i_c*ratioi != i && j_c*ratioj != j) {
347         cols[nc++] = col_shift + idx_c[col+(m_ghost_c+1)*dof]/dof;
348       }
349       ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
350     }
351   }
352   ierr = MatCreate(((PetscObject)daf)->comm,&mat);CHKERRQ(ierr);
353   ierr = MatSetSizes(mat,m_f*n_f,col_scale*m_c*n_c,mx*my,col_scale*Mx*My);CHKERRQ(ierr);
354   ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
355   ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
356   ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
357   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
358 
359   ierr = DMDAGetCoordinates(daf,&vcoors);CHKERRQ(ierr);
360   if (vcoors) {
361     ierr = DMDAGetGhostedCoordinates(dac,&cvcoors);CHKERRQ(ierr);
362     ierr = DMDAVecGetArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
363     ierr = DMDAVecGetArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
364   }
365 
366   /* loop over local fine grid nodes setting interpolation for those*/
367   // if (!vcoors) {
368   if (1) {
369 
370     for (j=j_start; j<j_start+n_f; j++) {
371       for (i=i_start; i<i_start+m_f; i++) {
372         /* convert to local "natural" numbering and then to PETSc global numbering */
373         row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
374 
375         i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
376         j_c = (j/ratioj);    /* coarse grid node below fine grid node */
377 
378         /*
379          Only include those interpolation points that are truly
380          nonzero. Note this is very important for final grid lines
381          in x and y directions; since they have no right/top neighbors
382          */
383         x  = ((double)(i - i_c*ratioi))/((double)ratioi);
384         y  = ((double)(j - j_c*ratioj))/((double)ratioj);
385 
386         nc = 0;
387         /* one left and below; or we are right on it */
388         col      = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
389         cols[nc] = col_shift + idx_c[col]/dof;
390         v[nc++]  = x*y - x - y + 1.0;
391         /* one right and below */
392         if (i_c*ratioi != i) {
393           cols[nc] = col_shift + idx_c[col+dof]/dof;
394           v[nc++]  = -x*y + x;
395         }
396         /* one left and above */
397         if (j_c*ratioj != j) {
398           cols[nc] = col_shift + idx_c[col+m_ghost_c*dof]/dof;
399           v[nc++]  = -x*y + y;
400         }
401         /* one right and above */
402         if (j_c*ratioj != j && i_c*ratioi != i) {
403           cols[nc] = col_shift + idx_c[col+(m_ghost_c+1)*dof]/dof;
404           v[nc++]  = x*y;
405         }
406         ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr);
407       }
408     }
409 
410   } else {
411     PetscScalar    Ni[4];
412     PetscScalar    *xi,*eta;
413     PetscInt       li,nxi,lj,neta;
414 
415     /* compute local coordinate arrays */
416     nxi  = ratioi + 1;
417     neta = ratioj + 1;
418     ierr = PetscMalloc(sizeof(PetscScalar)*nxi,&xi);CHKERRQ(ierr);
419     ierr = PetscMalloc(sizeof(PetscScalar)*neta,&eta);CHKERRQ(ierr);
420     for (li=0; li<nxi; li++) {
421       xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
422     }
423     for (lj=0; lj<neta; lj++) {
424       eta[lj] = -1.0 + (PetscScalar)lj*(2.0/(PetscScalar)(neta-1));
425     }
426 
427     /* loop over local fine grid nodes setting interpolation for those*/
428     for (j=j_start; j<j_start+n_f; j++) {
429       for (i=i_start; i<i_start+m_f; i++) {
430         /* convert to local "natural" numbering and then to PETSc global numbering */
431         row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
432 
433         i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
434         j_c = (j/ratioj);    /* coarse grid node below fine grid node */
435 
436         /* remainders */
437         li = i - ratioi * (i/ratioi);
438         if (i==mx-1){ li = nxi-1; }
439         lj = j - ratioj * (j/ratioj);
440         if (j==my-1){ lj = neta-1; }
441 
442         /* corners */
443         col     = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
444         cols[0] = col_shift + idx_c[col]/dof; /* left, below */
445         Ni[0]   = 1.0;
446         if ( (li==0) || (li==nxi-1) ) {
447           if ( (lj==0) || (lj==neta-1) ) {
448             ierr = MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);CHKERRQ(ierr);
449             continue;
450           }
451         }
452 
453         /* edges + interior */
454         /* remainders */
455         if (i==mx-1){ i_c--; }
456         if (j==my-1){ j_c--; }
457 
458         col     = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
459         cols[0] = col_shift + idx_c[col]/dof; /* left, below */
460         cols[1] = col_shift + idx_c[col+dof]/dof; /* right, below */
461         cols[2] = col_shift + idx_c[col+m_ghost_c*dof]/dof; /* left, above */
462         cols[3] = col_shift + idx_c[col+(m_ghost_c+1)*dof]/dof; /* right, above */
463 
464         Ni[0] = 0.25*(1.0-xi[li])*(1.0-eta[lj]);
465         Ni[1] = 0.25*(1.0+xi[li])*(1.0-eta[lj]);
466         Ni[2] = 0.25*(1.0-xi[li])*(1.0+eta[lj]);
467         Ni[3] = 0.25*(1.0+xi[li])*(1.0+eta[lj]);
468 
469         nc = 0;
470         if( PetscAbsScalar(Ni[0])<1.0e-32) { cols[0]=-1; }
471         if( PetscAbsScalar(Ni[1])<1.0e-32) { cols[1]=-1; }
472         if( PetscAbsScalar(Ni[2])<1.0e-32) { cols[2]=-1; }
473         if( PetscAbsScalar(Ni[3])<1.0e-32) { cols[3]=-1; }
474 
475         ierr = MatSetValues(mat,1,&row,4,cols,Ni,INSERT_VALUES);CHKERRQ(ierr);
476       }
477     }
478     ierr = PetscFree(xi);CHKERRQ(ierr);
479     ierr = PetscFree(eta);CHKERRQ(ierr);
480   }
481   if (vcoors) {
482     ierr = DMDAVecRestoreArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
483     ierr = DMDAVecRestoreArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
484   }
485   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
486   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
487   ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
488   ierr = MatDestroy(&mat);CHKERRQ(ierr);
489   PetscFunctionReturn(0);
490 }
491 
492 /*
493        Contributed by Andrei Draganescu <aidraga@sandia.gov>
494 */
495 #undef __FUNCT__
496 #define __FUNCT__ "DMGetInterpolation_DA_2D_Q0"
497 PetscErrorCode DMGetInterpolation_DA_2D_Q0(DM dac,DM daf,Mat *A)
498 {
499   PetscErrorCode   ierr;
500   PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof;
501   PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,*dnz,*onz;
502   PetscInt         row,col,i_start_ghost,j_start_ghost,cols[4],mx,m_c,my,nc,ratioi,ratioj;
503   PetscInt         i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c,col_shift,col_scale;
504   PetscMPIInt      size_c,size_f,rank_f;
505   PetscScalar      v[4];
506   Mat              mat;
507   DMDABoundaryType bx,by;
508 
509   PetscFunctionBegin;
510   ierr = DMDAGetInfo(dac,0,&Mx,&My,0,0,0,0,0,0,&bx,&by,0,0);CHKERRQ(ierr);
511   ierr = DMDAGetInfo(daf,0,&mx,&my,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
512   if (bx == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in x");
513   if (by == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in y");
514   ratioi = mx/Mx;
515   ratioj = my/My;
516   if (ratioi*Mx != mx) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in x");
517   if (ratioj*My != my) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in y");
518   if (ratioi != 2) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in x must be 2");
519   if (ratioj != 2) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in y must be 2");
520 
521   ierr = DMDAGetCorners(daf,&i_start,&j_start,0,&m_f,&n_f,0);CHKERRQ(ierr);
522   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);CHKERRQ(ierr);
523   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
524 
525   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,0,&m_c,&n_c,0);CHKERRQ(ierr);
526   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);CHKERRQ(ierr);
527   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
528 
529   /*
530      Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
531      The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the
532      processors). It's effective length is hence 4 times its normal length, this is
533      why the col_scale is multiplied by the interpolation matrix column sizes.
534      sol_shift allows each set of 1/4 processors do its own interpolation using ITS
535      copy of the coarse vector. A bit of a hack but you do better.
536 
537      In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
538   */
539   ierr = MPI_Comm_size(((PetscObject)dac)->comm,&size_c);CHKERRQ(ierr);
540   ierr = MPI_Comm_size(((PetscObject)daf)->comm,&size_f);CHKERRQ(ierr);
541   ierr = MPI_Comm_rank(((PetscObject)daf)->comm,&rank_f);CHKERRQ(ierr);
542   col_scale = size_f/size_c;
543   col_shift = Mx*My*(rank_f/size_c);
544 
545   ierr = MatPreallocateInitialize(((PetscObject)daf)->comm,m_f*n_f,col_scale*m_c*n_c,dnz,onz);CHKERRQ(ierr);
546   for (j=j_start; j<j_start+n_f; j++) {
547     for (i=i_start; i<i_start+m_f; i++) {
548       /* convert to local "natural" numbering and then to PETSc global numbering */
549       row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
550 
551       i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
552       j_c = (j/ratioj);    /* coarse grid node below fine grid node */
553 
554       if (j_c < j_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
555     j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
556       if (i_c < i_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
557     i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
558 
559       /*
560          Only include those interpolation points that are truly
561          nonzero. Note this is very important for final grid lines
562          in x and y directions; since they have no right/top neighbors
563       */
564       nc = 0;
565       /* one left and below; or we are right on it */
566       col        = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
567       cols[nc++] = col_shift + idx_c[col]/dof;
568       ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
569     }
570   }
571   ierr = MatCreate(((PetscObject)daf)->comm,&mat);CHKERRQ(ierr);
572   ierr = MatSetSizes(mat,m_f*n_f,col_scale*m_c*n_c,mx*my,col_scale*Mx*My);CHKERRQ(ierr);
573   ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
574   ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
575   ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
576   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
577 
578   /* loop over local fine grid nodes setting interpolation for those*/
579   for (j=j_start; j<j_start+n_f; j++) {
580     for (i=i_start; i<i_start+m_f; i++) {
581       /* convert to local "natural" numbering and then to PETSc global numbering */
582       row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
583 
584       i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
585       j_c = (j/ratioj);    /* coarse grid node below fine grid node */
586       nc = 0;
587       /* one left and below; or we are right on it */
588       col      = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
589       cols[nc] = col_shift + idx_c[col]/dof;
590       v[nc++]  = 1.0;
591 
592       ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr);
593     }
594   }
595   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
596   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
597   ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
598   ierr = MatDestroy(&mat);CHKERRQ(ierr);
599   ierr = PetscLogFlops(13.0*m_f*n_f);CHKERRQ(ierr);
600   PetscFunctionReturn(0);
601 }
602 
603 /*
604        Contributed by Jianming Yang <jianming-yang@uiowa.edu>
605 */
606 #undef __FUNCT__
607 #define __FUNCT__ "DMGetInterpolation_DA_3D_Q0"
608 PetscErrorCode DMGetInterpolation_DA_3D_Q0(DM dac,DM daf,Mat *A)
609 {
610   PetscErrorCode   ierr;
611   PetscInt         i,j,l,i_start,j_start,l_start,m_f,n_f,p_f,Mx,My,Mz,*idx_f,dof;
612   PetscInt         m_ghost,n_ghost,p_ghost,*idx_c,m_ghost_c,n_ghost_c,p_ghost_c,nc,*dnz,*onz;
613   PetscInt         row,col,i_start_ghost,j_start_ghost,l_start_ghost,cols[8],mx,m_c,my,n_c,mz,p_c,ratioi,ratioj,ratiol;
614   PetscInt         i_c,j_c,l_c,i_start_c,j_start_c,l_start_c,i_start_ghost_c,j_start_ghost_c,l_start_ghost_c,col_shift,col_scale;
615   PetscMPIInt      size_c,size_f,rank_f;
616   PetscScalar      v[8];
617   Mat              mat;
618   DMDABoundaryType bx,by,bz;
619 
620   PetscFunctionBegin;
621   ierr = DMDAGetInfo(dac,0,&Mx,&My,&Mz,0,0,0,0,0,&bx,&by,&bz,0);CHKERRQ(ierr);
622   ierr = DMDAGetInfo(daf,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
623   if (bx == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in x");
624   if (by == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in y");
625   if (bz == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in z");
626   ratioi = mx/Mx;
627   ratioj = my/My;
628   ratiol = mz/Mz;
629   if (ratioi*Mx != mx) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in x");
630   if (ratioj*My != my) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in y");
631   if (ratiol*Mz != mz) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in z");
632   if (ratioi != 2 && ratioi != 1) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in x must be 1 or 2");
633   if (ratioj != 2 && ratioj != 1) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in y must be 1 or 2");
634   if (ratiol != 2 && ratiol != 1) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in z must be 1 or 2");
635 
636   ierr = DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
637   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
638   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
639 
640   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
641   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&l_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);CHKERRQ(ierr);
642   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
643   /*
644      Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
645      The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the
646      processors). It's effective length is hence 4 times its normal length, this is
647      why the col_scale is multiplied by the interpolation matrix column sizes.
648      sol_shift allows each set of 1/4 processors do its own interpolation using ITS
649      copy of the coarse vector. A bit of a hack but you do better.
650 
651      In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
652   */
653   ierr = MPI_Comm_size(((PetscObject)dac)->comm,&size_c);CHKERRQ(ierr);
654   ierr = MPI_Comm_size(((PetscObject)daf)->comm,&size_f);CHKERRQ(ierr);
655   ierr = MPI_Comm_rank(((PetscObject)daf)->comm,&rank_f);CHKERRQ(ierr);
656   col_scale = size_f/size_c;
657   col_shift = Mx*My*Mz*(rank_f/size_c);
658 
659   ierr = MatPreallocateInitialize(((PetscObject)daf)->comm,m_f*n_f*p_f,col_scale*m_c*n_c*p_c,dnz,onz);CHKERRQ(ierr);
660   for (l=l_start; l<l_start+p_f; l++) {
661     for (j=j_start; j<j_start+n_f; j++) {
662       for (i=i_start; i<i_start+m_f; i++) {
663 	/* convert to local "natural" numbering and then to PETSc global numbering */
664 	row    = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
665 
666 	i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
667 	j_c = (j/ratioj);    /* coarse grid node below fine grid node */
668 	l_c = (l/ratiol);
669 
670 	if (l_c < l_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
671     l_start %D l_c %D l_start_ghost_c %D",l_start,l_c,l_start_ghost_c);
672 	if (j_c < j_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
673     j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
674 	if (i_c < i_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
675     i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
676 
677 	/*
678 	   Only include those interpolation points that are truly
679 	   nonzero. Note this is very important for final grid lines
680 	   in x and y directions; since they have no right/top neighbors
681 	*/
682 	nc = 0;
683 	/* one left and below; or we are right on it */
684 	col        = dof*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
685 	cols[nc++] = col_shift + idx_c[col]/dof;
686 	ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
687       }
688     }
689   }
690   ierr = MatCreate(((PetscObject)daf)->comm,&mat);CHKERRQ(ierr);
691   ierr = MatSetSizes(mat,m_f*n_f*p_f,col_scale*m_c*n_c*p_c,mx*my*mz,col_scale*Mx*My*Mz);CHKERRQ(ierr);
692   ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
693   ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
694   ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
695   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
696 
697   /* loop over local fine grid nodes setting interpolation for those*/
698   for (l=l_start; l<l_start+p_f; l++) {
699     for (j=j_start; j<j_start+n_f; j++) {
700       for (i=i_start; i<i_start+m_f; i++) {
701 	/* convert to local "natural" numbering and then to PETSc global numbering */
702 	row    = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
703 
704 	i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
705 	j_c = (j/ratioj);    /* coarse grid node below fine grid node */
706 	l_c = (l/ratiol);
707 	nc = 0;
708 	/* one left and below; or we are right on it */
709 	col      = dof*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
710 	cols[nc] = col_shift + idx_c[col]/dof;
711 	v[nc++]  = 1.0;
712 
713 	ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr);
714       }
715     }
716   }
717   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
718   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
719   ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
720   ierr = MatDestroy(&mat);CHKERRQ(ierr);
721   ierr = PetscLogFlops(13.0*m_f*n_f*p_f);CHKERRQ(ierr);
722   PetscFunctionReturn(0);
723 }
724 
725 #undef __FUNCT__
726 #define __FUNCT__ "DMGetInterpolation_DA_3D_Q1"
727 PetscErrorCode DMGetInterpolation_DA_3D_Q1(DM dac,DM daf,Mat *A)
728 {
729   PetscErrorCode   ierr;
730   PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof,l;
731   PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,Mz,mz;
732   PetscInt         row,col,i_start_ghost,j_start_ghost,cols[8],mx,m_c,my,nc,ratioi,ratioj,ratiok;
733   PetscInt         i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c;
734   PetscInt         l_start,p_f,l_start_ghost,p_ghost,l_start_c,p_c;
735   PetscInt         l_start_ghost_c,p_ghost_c,l_c,*dnz,*onz;
736   PetscScalar      v[8],x,y,z;
737   Mat              mat;
738   DMDABoundaryType bx,by,bz;
739   DMDACoor3d       ***coors = 0,***ccoors;
740   Vec              vcoors,cvcoors;
741   DM_DA            *ddc = (DM_DA*)dac->data, *ddf = (DM_DA*)daf->data;
742 
743   PetscFunctionBegin;
744   ierr = DMDAGetInfo(dac,0,&Mx,&My,&Mz,0,0,0,0,0,&bx,&by,&bz,0);CHKERRQ(ierr);
745   ierr = DMDAGetInfo(daf,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
746   if (mx == Mx) {
747     ratioi = 1;
748   } else if (bx == DMDA_BOUNDARY_PERIODIC) {
749     ratioi = mx/Mx;
750     if (ratioi*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
751   } else {
752     ratioi = (mx-1)/(Mx-1);
753     if (ratioi*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
754   }
755   if (my == My) {
756     ratioj = 1;
757   } else if (by == DMDA_BOUNDARY_PERIODIC) {
758     ratioj = my/My;
759     if (ratioj*My != my) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: my/My  must be integer: my %D My %D",my,My);
760   } else {
761     ratioj = (my-1)/(My-1);
762     if (ratioj*(My-1) != my-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (my - 1)/(My - 1) must be integer: my %D My %D",my,My);
763   }
764   if (mz == Mz) {
765     ratiok = 1;
766   } else if (bz == DMDA_BOUNDARY_PERIODIC) {
767     ratiok = mz/Mz;
768     if (ratiok*Mz != mz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mz/Mz  must be integer: mz %D Mz %D",mz,Mz);
769   } else {
770     ratiok = (mz-1)/(Mz-1);
771     if (ratiok*(Mz-1) != mz-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mz - 1)/(Mz - 1) must be integer: mz %D Mz %D",mz,Mz);
772   }
773 
774   ierr = DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
775   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
776   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
777 
778   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
779   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&l_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);CHKERRQ(ierr);
780   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
781 
782   /* create interpolation matrix, determining exact preallocation */
783   ierr = MatPreallocateInitialize(((PetscObject)dac)->comm,m_f*n_f*p_f,m_c*n_c*p_c,dnz,onz);CHKERRQ(ierr);
784   /* loop over local fine grid nodes counting interpolating points */
785   for (l=l_start; l<l_start+p_f; l++) {
786     for (j=j_start; j<j_start+n_f; j++) {
787       for (i=i_start; i<i_start+m_f; i++) {
788         /* convert to local "natural" numbering and then to PETSc global numbering */
789         row = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
790         i_c = (i/ratioi);
791         j_c = (j/ratioj);
792         l_c = (l/ratiok);
793         if (l_c < l_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
794                                             l_start %D l_c %D l_start_ghost_c %D",l_start,l_c,l_start_ghost_c);
795         if (j_c < j_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
796                                             j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
797         if (i_c < i_start_ghost_c) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
798                                             i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
799 
800         /*
801          Only include those interpolation points that are truly
802          nonzero. Note this is very important for final grid lines
803          in x and y directions; since they have no right/top neighbors
804          */
805         nc       = 0;
806         col      = dof*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
807         cols[nc++] = idx_c[col]/dof;
808         if (i_c*ratioi != i) {
809           cols[nc++] = idx_c[col+dof]/dof;
810         }
811         if (j_c*ratioj != j) {
812           cols[nc++] = idx_c[col+m_ghost_c*dof]/dof;
813         }
814         if (l_c*ratiok != l) {
815           cols[nc++] = idx_c[col+m_ghost_c*n_ghost_c*dof]/dof;
816         }
817         if (j_c*ratioj != j && i_c*ratioi != i) {
818           cols[nc++] = idx_c[col+(m_ghost_c+1)*dof]/dof;
819         }
820         if (j_c*ratioj != j && l_c*ratiok != l) {
821           cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)*dof]/dof;
822         }
823         if (i_c*ratioi != i && l_c*ratiok != l) {
824           cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+1)*dof]/dof;
825         }
826         if (i_c*ratioi != i && l_c*ratiok != l && j_c*ratioj != j) {
827           cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)*dof]/dof;
828         }
829         ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
830       }
831     }
832   }
833   ierr = MatCreate(((PetscObject)dac)->comm,&mat);CHKERRQ(ierr);
834   ierr = MatSetSizes(mat,m_f*n_f*p_f,m_c*n_c*p_c,mx*my*mz,Mx*My*Mz);CHKERRQ(ierr);
835   ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
836   ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
837   ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
838   ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
839 
840   ierr = DMDAGetCoordinates(daf,&vcoors);CHKERRQ(ierr);
841   if (vcoors) {
842     ierr = DMDAGetGhostedCoordinates(dac,&cvcoors);CHKERRQ(ierr);
843     ierr = DMDAVecGetArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
844     ierr = DMDAVecGetArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
845   }
846 
847   /* loop over local fine grid nodes setting interpolation for those*/
848   if (!vcoors) {
849 
850     for (l=l_start; l<l_start+p_f; l++) {
851       for (j=j_start; j<j_start+n_f; j++) {
852         for (i=i_start; i<i_start+m_f; i++) {
853           /* convert to local "natural" numbering and then to PETSc global numbering */
854           row = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
855 
856           i_c = (i/ratioi);
857           j_c = (j/ratioj);
858           l_c = (l/ratiok);
859 
860         /*
861          Only include those interpolation points that are truly
862          nonzero. Note this is very important for final grid lines
863          in x and y directions; since they have no right/top neighbors
864          */
865           x  = ((double)(i - i_c*ratioi))/((double)ratioi);
866           y  = ((double)(j - j_c*ratioj))/((double)ratioj);
867           z  = ((double)(l - l_c*ratiok))/((double)ratiok);
868 
869           nc = 0;
870           /* one left and below; or we are right on it */
871           col      = dof*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c)+m_ghost_c*(j_c-j_start_ghost_c)+(i_c-i_start_ghost_c));
872 
873           cols[nc] = idx_c[col]/dof;
874           v[nc++]  = .125*(1. - (2.0*x-1.))*(1. - (2.0*y-1.))*(1. - (2.0*z-1.));
875 
876           if (i_c*ratioi != i) {
877             cols[nc] = idx_c[col+dof]/dof;
878             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. - (2.0*y-1.))*(1. - (2.0*z-1.));
879           }
880 
881           if (j_c*ratioj != j) {
882             cols[nc] = idx_c[col+m_ghost_c*dof]/dof;
883             v[nc++]  = .125*(1. - (2.0*x-1.))*(1. + (2.0*y-1.))*(1. - (2.0*z-1.));
884           }
885 
886           if (l_c*ratiok != l) {
887             cols[nc] = idx_c[col+m_ghost_c*n_ghost_c*dof]/dof;
888             v[nc++]  = .125*(1. - (2.0*x-1.))*(1. - (2.0*y-1.))*(1. + (2.0*z-1.));
889           }
890 
891           if (j_c*ratioj != j && i_c*ratioi != i) {
892             cols[nc] = idx_c[col+(m_ghost_c+1)*dof]/dof;
893             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. + (2.0*y-1.))*(1. - (2.0*z-1.));
894           }
895 
896           if (j_c*ratioj != j && l_c*ratiok != l) {
897             cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)*dof]/dof;
898             v[nc++]  = .125*(1. - (2.0*x-1.))*(1. + (2.0*y-1.))*(1. + (2.0*z-1.));
899           }
900 
901           if (i_c*ratioi != i && l_c*ratiok != l) {
902             cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+1)*dof]/dof;
903             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. - (2.0*y-1.))*(1. + (2.0*z-1.));
904           }
905 
906           if (i_c*ratioi != i && l_c*ratiok != l && j_c*ratioj != j) {
907             cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)*dof]/dof;
908             v[nc++]  = .125*(1. + (2.0*x-1.))*(1. + (2.0*y-1.))*(1. + (2.0*z-1.));
909           }
910           ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr);
911         }
912       }
913     }
914 
915   } else {
916     PetscScalar    *xi,*eta,*zeta;
917     PetscInt       li,nxi,lj,neta,lk,nzeta,n;
918     PetscScalar    Ni[8];
919 
920     /* compute local coordinate arrays */
921     nxi   = ratioi + 1;
922     neta  = ratioj + 1;
923     nzeta = ratiok + 1;
924     ierr = PetscMalloc(sizeof(PetscScalar)*nxi,&xi);CHKERRQ(ierr);
925     ierr = PetscMalloc(sizeof(PetscScalar)*neta,&eta);CHKERRQ(ierr);
926     ierr = PetscMalloc(sizeof(PetscScalar)*nzeta,&zeta);CHKERRQ(ierr);
927     for (li=0; li<nxi; li++) {
928       xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
929     }
930     for (lj=0; lj<neta; lj++) {
931       eta[lj] = -1.0 + (PetscScalar)lj*(2.0/(PetscScalar)(neta-1));
932     }
933     for (lk=0; lk<nzeta; lk++) {
934       zeta[lk] = -1.0 + (PetscScalar)lk*(2.0/(PetscScalar)(nzeta-1));
935     }
936 
937     for (l=l_start; l<l_start+p_f; l++) {
938       for (j=j_start; j<j_start+n_f; j++) {
939         for (i=i_start; i<i_start+m_f; i++) {
940           /* convert to local "natural" numbering and then to PETSc global numbering */
941           row = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
942 
943           i_c = (i/ratioi);
944           j_c = (j/ratioj);
945           l_c = (l/ratiok);
946 
947           /* remainders */
948           li = i - ratioi * (i/ratioi);
949           if (i==mx-1){ li = nxi-1; }
950           lj = j - ratioj * (j/ratioj);
951           if (j==my-1){ lj = neta-1; }
952           lk = l - ratiok * (l/ratiok);
953           if (l==mz-1){ lk = nzeta-1; }
954 
955           /* corners */
956           col     = dof*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c)+m_ghost_c*(j_c-j_start_ghost_c)+(i_c-i_start_ghost_c));
957           cols[0] = idx_c[col]/dof;
958           Ni[0]   = 1.0;
959           if ( (li==0) || (li==nxi-1) ) {
960             if ( (lj==0) || (lj==neta-1) ) {
961               if ( (lk==0) || (lk==nzeta-1) ) {
962                 ierr = MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);CHKERRQ(ierr);
963                 continue;
964               }
965             }
966           }
967 
968           /* edges + interior */
969           /* remainders */
970           if (i==mx-1){ i_c--; }
971           if (j==my-1){ j_c--; }
972           if (l==mz-1){ l_c--; }
973 
974           col      = dof*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
975           cols[0] = idx_c[col]/dof; /* one left and below; or we are right on it */
976           cols[1] = idx_c[col+dof]/dof; /* one right and below */
977           cols[2] = idx_c[col+m_ghost_c*dof]/dof;  /* one left and above */
978           cols[3] = idx_c[col+(m_ghost_c+1)*dof]/dof; /* one right and above */
979 
980           cols[4] = idx_c[col+m_ghost_c*n_ghost_c*dof]/dof; /* one left and below and front; or we are right on it */
981           cols[5] = idx_c[col+(m_ghost_c*n_ghost_c+1)*dof]/dof; /* one right and below, and front */
982           cols[6] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)*dof]/dof;/* one left and above and front*/
983           cols[7] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)*dof]/dof; /* one right and above and front */
984 
985           Ni[0] = 0.125*(1.0-xi[li])*(1.0-eta[lj])*(1.0-zeta[lk]);
986           Ni[1] = 0.125*(1.0+xi[li])*(1.0-eta[lj])*(1.0-zeta[lk]);
987           Ni[2] = 0.125*(1.0-xi[li])*(1.0+eta[lj])*(1.0-zeta[lk]);
988           Ni[3] = 0.125*(1.0+xi[li])*(1.0+eta[lj])*(1.0-zeta[lk]);
989 
990           Ni[4] = 0.125*(1.0-xi[li])*(1.0-eta[lj])*(1.0+zeta[lk]);
991           Ni[5] = 0.125*(1.0+xi[li])*(1.0-eta[lj])*(1.0+zeta[lk]);
992           Ni[6] = 0.125*(1.0-xi[li])*(1.0+eta[lj])*(1.0+zeta[lk]);
993           Ni[7] = 0.125*(1.0+xi[li])*(1.0+eta[lj])*(1.0+zeta[lk]);
994 
995           for (n=0; n<8; n++) {
996             if( PetscAbsScalar(Ni[n])<1.0e-32) { cols[n]=-1; }
997           }
998           ierr = MatSetValues(mat,1,&row,8,cols,Ni,INSERT_VALUES);CHKERRQ(ierr);
999 
1000         }
1001       }
1002     }
1003     ierr = PetscFree(xi);CHKERRQ(ierr);
1004     ierr = PetscFree(eta);CHKERRQ(ierr);
1005     ierr = PetscFree(zeta);CHKERRQ(ierr);
1006   }
1007 
1008   if (vcoors) {
1009     ierr = DMDAVecRestoreArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
1010     ierr = DMDAVecRestoreArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
1011   }
1012   ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1013   ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1014 
1015   ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
1016   ierr = MatDestroy(&mat);CHKERRQ(ierr);
1017   PetscFunctionReturn(0);
1018 }
1019 
1020 #undef __FUNCT__
1021 #define __FUNCT__ "DMGetInterpolation_DA"
1022 PetscErrorCode  DMGetInterpolation_DA(DM dac,DM daf,Mat *A,Vec *scale)
1023 {
1024   PetscErrorCode   ierr;
1025   PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc,dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
1026   DMDABoundaryType bxc,byc,bzc,bxf,byf,bzf;
1027   DMDAStencilType  stc,stf;
1028   DM_DA            *ddc = (DM_DA*)dac->data;
1029 
1030   PetscFunctionBegin;
1031   PetscValidHeaderSpecific(dac,DM_CLASSID,1);
1032   PetscValidHeaderSpecific(daf,DM_CLASSID,2);
1033   PetscValidPointer(A,3);
1034   if (scale) PetscValidPointer(scale,4);
1035 
1036   ierr = DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);CHKERRQ(ierr);
1037   ierr = DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);CHKERRQ(ierr);
1038   if (dimc != dimf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Dimensions of DMDA do not match %D %D",dimc,dimf);CHKERRQ(ierr);
1039   if (dofc != doff) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"DOF of DMDA do not match %D %D",dofc,doff);CHKERRQ(ierr);
1040   if (sc != sf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil width of DMDA do not match %D %D",sc,sf);CHKERRQ(ierr);
1041   if (bxc != bxf || byc != byf || bzc != bzf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Boundary type different in two DMDAs");CHKERRQ(ierr);
1042   if (stc != stf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil type different in two DMDAs");CHKERRQ(ierr);
1043   if (Mc < 2 && Mf > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in x direction");
1044   if (dimc > 1 && Nc < 2 && Nf > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in y direction");
1045   if (dimc > 2 && Pc < 2 && Pf > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in z direction");
1046 
1047   if (ddc->interptype == DMDA_Q1){
1048     if (dimc == 1){
1049       ierr = DMGetInterpolation_DA_1D_Q1(dac,daf,A);CHKERRQ(ierr);
1050     } else if (dimc == 2){
1051       ierr = DMGetInterpolation_DA_2D_Q1(dac,daf,A);CHKERRQ(ierr);
1052     } else if (dimc == 3){
1053       ierr = DMGetInterpolation_DA_3D_Q1(dac,daf,A);CHKERRQ(ierr);
1054     } else {
1055       SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_SUP,"No support for this DMDA dimension %D for interpolation type %d",dimc,(int)ddc->interptype);
1056     }
1057   } else if (ddc->interptype == DMDA_Q0){
1058     if (dimc == 1){
1059       ierr = DMGetInterpolation_DA_1D_Q0(dac,daf,A);CHKERRQ(ierr);
1060     } else if (dimc == 2){
1061        ierr = DMGetInterpolation_DA_2D_Q0(dac,daf,A);CHKERRQ(ierr);
1062     } else if (dimc == 3){
1063        ierr = DMGetInterpolation_DA_3D_Q0(dac,daf,A);CHKERRQ(ierr);
1064     } else {
1065       SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_SUP,"No support for this DMDA dimension %D for interpolation type %d",dimc,(int)ddc->interptype);
1066     }
1067   }
1068   if (scale) {
1069     ierr = DMGetInterpolationScale((DM)dac,(DM)daf,*A,scale);CHKERRQ(ierr);
1070   }
1071   PetscFunctionReturn(0);
1072 }
1073 
1074 #undef __FUNCT__
1075 #define __FUNCT__ "DMGetInjection_DA_1D"
1076 PetscErrorCode DMGetInjection_DA_1D(DM dac,DM daf,VecScatter *inject)
1077 {
1078     PetscErrorCode   ierr;
1079     PetscInt         i,i_start,m_f,Mx,*idx_f,dof;
1080     PetscInt         m_ghost,*idx_c,m_ghost_c;
1081     PetscInt         row,i_start_ghost,mx,m_c,nc,ratioi;
1082     PetscInt         i_start_c,i_start_ghost_c;
1083     PetscInt         *cols;
1084     DMDABoundaryType bx;
1085     Vec              vecf,vecc;
1086     IS               isf;
1087 
1088     PetscFunctionBegin;
1089     ierr = DMDAGetInfo(dac,0,&Mx,0,0,0,0,0,0,0,&bx,0,0,0);CHKERRQ(ierr);
1090     ierr = DMDAGetInfo(daf,0,&mx,0,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
1091     if (bx == DMDA_BOUNDARY_PERIODIC) {
1092         ratioi = mx/Mx;
1093         if (ratioi*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
1094     } else {
1095         ratioi = (mx-1)/(Mx-1);
1096         if (ratioi*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
1097     }
1098 
1099     ierr = DMDAGetCorners(daf,&i_start,0,0,&m_f,0,0);CHKERRQ(ierr);
1100     ierr = DMDAGetGhostCorners(daf,&i_start_ghost,0,0,&m_ghost,0,0);CHKERRQ(ierr);
1101     ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
1102 
1103     ierr = DMDAGetCorners(dac,&i_start_c,0,0,&m_c,0,0);CHKERRQ(ierr);
1104     ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,0,0,&m_ghost_c,0,0);CHKERRQ(ierr);
1105     ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
1106 
1107 
1108     /* loop over local fine grid nodes setting interpolation for those*/
1109     nc = 0;
1110     ierr = PetscMalloc(m_f*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1111 
1112 
1113     for (i=i_start_c; i<i_start_c+m_c; i++) {
1114         PetscInt i_f = i*ratioi;
1115 
1116            if (i_f < i_start_ghost || i_f >= i_start_ghost+m_ghost) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
1117  i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
1118             row = idx_f[dof*(i_f-i_start_ghost)];
1119             cols[nc++] = row/dof;
1120     }
1121 
1122 
1123     ierr = ISCreateBlock(((PetscObject)daf)->comm,dof,nc,cols,PETSC_OWN_POINTER,&isf);CHKERRQ(ierr);
1124     ierr = DMGetGlobalVector(dac,&vecc);CHKERRQ(ierr);
1125     ierr = DMGetGlobalVector(daf,&vecf);CHKERRQ(ierr);
1126     ierr = VecScatterCreate(vecf,isf,vecc,PETSC_NULL,inject);CHKERRQ(ierr);
1127     ierr = DMRestoreGlobalVector(dac,&vecc);CHKERRQ(ierr);
1128     ierr = DMRestoreGlobalVector(daf,&vecf);CHKERRQ(ierr);
1129     ierr = ISDestroy(&isf);CHKERRQ(ierr);
1130     PetscFunctionReturn(0);
1131 }
1132 
1133 #undef __FUNCT__
1134 #define __FUNCT__ "DMGetInjection_DA_2D"
1135 PetscErrorCode DMGetInjection_DA_2D(DM dac,DM daf,VecScatter *inject)
1136 {
1137   PetscErrorCode   ierr;
1138   PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof;
1139   PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c;
1140   PetscInt         row,i_start_ghost,j_start_ghost,mx,m_c,my,nc,ratioi,ratioj;
1141   PetscInt         i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c;
1142   PetscInt         *cols;
1143   DMDABoundaryType bx,by;
1144   Vec              vecf,vecc;
1145   IS               isf;
1146 
1147   PetscFunctionBegin;
1148   ierr = DMDAGetInfo(dac,0,&Mx,&My,0,0,0,0,0,0,&bx,&by,0,0);CHKERRQ(ierr);
1149   ierr = DMDAGetInfo(daf,0,&mx,&my,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
1150   if (bx == DMDA_BOUNDARY_PERIODIC) {
1151     ratioi = mx/Mx;
1152     if (ratioi*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
1153   } else {
1154     ratioi = (mx-1)/(Mx-1);
1155     if (ratioi*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
1156   }
1157   if (by == DMDA_BOUNDARY_PERIODIC) {
1158     ratioj = my/My;
1159     if (ratioj*My != my) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: my/My  must be integer: my %D My %D",my,My);
1160   } else {
1161     ratioj = (my-1)/(My-1);
1162     if (ratioj*(My-1) != my-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (my - 1)/(My - 1) must be integer: my %D My %D",my,My);
1163   }
1164 
1165   ierr = DMDAGetCorners(daf,&i_start,&j_start,0,&m_f,&n_f,0);CHKERRQ(ierr);
1166   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);CHKERRQ(ierr);
1167   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
1168 
1169   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,0,&m_c,&n_c,0);CHKERRQ(ierr);
1170   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);CHKERRQ(ierr);
1171   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
1172 
1173 
1174   /* loop over local fine grid nodes setting interpolation for those*/
1175   nc = 0;
1176   ierr = PetscMalloc(n_f*m_f*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1177   for (j=j_start_c; j<j_start_c+n_c; j++) {
1178     for (i=i_start_c; i<i_start_c+m_c; i++) {
1179       PetscInt i_f = i*ratioi,j_f = j*ratioj;
1180       if (j_f < j_start_ghost || j_f >= j_start_ghost+n_ghost) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
1181     j_c %D j_f %D fine ghost range [%D,%D]",j,j_f,j_start_ghost,j_start_ghost+n_ghost);
1182       if (i_f < i_start_ghost || i_f >= i_start_ghost+m_ghost) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA\n\
1183     i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
1184       row = idx_f[dof*(m_ghost*(j_f-j_start_ghost) + (i_f-i_start_ghost))];
1185       cols[nc++] = row/dof;
1186     }
1187   }
1188 
1189   ierr = ISCreateBlock(((PetscObject)daf)->comm,dof,nc,cols,PETSC_OWN_POINTER,&isf);CHKERRQ(ierr);
1190   ierr = DMGetGlobalVector(dac,&vecc);CHKERRQ(ierr);
1191   ierr = DMGetGlobalVector(daf,&vecf);CHKERRQ(ierr);
1192   ierr = VecScatterCreate(vecf,isf,vecc,PETSC_NULL,inject);CHKERRQ(ierr);
1193   ierr = DMRestoreGlobalVector(dac,&vecc);CHKERRQ(ierr);
1194   ierr = DMRestoreGlobalVector(daf,&vecf);CHKERRQ(ierr);
1195   ierr = ISDestroy(&isf);CHKERRQ(ierr);
1196   PetscFunctionReturn(0);
1197 }
1198 
1199 #undef __FUNCT__
1200 #define __FUNCT__ "DMGetInjection_DA_3D"
1201 PetscErrorCode DMGetInjection_DA_3D(DM dac,DM daf,VecScatter *inject)
1202 {
1203   PetscErrorCode   ierr;
1204   PetscInt         i,j,k,i_start,j_start,k_start,m_f,n_f,p_f,Mx,My,Mz;
1205   PetscInt         m_ghost,n_ghost,p_ghost,m_ghost_c,n_ghost_c,p_ghost_c;
1206   PetscInt         i_start_ghost,j_start_ghost,k_start_ghost;
1207   PetscInt         mx,my,mz,ratioi,ratioj,ratiok;
1208   PetscInt         i_start_c,j_start_c,k_start_c;
1209   PetscInt         m_c,n_c,p_c;
1210   PetscInt         i_start_ghost_c,j_start_ghost_c,k_start_ghost_c;
1211   PetscInt         row,nc,dof;
1212   PetscInt         *idx_c,*idx_f;
1213   PetscInt         *cols;
1214   DMDABoundaryType bx,by,bz;
1215   Vec              vecf,vecc;
1216   IS               isf;
1217 
1218   PetscFunctionBegin;
1219   ierr = DMDAGetInfo(dac,0,&Mx,&My,&Mz,0,0,0,0,0,&bx,&by,&bz,0);CHKERRQ(ierr);
1220   ierr = DMDAGetInfo(daf,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
1221 
1222   if (bx == DMDA_BOUNDARY_PERIODIC){
1223     ratioi = mx/Mx;
1224     if (ratioi*Mx != mx) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mx/Mx  must be integer: mx %D Mx %D",mx,Mx);
1225   } else {
1226     ratioi = (mx-1)/(Mx-1);
1227     if (ratioi*(Mx-1) != mx-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mx - 1)/(Mx - 1) must be integer: mx %D Mx %D",mx,Mx);
1228   }
1229   if (by == DMDA_BOUNDARY_PERIODIC){
1230     ratioj = my/My;
1231     if (ratioj*My != my) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: my/My  must be integer: my %D My %D",my,My);
1232   } else {
1233     ratioj = (my-1)/(My-1);
1234     if (ratioj*(My-1) != my-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (my - 1)/(My - 1) must be integer: my %D My %D",my,My);
1235   }
1236   if (bz == DMDA_BOUNDARY_PERIODIC){
1237     ratiok = mz/Mz;
1238     if (ratiok*Mz != mz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: mz/Mz  must be integer: mz %D My %D",mz,Mz);
1239   } else {
1240     ratiok = (mz-1)/(Mz-1);
1241     if (ratiok*(Mz-1) != mz-1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Ratio between levels: (mz - 1)/(Mz - 1) must be integer: mz %D Mz %D",mz,Mz);
1242   }
1243 
1244   ierr = DMDAGetCorners(daf,&i_start,&j_start,&k_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
1245   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&k_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
1246   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
1247 
1248   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&k_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
1249   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&k_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);CHKERRQ(ierr);
1250   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
1251 
1252 
1253   /* loop over local fine grid nodes setting interpolation for those*/
1254   nc = 0;
1255   ierr = PetscMalloc(n_f*m_f*p_f*sizeof(PetscInt),&cols);CHKERRQ(ierr);
1256   for (k=k_start_c; k<k_start_c+p_c; k++) {
1257     for (j=j_start_c; j<j_start_c+n_c; j++) {
1258       for (i=i_start_c; i<i_start_c+m_c; i++) {
1259         PetscInt i_f = i*ratioi,j_f = j*ratioj,k_f = k*ratiok;
1260         if (k_f < k_start_ghost || k_f >= k_start_ghost+p_ghost) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA  "
1261                                                                           "k_c %D k_f %D fine ghost range [%D,%D]",k,k_f,k_start_ghost,k_start_ghost+p_ghost);
1262         if (j_f < j_start_ghost || j_f >= j_start_ghost+n_ghost) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA  "
1263                                                                           "j_c %D j_f %D fine ghost range [%D,%D]",j,j_f,j_start_ghost,j_start_ghost+n_ghost);
1264         if (i_f < i_start_ghost || i_f >= i_start_ghost+m_ghost) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Processor's coarse DMDA must lie over fine DMDA  "
1265                                                                           "i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
1266         row = idx_f[dof*(m_ghost*n_ghost*(k_f-k_start_ghost) + m_ghost*(j_f-j_start_ghost) + (i_f-i_start_ghost))];
1267         cols[nc++] = row/dof;
1268       }
1269     }
1270   }
1271 
1272   ierr = ISCreateBlock(((PetscObject)daf)->comm,dof,nc,cols,PETSC_OWN_POINTER,&isf);CHKERRQ(ierr);
1273   ierr = DMGetGlobalVector(dac,&vecc);CHKERRQ(ierr);
1274   ierr = DMGetGlobalVector(daf,&vecf);CHKERRQ(ierr);
1275   ierr = VecScatterCreate(vecf,isf,vecc,PETSC_NULL,inject);CHKERRQ(ierr);
1276   ierr = DMRestoreGlobalVector(dac,&vecc);CHKERRQ(ierr);
1277   ierr = DMRestoreGlobalVector(daf,&vecf);CHKERRQ(ierr);
1278   ierr = ISDestroy(&isf);CHKERRQ(ierr);
1279   PetscFunctionReturn(0);
1280 }
1281 
1282 #undef __FUNCT__
1283 #define __FUNCT__ "DMGetInjection_DA"
1284 PetscErrorCode  DMGetInjection_DA(DM dac,DM daf,VecScatter *inject)
1285 {
1286   PetscErrorCode   ierr;
1287   PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc,dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
1288   DMDABoundaryType bxc,byc,bzc,bxf,byf,bzf;
1289   DMDAStencilType  stc,stf;
1290 
1291   PetscFunctionBegin;
1292   PetscValidHeaderSpecific(dac,DM_CLASSID,1);
1293   PetscValidHeaderSpecific(daf,DM_CLASSID,2);
1294   PetscValidPointer(inject,3);
1295 
1296   ierr = DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);CHKERRQ(ierr);
1297   ierr = DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);CHKERRQ(ierr);
1298   if (dimc != dimf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Dimensions of DMDA do not match %D %D",dimc,dimf);CHKERRQ(ierr);
1299   if (dofc != doff) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"DOF of DMDA do not match %D %D",dofc,doff);CHKERRQ(ierr);
1300   if (sc != sf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil width of DMDA do not match %D %D",sc,sf);CHKERRQ(ierr);
1301   if (bxc != bxf || byc != byf || bzc != bzf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Boundary type different in two DMDAs");CHKERRQ(ierr);
1302   if (stc != stf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil type different in two DMDAs");CHKERRQ(ierr);
1303   if (Mc < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in x direction");
1304   if (dimc > 1 && Nc < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in y direction");
1305   if (dimc > 2 && Pc < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in z direction");
1306 
1307   if (dimc == 1){
1308     ierr = DMGetInjection_DA_1D(dac,daf,inject);CHKERRQ(ierr);
1309   } else if (dimc == 2) {
1310     ierr = DMGetInjection_DA_2D(dac,daf,inject);CHKERRQ(ierr);
1311   } else if (dimc == 3) {
1312     ierr = DMGetInjection_DA_3D(dac,daf,inject);CHKERRQ(ierr);
1313   }
1314   PetscFunctionReturn(0);
1315 }
1316 
1317 #undef __FUNCT__
1318 #define __FUNCT__ "DMGetAggregates_DA"
1319 PetscErrorCode  DMGetAggregates_DA(DM dac,DM daf,Mat *rest)
1320 {
1321   PetscErrorCode   ierr;
1322   PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc;
1323   PetscInt         dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
1324   DMDABoundaryType bxc,byc,bzc,bxf,byf,bzf;
1325   DMDAStencilType  stc,stf;
1326   PetscInt         i,j,l;
1327   PetscInt         i_start,j_start,l_start, m_f,n_f,p_f;
1328   PetscInt         i_start_ghost,j_start_ghost,l_start_ghost,m_ghost,n_ghost,p_ghost;
1329   PetscInt         *idx_f;
1330   PetscInt         i_c,j_c,l_c;
1331   PetscInt         i_start_c,j_start_c,l_start_c, m_c,n_c,p_c;
1332   PetscInt         i_start_ghost_c,j_start_ghost_c,l_start_ghost_c,m_ghost_c,n_ghost_c,p_ghost_c;
1333   PetscInt         *idx_c;
1334   PetscInt         d;
1335   PetscInt         a;
1336   PetscInt         max_agg_size;
1337   PetscInt         *fine_nodes;
1338   PetscScalar      *one_vec;
1339   PetscInt         fn_idx;
1340 
1341   PetscFunctionBegin;
1342   PetscValidHeaderSpecific(dac,DM_CLASSID,1);
1343   PetscValidHeaderSpecific(daf,DM_CLASSID,2);
1344   PetscValidPointer(rest,3);
1345 
1346   ierr = DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);CHKERRQ(ierr);
1347   ierr = DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);CHKERRQ(ierr);
1348   if (dimc != dimf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Dimensions of DMDA do not match %D %D",dimc,dimf);CHKERRQ(ierr);
1349   if (dofc != doff) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"DOF of DMDA do not match %D %D",dofc,doff);CHKERRQ(ierr);
1350   if (sc != sf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil width of DMDA do not match %D %D",sc,sf);CHKERRQ(ierr);
1351   if (bxc != bxf || byc != byf || bzc != bzf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Boundary type different in two DMDAs");CHKERRQ(ierr);
1352   if (stc != stf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil type different in two DMDAs");CHKERRQ(ierr);
1353 
1354   if( Mf < Mc ) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Coarse grid has more points than fine grid, Mc %D, Mf %D", Mc, Mf);
1355   if( Nf < Nc ) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Coarse grid has more points than fine grid, Nc %D, Nf %D", Nc, Nf);
1356   if( Pf < Pc ) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Coarse grid has more points than fine grid, Pc %D, Pf %D", Pc, Pf);
1357 
1358   if (Pc < 0) Pc = 1;
1359   if (Pf < 0) Pf = 1;
1360   if (Nc < 0) Nc = 1;
1361   if (Nf < 0) Nf = 1;
1362 
1363   ierr = DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
1364   ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
1365   ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
1366 
1367   ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
1368   ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,&l_start_ghost_c,&m_ghost_c,&n_ghost_c,&p_ghost_c);CHKERRQ(ierr);
1369   ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
1370 
1371   /*
1372      Basic idea is as follows. Here's a 2D example, suppose r_x, r_y are the ratios
1373      for dimension 1 and 2 respectively.
1374      Let (i,j) be a coarse grid node. All the fine grid nodes between r_x*i and r_x*(i+1)
1375      and r_y*j and r_y*(j+1) will be grouped into the same coarse grid agregate.
1376      Each specific dof on the fine grid is mapped to one dof on the coarse grid.
1377   */
1378 
1379   max_agg_size = (Mf/Mc+1)*(Nf/Nc+1)*(Pf/Pc+1);
1380 
1381   /* create the matrix that will contain the restriction operator */
1382   ierr = MatCreateMPIAIJ( ((PetscObject)daf)->comm, m_c*n_c*p_c*dofc, m_f*n_f*p_f*doff, Mc*Nc*Pc*dofc, Mf*Nf*Pf*doff,
1383 			  max_agg_size, PETSC_NULL, max_agg_size, PETSC_NULL, rest);CHKERRQ(ierr);
1384 
1385   /* store nodes in the fine grid here */
1386   ierr = PetscMalloc2(max_agg_size,PetscScalar, &one_vec,max_agg_size,PetscInt, &fine_nodes);CHKERRQ(ierr);
1387   for(i=0; i<max_agg_size; i++) one_vec[i] = 1.0;
1388 
1389   /* loop over all coarse nodes */
1390   for (l_c=l_start_c; l_c<l_start_c+p_c; l_c++) {
1391     for (j_c=j_start_c; j_c<j_start_c+n_c; j_c++) {
1392       for (i_c=i_start_c; i_c<i_start_c+m_c; i_c++) {
1393 	for(d=0; d<dofc; d++) {
1394 	  /* convert to local "natural" numbering and then to PETSc global numbering */
1395 	  a = idx_c[dofc*(m_ghost_c*n_ghost_c*(l_c-l_start_ghost_c) + m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c))] + d;
1396 
1397 	  fn_idx = 0;
1398 	  /* Corresponding fine points are all points (i_f, j_f, l_f) such that
1399 	     i_c*Mf/Mc <= i_f < (i_c+1)*Mf/Mc
1400 	     (same for other dimensions)
1401 	  */
1402 	  for (l=l_c*Pf/Pc; l<PetscMin((l_c+1)*Pf/Pc,Pf); l++) {
1403 	    for (j=j_c*Nf/Nc; j<PetscMin((j_c+1)*Nf/Nc,Nf); j++) {
1404 	      for (i=i_c*Mf/Mc; i<PetscMin((i_c+1)*Mf/Mc,Mf); i++) {
1405 		fine_nodes[fn_idx] = idx_f[doff*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))] + d;
1406 		fn_idx++;
1407 	      }
1408 	    }
1409 	  }
1410 	  /* add all these points to one aggregate */
1411 	  ierr = MatSetValues(*rest, 1, &a, fn_idx, fine_nodes, one_vec, INSERT_VALUES);CHKERRQ(ierr);
1412 	}
1413       }
1414     }
1415   }
1416   ierr = PetscFree2(one_vec,fine_nodes);CHKERRQ(ierr);
1417   ierr = MatAssemblyBegin(*rest, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1418   ierr = MatAssemblyEnd(*rest, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1419   PetscFunctionReturn(0);
1420 }
1421