/*
  Code for interpolating between grids represented by DMDAs
*/

#include <private/daimpl.h>    /*I   "petscdmda.h"   I*/
#include <petscpcmg.h>

#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolationScale"
/*@
    DMGetInterpolationScale - Forms L = R*1/diag(R*1) - L.*v is like a coarse grid average of the 
      nearby fine grid points.

  Input Parameters:
+      dac - DM that defines a coarse mesh
.      daf - DM that defines a fine mesh
-      mat - the restriction (or interpolation operator) from fine to coarse

  Output Parameter:
.    scale - the scaled vector

  Level: developer

.seealso: DMGetInterpolation()

@*/
PetscErrorCode  DMGetInterpolationScale(DM dac,DM daf,Mat mat,Vec *scale)
{
  PetscErrorCode ierr;
  Vec            fine;
  PetscScalar    one = 1.0;

  PetscFunctionBegin;
  ierr = DMCreateGlobalVector(daf,&fine);CHKERRQ(ierr);
  ierr = DMCreateGlobalVector(dac,scale);CHKERRQ(ierr);
  ierr = VecSet(fine,one);CHKERRQ(ierr);
  ierr = MatRestrict(mat,fine,*scale);CHKERRQ(ierr);
  ierr = VecDestroy(&fine);CHKERRQ(ierr);
  ierr = VecReciprocal(*scale);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA_1D_Q1"
PetscErrorCode DMGetInterpolation_DA_1D_Q1(DM dac,DM daf,Mat *A)
{
  PetscErrorCode   ierr;
  PetscInt         i,i_start,m_f,Mx,*idx_f;
  PetscInt         m_ghost,*idx_c,m_ghost_c;
  PetscInt         row,col,i_start_ghost,mx,m_c,nc,ratio;
  PetscInt         i_c,i_start_c,i_start_ghost_c,cols[2],dof;
  PetscScalar      v[2],x,*coors = 0,*ccoors;
  Mat              mat;
  DMDABoundaryType bx;
  Vec              vcoors,cvcoors;
  DM_DA            *ddc = (DM_DA*)dac->data, *ddf = (DM_DA*)daf->data;
  
  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,0,0,0,0,0,0,0,&bx,0,0,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,0,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (bx == DMDA_BOUNDARY_PERIODIC){
    ratio = mx/Mx;
    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);
  } else {
    ratio = (mx-1)/(Mx-1);
    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);
  }
  
  ierr = DMDAGetCorners(daf,&i_start,0,0,&m_f,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,0,0,&m_ghost,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
  
  ierr = DMDAGetCorners(dac,&i_start_c,0,0,&m_c,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,0,0,&m_ghost_c,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
  
  /* create interpolation matrix */
  ierr = MatCreate(((PetscObject)dac)->comm,&mat);CHKERRQ(ierr);
  ierr = MatSetSizes(mat,m_f,m_c,mx,Mx);CHKERRQ(ierr);
  ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(mat,2,PETSC_NULL);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(mat,2,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);
  
  ierr = DMDAGetCoordinates(daf,&vcoors);CHKERRQ(ierr);
  if (vcoors) {
    ierr = DMDAGetGhostedCoordinates(dac,&cvcoors);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
  }
  /* loop over local fine grid nodes setting interpolation for those*/
  if (!vcoors) {

    for (i=i_start; i<i_start+m_f; i++) {
      /* convert to local "natural" numbering and then to PETSc global numbering */
      row    = idx_f[dof*(i-i_start_ghost)]/dof;
      
      i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
      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\
                                          i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
      
      /* 
       Only include those interpolation points that are truly 
       nonzero. Note this is very important for final grid lines
       in x direction; since they have no right neighbor
       */
      x  = ((double)(i - i_c*ratio))/((double)ratio);
      nc = 0;
      /* one left and below; or we are right on it */
      col      = dof*(i_c-i_start_ghost_c);
      cols[nc] = idx_c[col]/dof; 
      v[nc++]  = - x + 1.0;
      /* one right? */
      if (i_c*ratio != i) { 
        cols[nc] = idx_c[col+dof]/dof;
        v[nc++]  = x;
      }
      ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr); 
    }
    
  } else {
    PetscScalar    *xi;
    PetscInt       li,nxi,n;
    PetscScalar    Ni[2];
    
    /* compute local coordinate arrays */
    nxi   = ratio + 1;
    ierr = PetscMalloc(sizeof(PetscScalar)*nxi,&xi);CHKERRQ(ierr);
    for (li=0; li<nxi; li++) {
      xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
    }

    for (i=i_start; i<i_start+m_f; i++) {
      /* convert to local "natural" numbering and then to PETSc global numbering */
      row    = idx_f[dof*(i-i_start_ghost)]/dof;
      
      i_c = (i/ratio);    /* coarse grid node to left of fine grid node */
      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\
                                          i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

      /* remainders */
      li = i - ratio * (i/ratio);
      if (i==mx-1){ li = nxi-1; }
      
      /* corners */
      col     = dof*(i_c-i_start_ghost_c);
      cols[0] = idx_c[col]/dof; 
      Ni[0]   = 1.0;
      if ( (li==0) || (li==nxi-1) ) {
        ierr = MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);CHKERRQ(ierr);
        continue;
      }
      
      /* edges + interior */
      /* remainders */
      if (i==mx-1){ i_c--; }
      
      col     = dof*(i_c-i_start_ghost_c);
      cols[0] = idx_c[col]/dof; /* one left and below; or we are right on it */
      cols[1] = idx_c[col+dof]/dof;

      Ni[0] = 0.5*(1.0-xi[li]);
      Ni[1] = 0.5*(1.0+xi[li]);
      for (n=0; n<2; n++) {
        if( PetscAbsScalar(Ni[n])<1.0e-32) { cols[n]=-1; }
      }
      ierr = MatSetValues(mat,1,&row,2,cols,Ni,INSERT_VALUES);CHKERRQ(ierr); 
    }
    ierr = PetscFree(xi);CHKERRQ(ierr);
  }
  if (vcoors) {
    ierr = DMDAVecRestoreArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
    ierr = DMDAVecRestoreArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
  ierr = MatDestroy(&mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA_1D_Q0"
PetscErrorCode DMGetInterpolation_DA_1D_Q0(DM dac,DM daf,Mat *A)
{
  PetscErrorCode   ierr;
  PetscInt         i,i_start,m_f,Mx,*idx_f;
  PetscInt         m_ghost,*idx_c,m_ghost_c;
  PetscInt         row,col,i_start_ghost,mx,m_c,nc,ratio;
  PetscInt         i_c,i_start_c,i_start_ghost_c,cols[2],dof;
  PetscScalar      v[2],x;
  Mat              mat;
  DMDABoundaryType bx;
  
  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,0,0,0,0,0,0,0,&bx,0,0,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,0,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (bx == DMDA_BOUNDARY_PERIODIC){
    ratio = mx/Mx;
    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);
  } else {
    ratio = (mx-1)/(Mx-1);
    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);
  }

  ierr = DMDAGetCorners(daf,&i_start,0,0,&m_f,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,0,0,&m_ghost,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);

  ierr = DMDAGetCorners(dac,&i_start_c,0,0,&m_c,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,0,0,&m_ghost_c,0,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);

  /* create interpolation matrix */
  ierr = MatCreate(((PetscObject)dac)->comm,&mat);CHKERRQ(ierr);
  ierr = MatSetSizes(mat,m_f,m_c,mx,Mx);CHKERRQ(ierr);
  ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(mat,2,PETSC_NULL);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(mat,2,PETSC_NULL,0,PETSC_NULL);CHKERRQ(ierr);

  /* loop over local fine grid nodes setting interpolation for those*/
  for (i=i_start; i<i_start+m_f; i++) {
    /* convert to local "natural" numbering and then to PETSc global numbering */
    row    = idx_f[dof*(i-i_start_ghost)]/dof;

    i_c = (i/ratio);    /* coarse grid node to left of fine grid node */

    /* 
         Only include those interpolation points that are truly 
         nonzero. Note this is very important for final grid lines
         in x direction; since they have no right neighbor
    */
    x  = ((double)(i - i_c*ratio))/((double)ratio);
    nc = 0;
      /* one left and below; or we are right on it */
    col      = dof*(i_c-i_start_ghost_c);
    cols[nc] = idx_c[col]/dof; 
    v[nc++]  = - x + 1.0;
    /* one right? */
    if (i_c*ratio != i) { 
      cols[nc] = idx_c[col+dof]/dof;
      v[nc++]  = x;
    }
    ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr); 
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
  ierr = MatDestroy(&mat);CHKERRQ(ierr);
  ierr = PetscLogFlops(5.0*m_f);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA_2D_Q1"
PetscErrorCode DMGetInterpolation_DA_2D_Q1(DM dac,DM daf,Mat *A)
{
  PetscErrorCode   ierr;
  PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof;
  PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,*dnz,*onz;
  PetscInt         row,col,i_start_ghost,j_start_ghost,cols[4],mx,m_c,my,nc,ratioi,ratioj;
  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;
  PetscMPIInt      size_c,size_f,rank_f;
  PetscScalar      v[4],x,y;
  Mat              mat;
  DMDABoundaryType bx,by;
  DMDACoor2d       **coors = 0,**ccoors;
  Vec              vcoors,cvcoors;
  DM_DA            *ddc = (DM_DA*)dac->data, *ddf = (DM_DA*)daf->data;
  
  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,&My,0,0,0,0,0,0,&bx,&by,0,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,&my,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (bx == DMDA_BOUNDARY_PERIODIC){
    ratioi = mx/Mx;
    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);
  } else {
    ratioi = (mx-1)/(Mx-1);
    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);
  }
  if (by == DMDA_BOUNDARY_PERIODIC){
    ratioj = my/My;
    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);
  } else {
    ratioj = (my-1)/(My-1);
    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);
  }
  
  
  ierr = DMDAGetCorners(daf,&i_start,&j_start,0,&m_f,&n_f,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
  
  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,0,&m_c,&n_c,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
  
  /*
   Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
   The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the 
   processors). It's effective length is hence 4 times its normal length, this is
   why the col_scale is multiplied by the interpolation matrix column sizes.
   sol_shift allows each set of 1/4 processors do its own interpolation using ITS
   copy of the coarse vector. A bit of a hack but you do better.
   
   In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
   */
  ierr = MPI_Comm_size(((PetscObject)dac)->comm,&size_c);CHKERRQ(ierr);
  ierr = MPI_Comm_size(((PetscObject)daf)->comm,&size_f);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(((PetscObject)daf)->comm,&rank_f);CHKERRQ(ierr);
  col_scale = size_f/size_c;
  col_shift = Mx*My*(rank_f/size_c);
  
  ierr = MatPreallocateInitialize(((PetscObject)daf)->comm,m_f*n_f,col_scale*m_c*n_c,dnz,onz);CHKERRQ(ierr);
  for (j=j_start; j<j_start+n_f; j++) {
    for (i=i_start; i<i_start+m_f; i++) {
      /* convert to local "natural" numbering and then to PETSc global numbering */
      row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
      
      i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
      j_c = (j/ratioj);    /* coarse grid node below fine grid node */
      
      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\
                                          j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
      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\
                                          i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
      
      /* 
       Only include those interpolation points that are truly 
       nonzero. Note this is very important for final grid lines
       in x and y directions; since they have no right/top neighbors
       */
      nc = 0;
      /* one left and below; or we are right on it */
      col        = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
      cols[nc++] = col_shift + idx_c[col]/dof; 
      /* one right and below */
      if (i_c*ratioi != i) { 
        cols[nc++] = col_shift + idx_c[col+dof]/dof;
      }
      /* one left and above */
      if (j_c*ratioj != j) { 
        cols[nc++] = col_shift + idx_c[col+m_ghost_c*dof]/dof;
      }
      /* one right and above */
      if (i_c*ratioi != i && j_c*ratioj != j) {
        cols[nc++] = col_shift + idx_c[col+(m_ghost_c+1)*dof]/dof;
      }
      ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
    }
  }
  ierr = MatCreate(((PetscObject)daf)->comm,&mat);CHKERRQ(ierr);
  ierr = MatSetSizes(mat,m_f*n_f,col_scale*m_c*n_c,mx*my,col_scale*Mx*My);CHKERRQ(ierr);
  ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
  
  ierr = DMDAGetCoordinates(daf,&vcoors);CHKERRQ(ierr);
  if (vcoors) {
    ierr = DMDAGetGhostedCoordinates(dac,&cvcoors);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
  }
  
  /* loop over local fine grid nodes setting interpolation for those*/
  if (!vcoors) {
    
    for (j=j_start; j<j_start+n_f; j++) {
      for (i=i_start; i<i_start+m_f; i++) {
        /* convert to local "natural" numbering and then to PETSc global numbering */
        row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
        
        i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
        j_c = (j/ratioj);    /* coarse grid node below fine grid node */
        
        /* 
         Only include those interpolation points that are truly 
         nonzero. Note this is very important for final grid lines
         in x and y directions; since they have no right/top neighbors
         */
        x  = ((double)(i - i_c*ratioi))/((double)ratioi);
        y  = ((double)(j - j_c*ratioj))/((double)ratioj);
        
        nc = 0;
        /* one left and below; or we are right on it */
        col      = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
        cols[nc] = col_shift + idx_c[col]/dof; 
        v[nc++]  = x*y - x - y + 1.0;
        /* one right and below */
        if (i_c*ratioi != i) { 
          cols[nc] = col_shift + idx_c[col+dof]/dof;
          v[nc++]  = -x*y + x;
        }
        /* one left and above */
        if (j_c*ratioj != j) { 
          cols[nc] = col_shift + idx_c[col+m_ghost_c*dof]/dof;
          v[nc++]  = -x*y + y;
        }
        /* one right and above */
        if (j_c*ratioj != j && i_c*ratioi != i) { 
          cols[nc] = col_shift + idx_c[col+(m_ghost_c+1)*dof]/dof;
          v[nc++]  = x*y;
        }
        ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr); 
      }
    }
    
  } else {
    PetscScalar    Ni[4];
    PetscScalar    *xi,*eta;
    PetscInt       li,nxi,lj,neta;
    
    /* compute local coordinate arrays */
    nxi  = ratioi + 1;
    neta = ratioj + 1;
    ierr = PetscMalloc(sizeof(PetscScalar)*nxi,&xi);CHKERRQ(ierr);
    ierr = PetscMalloc(sizeof(PetscScalar)*neta,&eta);CHKERRQ(ierr);
    for (li=0; li<nxi; li++) {
      xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
    }
    for (lj=0; lj<neta; lj++) {
      eta[lj] = -1.0 + (PetscScalar)lj*(2.0/(PetscScalar)(neta-1));
    }

    /* loop over local fine grid nodes setting interpolation for those*/
    for (j=j_start; j<j_start+n_f; j++) {
      for (i=i_start; i<i_start+m_f; i++) {
        /* convert to local "natural" numbering and then to PETSc global numbering */
        row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
        
        i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
        j_c = (j/ratioj);    /* coarse grid node below fine grid node */
        
        /* remainders */
        li = i - ratioi * (i/ratioi);
        if (i==mx-1){ li = nxi-1; }
        lj = j - ratioj * (j/ratioj);
        if (j==my-1){ lj = neta-1; }
        
        /* corners */
        col     = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
        cols[0] = col_shift + idx_c[col]/dof; /* left, below */
        Ni[0]   = 1.0;
        if ( (li==0) || (li==nxi-1) ) {
          if ( (lj==0) || (lj==neta-1) ) {
            ierr = MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);CHKERRQ(ierr); 
            continue;
          }
        }
        
        /* edges + interior */
        /* remainders */
        if (i==mx-1){ i_c--; }
        if (j==my-1){ j_c--; }

        col     = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
        cols[0] = col_shift + idx_c[col]/dof; /* left, below */
        cols[1] = col_shift + idx_c[col+dof]/dof; /* right, below */
        cols[2] = col_shift + idx_c[col+m_ghost_c*dof]/dof; /* left, above */
        cols[3] = col_shift + idx_c[col+(m_ghost_c+1)*dof]/dof; /* right, above */

        Ni[0] = 0.25*(1.0-xi[li])*(1.0-eta[lj]);
        Ni[1] = 0.25*(1.0+xi[li])*(1.0-eta[lj]);
        Ni[2] = 0.25*(1.0-xi[li])*(1.0+eta[lj]);
        Ni[3] = 0.25*(1.0+xi[li])*(1.0+eta[lj]);

        nc = 0;
        if( PetscAbsScalar(Ni[0])<1.0e-32) { cols[0]=-1; }
        if( PetscAbsScalar(Ni[1])<1.0e-32) { cols[1]=-1; }
        if( PetscAbsScalar(Ni[2])<1.0e-32) { cols[2]=-1; }
        if( PetscAbsScalar(Ni[3])<1.0e-32) { cols[3]=-1; }
        
        ierr = MatSetValues(mat,1,&row,4,cols,Ni,INSERT_VALUES);CHKERRQ(ierr); 
      }
    }
    ierr = PetscFree(xi);CHKERRQ(ierr);
    ierr = PetscFree(eta);CHKERRQ(ierr);
  }  
  if (vcoors) {
    ierr = DMDAVecRestoreArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
    ierr = DMDAVecRestoreArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
  ierr = MatDestroy(&mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* 
       Contributed by Andrei Draganescu <aidraga@sandia.gov>
*/
#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA_2D_Q0"
PetscErrorCode DMGetInterpolation_DA_2D_Q0(DM dac,DM daf,Mat *A)
{
  PetscErrorCode   ierr;
  PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof;
  PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,*dnz,*onz;
  PetscInt         row,col,i_start_ghost,j_start_ghost,cols[4],mx,m_c,my,nc,ratioi,ratioj;
  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;
  PetscMPIInt      size_c,size_f,rank_f;
  PetscScalar      v[4];
  Mat              mat;
  DMDABoundaryType bx,by;

  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,&My,0,0,0,0,0,0,&bx,&by,0,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,&my,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (bx == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in x");
  if (by == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in y");
  ratioi = mx/Mx;
  ratioj = my/My;
  if (ratioi*Mx != mx) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in x");
  if (ratioj*My != my) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in y");
  if (ratioi != 2) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in x must be 2");
  if (ratioj != 2) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in y must be 2");

  ierr = DMDAGetCorners(daf,&i_start,&j_start,0,&m_f,&n_f,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);

  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,0,&m_c,&n_c,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);

  /*
     Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
     The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the 
     processors). It's effective length is hence 4 times its normal length, this is
     why the col_scale is multiplied by the interpolation matrix column sizes.
     sol_shift allows each set of 1/4 processors do its own interpolation using ITS
     copy of the coarse vector. A bit of a hack but you do better.

     In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
  */
  ierr = MPI_Comm_size(((PetscObject)dac)->comm,&size_c);CHKERRQ(ierr);
  ierr = MPI_Comm_size(((PetscObject)daf)->comm,&size_f);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(((PetscObject)daf)->comm,&rank_f);CHKERRQ(ierr);
  col_scale = size_f/size_c;
  col_shift = Mx*My*(rank_f/size_c);

  ierr = MatPreallocateInitialize(((PetscObject)daf)->comm,m_f*n_f,col_scale*m_c*n_c,dnz,onz);CHKERRQ(ierr);
  for (j=j_start; j<j_start+n_f; j++) {
    for (i=i_start; i<i_start+m_f; i++) {
      /* convert to local "natural" numbering and then to PETSc global numbering */
      row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;

      i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
      j_c = (j/ratioj);    /* coarse grid node below fine grid node */

      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\
    j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
      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\
    i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

      /* 
         Only include those interpolation points that are truly 
         nonzero. Note this is very important for final grid lines
         in x and y directions; since they have no right/top neighbors
      */
      nc = 0;
      /* one left and below; or we are right on it */
      col        = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
      cols[nc++] = col_shift + idx_c[col]/dof; 
      ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
    }
  }
  ierr = MatCreate(((PetscObject)daf)->comm,&mat);CHKERRQ(ierr);
  ierr = MatSetSizes(mat,m_f*n_f,col_scale*m_c*n_c,mx*my,col_scale*Mx*My);CHKERRQ(ierr);
  ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);

  /* loop over local fine grid nodes setting interpolation for those*/
  for (j=j_start; j<j_start+n_f; j++) {
    for (i=i_start; i<i_start+m_f; i++) {
      /* convert to local "natural" numbering and then to PETSc global numbering */
      row    = idx_f[dof*(m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;

      i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
      j_c = (j/ratioj);    /* coarse grid node below fine grid node */
      nc = 0;
      /* one left and below; or we are right on it */
      col      = dof*(m_ghost_c*(j_c-j_start_ghost_c) + (i_c-i_start_ghost_c));
      cols[nc] = col_shift + idx_c[col]/dof; 
      v[nc++]  = 1.0;
     
      ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr); 
    }
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
  ierr = MatDestroy(&mat);CHKERRQ(ierr);
  ierr = PetscLogFlops(13.0*m_f*n_f);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* 
       Contributed by Jianming Yang <jianming-yang@uiowa.edu>
*/
#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA_3D_Q0"
PetscErrorCode DMGetInterpolation_DA_3D_Q0(DM dac,DM daf,Mat *A)
{
  PetscErrorCode   ierr;
  PetscInt         i,j,l,i_start,j_start,l_start,m_f,n_f,p_f,Mx,My,Mz,*idx_f,dof;
  PetscInt         m_ghost,n_ghost,p_ghost,*idx_c,m_ghost_c,n_ghost_c,p_ghost_c,nc,*dnz,*onz;
  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;
  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;
  PetscMPIInt      size_c,size_f,rank_f;
  PetscScalar      v[8];
  Mat              mat;
  DMDABoundaryType bx,by,bz;
  
  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,&My,&Mz,0,0,0,0,0,&bx,&by,&bz,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (bx == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in x");
  if (by == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in y");
  if (bz == DMDA_BOUNDARY_PERIODIC) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Cannot handle periodic grid in z");
  ratioi = mx/Mx;
  ratioj = my/My;
  ratiol = mz/Mz;
  if (ratioi*Mx != mx) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in x");
  if (ratioj*My != my) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in y");
  if (ratiol*Mz != mz) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Fine grid points must be multiple of coarse grid points in z");
  if (ratioi != 2 && ratioi != 1) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in x must be 1 or 2");
  if (ratioj != 2 && ratioj != 1) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in y must be 1 or 2");
  if (ratiol != 2 && ratiol != 1) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_WRONG,"Coarsening factor in z must be 1 or 2");

  ierr = DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);

  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
  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);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
  /*
     Used for handling a coarse DMDA that lives on 1/4 the processors of the fine DMDA.
     The coarse vector is then duplicated 4 times (each time it lives on 1/4 of the 
     processors). It's effective length is hence 4 times its normal length, this is
     why the col_scale is multiplied by the interpolation matrix column sizes.
     sol_shift allows each set of 1/4 processors do its own interpolation using ITS
     copy of the coarse vector. A bit of a hack but you do better.

     In the standard case when size_f == size_c col_scale == 1 and col_shift == 0
  */
  ierr = MPI_Comm_size(((PetscObject)dac)->comm,&size_c);CHKERRQ(ierr);
  ierr = MPI_Comm_size(((PetscObject)daf)->comm,&size_f);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(((PetscObject)daf)->comm,&rank_f);CHKERRQ(ierr);
  col_scale = size_f/size_c;
  col_shift = Mx*My*Mz*(rank_f/size_c);

  ierr = MatPreallocateInitialize(((PetscObject)daf)->comm,m_f*n_f*p_f,col_scale*m_c*n_c*p_c,dnz,onz);CHKERRQ(ierr);
  for (l=l_start; l<l_start+p_f; l++) {
    for (j=j_start; j<j_start+n_f; j++) {
      for (i=i_start; i<i_start+m_f; i++) {
	/* convert to local "natural" numbering and then to PETSc global numbering */
	row    = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;

	i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
	j_c = (j/ratioj);    /* coarse grid node below fine grid node */
	l_c = (l/ratiol);   

	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\
    l_start %D l_c %D l_start_ghost_c %D",l_start,l_c,l_start_ghost_c);
	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\
    j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
	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\
    i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);

	/* 
	   Only include those interpolation points that are truly 
	   nonzero. Note this is very important for final grid lines
	   in x and y directions; since they have no right/top neighbors
	*/
	nc = 0;
	/* one left and below; or we are right on it */
	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));
	cols[nc++] = col_shift + idx_c[col]/dof; 
	ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
      }
    }
  }
  ierr = MatCreate(((PetscObject)daf)->comm,&mat);CHKERRQ(ierr);
  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);
  ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);

  /* loop over local fine grid nodes setting interpolation for those*/
  for (l=l_start; l<l_start+p_f; l++) {
    for (j=j_start; j<j_start+n_f; j++) {
      for (i=i_start; i<i_start+m_f; i++) {
	/* convert to local "natural" numbering and then to PETSc global numbering */
	row    = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
	
	i_c = (i/ratioi);    /* coarse grid node to left of fine grid node */
	j_c = (j/ratioj);    /* coarse grid node below fine grid node */
	l_c = (l/ratiol);   
	nc = 0;
	/* one left and below; or we are right on it */
	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));
	cols[nc] = col_shift + idx_c[col]/dof; 
	v[nc++]  = 1.0;
     
	ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr); 
      }
    }
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
  ierr = MatDestroy(&mat);CHKERRQ(ierr);
  ierr = PetscLogFlops(13.0*m_f*n_f*p_f);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA_3D_Q1"
PetscErrorCode DMGetInterpolation_DA_3D_Q1(DM dac,DM daf,Mat *A)
{
  PetscErrorCode   ierr;
  PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof,l;
  PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c,Mz,mz;
  PetscInt         row,col,i_start_ghost,j_start_ghost,cols[8],mx,m_c,my,nc,ratioi,ratioj,ratiok;
  PetscInt         i_c,j_c,i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c;
  PetscInt         l_start,p_f,l_start_ghost,p_ghost,l_start_c,p_c;
  PetscInt         l_start_ghost_c,p_ghost_c,l_c,*dnz,*onz;
  PetscScalar      v[8],x,y,z;
  Mat              mat;
  DMDABoundaryType bx,by,bz;
  DMDACoor3d       ***coors = 0,***ccoors;
  Vec              vcoors,cvcoors;
  DM_DA            *ddc = (DM_DA*)dac->data, *ddf = (DM_DA*)daf->data;
  
  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,&My,&Mz,0,0,0,0,0,&bx,&by,&bz,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (mx == Mx) {
    ratioi = 1;
  } else if (bx == DMDA_BOUNDARY_PERIODIC) {
    ratioi = mx/Mx;
    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);
  } else {
    ratioi = (mx-1)/(Mx-1);
    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);
  }
  if (my == My) {
    ratioj = 1;
  } else if (by == DMDA_BOUNDARY_PERIODIC) {
    ratioj = my/My;
    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);
  } else {
    ratioj = (my-1)/(My-1);
    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);
  }
  if (mz == Mz) {
    ratiok = 1;
  } else if (bz == DMDA_BOUNDARY_PERIODIC) {
    ratiok = mz/Mz;
    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);
  } else {
    ratiok = (mz-1)/(Mz-1);
    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);
  }
  
  ierr = DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
  
  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
  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);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
  
  /* create interpolation matrix, determining exact preallocation */
  ierr = MatPreallocateInitialize(((PetscObject)dac)->comm,m_f*n_f*p_f,m_c*n_c*p_c,dnz,onz);CHKERRQ(ierr);
  /* loop over local fine grid nodes counting interpolating points */
  for (l=l_start; l<l_start+p_f; l++) {
    for (j=j_start; j<j_start+n_f; j++) {
      for (i=i_start; i<i_start+m_f; i++) {
        /* convert to local "natural" numbering and then to PETSc global numbering */
        row = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
        i_c = (i/ratioi);
        j_c = (j/ratioj);
        l_c = (l/ratiok);
        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\
                                            l_start %D l_c %D l_start_ghost_c %D",l_start,l_c,l_start_ghost_c);
        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\
                                            j_start %D j_c %D j_start_ghost_c %D",j_start,j_c,j_start_ghost_c);
        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\
                                            i_start %D i_c %D i_start_ghost_c %D",i_start,i_c,i_start_ghost_c);
        
        /* 
         Only include those interpolation points that are truly 
         nonzero. Note this is very important for final grid lines
         in x and y directions; since they have no right/top neighbors
         */
        nc       = 0;
        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));
        cols[nc++] = idx_c[col]/dof; 
        if (i_c*ratioi != i) { 
          cols[nc++] = idx_c[col+dof]/dof;
        }
        if (j_c*ratioj != j) { 
          cols[nc++] = idx_c[col+m_ghost_c*dof]/dof;
        }
        if (l_c*ratiok != l) { 
          cols[nc++] = idx_c[col+m_ghost_c*n_ghost_c*dof]/dof;
        }
        if (j_c*ratioj != j && i_c*ratioi != i) { 
          cols[nc++] = idx_c[col+(m_ghost_c+1)*dof]/dof;
        }
        if (j_c*ratioj != j && l_c*ratiok != l) { 
          cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)*dof]/dof;
        }
        if (i_c*ratioi != i && l_c*ratiok != l) { 
          cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+1)*dof]/dof;
        }
        if (i_c*ratioi != i && l_c*ratiok != l && j_c*ratioj != j) { 
          cols[nc++] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)*dof]/dof;
        }
        ierr = MatPreallocateSet(row,nc,cols,dnz,onz);CHKERRQ(ierr);
      }
    }
  }
  ierr = MatCreate(((PetscObject)dac)->comm,&mat);CHKERRQ(ierr);
  ierr = MatSetSizes(mat,m_f*n_f*p_f,m_c*n_c*p_c,mx*my*mz,Mx*My*Mz);CHKERRQ(ierr);
  ierr = MatSetType(mat,MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(mat,0,dnz);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(mat,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
  
  ierr = DMDAGetCoordinates(daf,&vcoors);CHKERRQ(ierr);
  if (vcoors) {
    ierr = DMDAGetGhostedCoordinates(dac,&cvcoors);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
    ierr = DMDAVecGetArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
  }
  
  /* loop over local fine grid nodes setting interpolation for those*/
  if (!vcoors) {

    for (l=l_start; l<l_start+p_f; l++) {
      for (j=j_start; j<j_start+n_f; j++) {
        for (i=i_start; i<i_start+m_f; i++) {
          /* convert to local "natural" numbering and then to PETSc global numbering */
          row = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
          
          i_c = (i/ratioi);
          j_c = (j/ratioj);
          l_c = (l/ratiok);
          
        /* 
         Only include those interpolation points that are truly 
         nonzero. Note this is very important for final grid lines
         in x and y directions; since they have no right/top neighbors
         */
          x  = ((double)(i - i_c*ratioi))/((double)ratioi);
          y  = ((double)(j - j_c*ratioj))/((double)ratioj);
          z  = ((double)(l - l_c*ratiok))/((double)ratiok);

          nc = 0;
          /* one left and below; or we are right on it */
          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));
          
          cols[nc] = idx_c[col]/dof; 
          v[nc++]  = .125*(1. - (2.0*x-1.))*(1. - (2.0*y-1.))*(1. - (2.0*z-1.));
          
          if (i_c*ratioi != i) { 
            cols[nc] = idx_c[col+dof]/dof;
            v[nc++]  = .125*(1. + (2.0*x-1.))*(1. - (2.0*y-1.))*(1. - (2.0*z-1.));
          }
          
          if (j_c*ratioj != j) { 
            cols[nc] = idx_c[col+m_ghost_c*dof]/dof;
            v[nc++]  = .125*(1. - (2.0*x-1.))*(1. + (2.0*y-1.))*(1. - (2.0*z-1.));
          }
          
          if (l_c*ratiok != l) { 
            cols[nc] = idx_c[col+m_ghost_c*n_ghost_c*dof]/dof;
            v[nc++]  = .125*(1. - (2.0*x-1.))*(1. - (2.0*y-1.))*(1. + (2.0*z-1.));
          }
          
          if (j_c*ratioj != j && i_c*ratioi != i) { 
            cols[nc] = idx_c[col+(m_ghost_c+1)*dof]/dof;
            v[nc++]  = .125*(1. + (2.0*x-1.))*(1. + (2.0*y-1.))*(1. - (2.0*z-1.));
          }
          
          if (j_c*ratioj != j && l_c*ratiok != l) { 
            cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)*dof]/dof;
            v[nc++]  = .125*(1. - (2.0*x-1.))*(1. + (2.0*y-1.))*(1. + (2.0*z-1.));
          }
          
          if (i_c*ratioi != i && l_c*ratiok != l) { 
            cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+1)*dof]/dof;
            v[nc++]  = .125*(1. + (2.0*x-1.))*(1. - (2.0*y-1.))*(1. + (2.0*z-1.));
          }
          
          if (i_c*ratioi != i && l_c*ratiok != l && j_c*ratioj != j) { 
            cols[nc] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)*dof]/dof;
            v[nc++]  = .125*(1. + (2.0*x-1.))*(1. + (2.0*y-1.))*(1. + (2.0*z-1.));
          }
          ierr = MatSetValues(mat,1,&row,nc,cols,v,INSERT_VALUES);CHKERRQ(ierr); 
        }
      }
    }
    
  } else {
    PetscScalar    *xi,*eta,*zeta;
    PetscInt       li,nxi,lj,neta,lk,nzeta,n;
    PetscScalar    Ni[8];
    
    /* compute local coordinate arrays */
    nxi   = ratioi + 1;
    neta  = ratioj + 1;
    nzeta = ratiok + 1;
    ierr = PetscMalloc(sizeof(PetscScalar)*nxi,&xi);CHKERRQ(ierr);
    ierr = PetscMalloc(sizeof(PetscScalar)*neta,&eta);CHKERRQ(ierr);
    ierr = PetscMalloc(sizeof(PetscScalar)*nzeta,&zeta);CHKERRQ(ierr);
    for (li=0; li<nxi; li++) {
      xi[li] = -1.0 + (PetscScalar)li*(2.0/(PetscScalar)(nxi-1));
    }
    for (lj=0; lj<neta; lj++) {
      eta[lj] = -1.0 + (PetscScalar)lj*(2.0/(PetscScalar)(neta-1));
    }
    for (lk=0; lk<nzeta; lk++) {
      zeta[lk] = -1.0 + (PetscScalar)lk*(2.0/(PetscScalar)(nzeta-1));
    }
    
    for (l=l_start; l<l_start+p_f; l++) {
      for (j=j_start; j<j_start+n_f; j++) {
        for (i=i_start; i<i_start+m_f; i++) {
          /* convert to local "natural" numbering and then to PETSc global numbering */
          row = idx_f[dof*(m_ghost*n_ghost*(l-l_start_ghost) + m_ghost*(j-j_start_ghost) + (i-i_start_ghost))]/dof;
          
          i_c = (i/ratioi);
          j_c = (j/ratioj);
          l_c = (l/ratiok);

          /* remainders */
          li = i - ratioi * (i/ratioi);
          if (i==mx-1){ li = nxi-1; }
          lj = j - ratioj * (j/ratioj);
          if (j==my-1){ lj = neta-1; }
          lk = l - ratiok * (l/ratiok);
          if (l==mz-1){ lk = nzeta-1; }
          
          /* corners */
          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));
          cols[0] = idx_c[col]/dof; 
          Ni[0]   = 1.0;
          if ( (li==0) || (li==nxi-1) ) {
            if ( (lj==0) || (lj==neta-1) ) {
              if ( (lk==0) || (lk==nzeta-1) ) {
                ierr = MatSetValue(mat,row,cols[0],Ni[0],INSERT_VALUES);CHKERRQ(ierr);
                continue;
              }
            }
          }
          
          /* edges + interior */
          /* remainders */
          if (i==mx-1){ i_c--; }
          if (j==my-1){ j_c--; }
          if (l==mz-1){ l_c--; }
          
          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));
          cols[0] = idx_c[col]/dof; /* one left and below; or we are right on it */
          cols[1] = idx_c[col+dof]/dof; /* one right and below */
          cols[2] = idx_c[col+m_ghost_c*dof]/dof;  /* one left and above */
          cols[3] = idx_c[col+(m_ghost_c+1)*dof]/dof; /* one right and above */

          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 */
          cols[5] = idx_c[col+(m_ghost_c*n_ghost_c+1)*dof]/dof; /* one right and below, and front */
          cols[6] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c)*dof]/dof;/* one left and above and front*/
          cols[7] = idx_c[col+(m_ghost_c*n_ghost_c+m_ghost_c+1)*dof]/dof; /* one right and above and front */

          Ni[0] = 0.125*(1.0-xi[li])*(1.0-eta[lj])*(1.0-zeta[lk]);
          Ni[1] = 0.125*(1.0+xi[li])*(1.0-eta[lj])*(1.0-zeta[lk]);
          Ni[2] = 0.125*(1.0-xi[li])*(1.0+eta[lj])*(1.0-zeta[lk]);
          Ni[3] = 0.125*(1.0+xi[li])*(1.0+eta[lj])*(1.0-zeta[lk]);

          Ni[4] = 0.125*(1.0-xi[li])*(1.0-eta[lj])*(1.0+zeta[lk]);
          Ni[5] = 0.125*(1.0+xi[li])*(1.0-eta[lj])*(1.0+zeta[lk]);
          Ni[6] = 0.125*(1.0-xi[li])*(1.0+eta[lj])*(1.0+zeta[lk]);
          Ni[7] = 0.125*(1.0+xi[li])*(1.0+eta[lj])*(1.0+zeta[lk]);

          for (n=0; n<8; n++) {
            if( PetscAbsScalar(Ni[n])<1.0e-32) { cols[n]=-1; }
          }
          ierr = MatSetValues(mat,1,&row,8,cols,Ni,INSERT_VALUES);CHKERRQ(ierr); 
          
        }
      }
    }
    ierr = PetscFree(xi);CHKERRQ(ierr);
    ierr = PetscFree(eta);CHKERRQ(ierr);
    ierr = PetscFree(zeta);CHKERRQ(ierr);
  }
  
  if (vcoors) {
    ierr = DMDAVecRestoreArray(ddf->da_coordinates,vcoors,&coors);CHKERRQ(ierr);
    ierr = DMDAVecRestoreArray(ddc->da_coordinates,cvcoors,&ccoors);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  
  ierr = MatCreateMAIJ(mat,dof,A);CHKERRQ(ierr);
  ierr = MatDestroy(&mat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInterpolation_DA"
PetscErrorCode  DMGetInterpolation_DA(DM dac,DM daf,Mat *A,Vec *scale)
{
  PetscErrorCode   ierr;
  PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc,dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
  DMDABoundaryType bxc,byc,bzc,bxf,byf,bzf;
  DMDAStencilType  stc,stf;
  DM_DA            *ddc = (DM_DA*)dac->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dac,DM_CLASSID,1);
  PetscValidHeaderSpecific(daf,DM_CLASSID,2);
  PetscValidPointer(A,3);
  if (scale) PetscValidPointer(scale,4);

  ierr = DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);CHKERRQ(ierr);
  if (dimc != dimf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Dimensions of DMDA do not match %D %D",dimc,dimf);CHKERRQ(ierr);
  if (dofc != doff) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"DOF of DMDA do not match %D %D",dofc,doff);CHKERRQ(ierr);
  if (sc != sf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil width of DMDA do not match %D %D",sc,sf);CHKERRQ(ierr);
  if (bxc != bxf || byc != byf || bzc != bzf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Boundary type different in two DMDAs");CHKERRQ(ierr);
  if (stc != stf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil type different in two DMDAs");CHKERRQ(ierr);
  if (Mc < 2 && Mf > 1) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in x direction");
  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");
  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");

  if (ddc->interptype == DMDA_Q1){
    if (dimc == 1){
      ierr = DMGetInterpolation_DA_1D_Q1(dac,daf,A);CHKERRQ(ierr);
    } else if (dimc == 2){
      ierr = DMGetInterpolation_DA_2D_Q1(dac,daf,A);CHKERRQ(ierr);
    } else if (dimc == 3){
      ierr = DMGetInterpolation_DA_3D_Q1(dac,daf,A);CHKERRQ(ierr);
    } else {
      SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_SUP,"No support for this DMDA dimension %D for interpolation type %d",dimc,(int)ddc->interptype);
    }
  } else if (ddc->interptype == DMDA_Q0){
    if (dimc == 1){
      ierr = DMGetInterpolation_DA_1D_Q0(dac,daf,A);CHKERRQ(ierr);
    } else if (dimc == 2){
       ierr = DMGetInterpolation_DA_2D_Q0(dac,daf,A);CHKERRQ(ierr);
    } else if (dimc == 3){
       ierr = DMGetInterpolation_DA_3D_Q0(dac,daf,A);CHKERRQ(ierr);
    } else {
      SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_SUP,"No support for this DMDA dimension %D for interpolation type %d",dimc,(int)ddc->interptype);
    }
  }
  if (scale) {
    ierr = DMGetInterpolationScale((DM)dac,(DM)daf,*A,scale);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
} 

#undef __FUNCT__  
#define __FUNCT__ "DMGetInjection_DA_1D"
PetscErrorCode DMGetInjection_DA_1D(DM dac,DM daf,VecScatter *inject)
{
    PetscErrorCode   ierr;
    PetscInt         i,i_start,m_f,Mx,*idx_f,dof;
    PetscInt         m_ghost,*idx_c,m_ghost_c;
    PetscInt         row,i_start_ghost,mx,m_c,nc,ratioi;
    PetscInt         i_start_c,i_start_ghost_c;
    PetscInt         *cols;
    DMDABoundaryType bx;
    Vec              vecf,vecc;
    IS               isf;
    
    PetscFunctionBegin;
    ierr = DMDAGetInfo(dac,0,&Mx,0,0,0,0,0,0,0,&bx,0,0,0);CHKERRQ(ierr);
    ierr = DMDAGetInfo(daf,0,&mx,0,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
    if (bx == DMDA_BOUNDARY_PERIODIC) {
        ratioi = mx/Mx;
        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);
    } else {
        ratioi = (mx-1)/(Mx-1);
        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);
    }
   
    ierr = DMDAGetCorners(daf,&i_start,0,0,&m_f,0,0);CHKERRQ(ierr);
    ierr = DMDAGetGhostCorners(daf,&i_start_ghost,0,0,&m_ghost,0,0);CHKERRQ(ierr);
    ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);
    
    ierr = DMDAGetCorners(dac,&i_start_c,0,0,&m_c,0,0);CHKERRQ(ierr);
    ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,0,0,&m_ghost_c,0,0);CHKERRQ(ierr);
    ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);
    
    
    /* loop over local fine grid nodes setting interpolation for those*/
    nc = 0;
    ierr = PetscMalloc(m_f*sizeof(PetscInt),&cols);CHKERRQ(ierr);
   
   
    for (i=i_start_c; i<i_start_c+m_c; i++) {
        PetscInt i_f = i*ratioi;

           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\
 i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
            row = idx_f[dof*(i_f-i_start_ghost)];
            cols[nc++] = row/dof;
    }
   

    ierr = ISCreateBlock(((PetscObject)daf)->comm,dof,nc,cols,PETSC_OWN_POINTER,&isf);CHKERRQ(ierr);
    ierr = DMGetGlobalVector(dac,&vecc);CHKERRQ(ierr);
    ierr = DMGetGlobalVector(daf,&vecf);CHKERRQ(ierr);
    ierr = VecScatterCreate(vecf,isf,vecc,PETSC_NULL,inject);CHKERRQ(ierr);
    ierr = DMRestoreGlobalVector(dac,&vecc);CHKERRQ(ierr);
    ierr = DMRestoreGlobalVector(daf,&vecf);CHKERRQ(ierr);
    ierr = ISDestroy(&isf);CHKERRQ(ierr);
    PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInjection_DA_2D"
PetscErrorCode DMGetInjection_DA_2D(DM dac,DM daf,VecScatter *inject)
{
  PetscErrorCode   ierr;
  PetscInt         i,j,i_start,j_start,m_f,n_f,Mx,My,*idx_f,dof;
  PetscInt         m_ghost,n_ghost,*idx_c,m_ghost_c,n_ghost_c;
  PetscInt         row,i_start_ghost,j_start_ghost,mx,m_c,my,nc,ratioi,ratioj;
  PetscInt         i_start_c,j_start_c,n_c,i_start_ghost_c,j_start_ghost_c;
  PetscInt         *cols;
  DMDABoundaryType bx,by;
  Vec              vecf,vecc;
  IS               isf;

  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,&My,0,0,0,0,0,0,&bx,&by,0,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,&my,0,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);
  if (bx == DMDA_BOUNDARY_PERIODIC) {
    ratioi = mx/Mx;
    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);
  } else {
    ratioi = (mx-1)/(Mx-1);
    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);
  }
  if (by == DMDA_BOUNDARY_PERIODIC) {
    ratioj = my/My;
    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);
  } else {
    ratioj = (my-1)/(My-1);
    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);
  }

  ierr = DMDAGetCorners(daf,&i_start,&j_start,0,&m_f,&n_f,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,0,&m_ghost,&n_ghost,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);

  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,0,&m_c,&n_c,0);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(dac,&i_start_ghost_c,&j_start_ghost_c,0,&m_ghost_c,&n_ghost_c,0);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);


  /* loop over local fine grid nodes setting interpolation for those*/
  nc = 0;
  ierr = PetscMalloc(n_f*m_f*sizeof(PetscInt),&cols);CHKERRQ(ierr);
  for (j=j_start_c; j<j_start_c+n_c; j++) {
    for (i=i_start_c; i<i_start_c+m_c; i++) {
      PetscInt i_f = i*ratioi,j_f = j*ratioj;
      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\
    j_c %D j_f %D fine ghost range [%D,%D]",j,j_f,j_start_ghost,j_start_ghost+n_ghost);
      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\
    i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
      row = idx_f[dof*(m_ghost*(j_f-j_start_ghost) + (i_f-i_start_ghost))];
      cols[nc++] = row/dof;
    }
  }

  ierr = ISCreateBlock(((PetscObject)daf)->comm,dof,nc,cols,PETSC_OWN_POINTER,&isf);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(dac,&vecc);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(daf,&vecf);CHKERRQ(ierr);
  ierr = VecScatterCreate(vecf,isf,vecc,PETSC_NULL,inject);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(dac,&vecc);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(daf,&vecf);CHKERRQ(ierr);
  ierr = ISDestroy(&isf);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInjection_DA_3D"
PetscErrorCode DMGetInjection_DA_3D(DM dac,DM daf,VecScatter *inject)
{
  PetscErrorCode   ierr;
  PetscInt         i,j,k,i_start,j_start,k_start,m_f,n_f,p_f,Mx,My,Mz;
  PetscInt         m_ghost,n_ghost,p_ghost,m_ghost_c,n_ghost_c,p_ghost_c;
  PetscInt         i_start_ghost,j_start_ghost,k_start_ghost;
  PetscInt         mx,my,mz,ratioi,ratioj,ratiok;
  PetscInt         i_start_c,j_start_c,k_start_c;
  PetscInt         m_c,n_c,p_c;
  PetscInt         i_start_ghost_c,j_start_ghost_c,k_start_ghost_c;
  PetscInt         row,nc,dof;
  PetscInt         *idx_c,*idx_f;
  PetscInt         *cols;
  DMDABoundaryType bx,by,bz;
  Vec              vecf,vecc;
  IS               isf;

  PetscFunctionBegin;
  ierr = DMDAGetInfo(dac,0,&Mx,&My,&Mz,0,0,0,0,0,&bx,&by,&bz,0);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,0,&mx,&my,&mz,0,0,0,&dof,0,0,0,0,0);CHKERRQ(ierr);

  if (bx == DMDA_BOUNDARY_PERIODIC){
    ratioi = mx/Mx;
    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);
  } else {
    ratioi = (mx-1)/(Mx-1);
    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);
  }
  if (by == DMDA_BOUNDARY_PERIODIC){
    ratioj = my/My;
    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);
  } else {
    ratioj = (my-1)/(My-1);
    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);
  }
  if (bz == DMDA_BOUNDARY_PERIODIC){
    ratiok = mz/Mz;
    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);
  } else {
    ratiok = (mz-1)/(Mz-1);
    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);
  }

  ierr = DMDAGetCorners(daf,&i_start,&j_start,&k_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&k_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);

  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&k_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
  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);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);


  /* loop over local fine grid nodes setting interpolation for those*/
  nc = 0;
  ierr = PetscMalloc(n_f*m_f*p_f*sizeof(PetscInt),&cols);CHKERRQ(ierr);
  for (k=k_start_c; k<k_start_c+p_c; k++) {
    for (j=j_start_c; j<j_start_c+n_c; j++) {
      for (i=i_start_c; i<i_start_c+m_c; i++) {
        PetscInt i_f = i*ratioi,j_f = j*ratioj,k_f = k*ratiok;
        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  "
                                                                          "k_c %D k_f %D fine ghost range [%D,%D]",k,k_f,k_start_ghost,k_start_ghost+p_ghost);
        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  "
                                                                          "j_c %D j_f %D fine ghost range [%D,%D]",j,j_f,j_start_ghost,j_start_ghost+n_ghost);
        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  "
                                                                          "i_c %D i_f %D fine ghost range [%D,%D]",i,i_f,i_start_ghost,i_start_ghost+m_ghost);
        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))];
        cols[nc++] = row/dof;
      }
    }
  }

  ierr = ISCreateBlock(((PetscObject)daf)->comm,dof,nc,cols,PETSC_OWN_POINTER,&isf);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(dac,&vecc);CHKERRQ(ierr);
  ierr = DMGetGlobalVector(daf,&vecf);CHKERRQ(ierr);
  ierr = VecScatterCreate(vecf,isf,vecc,PETSC_NULL,inject);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(dac,&vecc);CHKERRQ(ierr);
  ierr = DMRestoreGlobalVector(daf,&vecf);CHKERRQ(ierr);
  ierr = ISDestroy(&isf);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetInjection_DA"
PetscErrorCode  DMGetInjection_DA(DM dac,DM daf,VecScatter *inject)
{
  PetscErrorCode   ierr;
  PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc,dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
  DMDABoundaryType bxc,byc,bzc,bxf,byf,bzf;
  DMDAStencilType  stc,stf;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dac,DM_CLASSID,1);
  PetscValidHeaderSpecific(daf,DM_CLASSID,2);
  PetscValidPointer(inject,3);

  ierr = DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);CHKERRQ(ierr);
  if (dimc != dimf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Dimensions of DMDA do not match %D %D",dimc,dimf);CHKERRQ(ierr);
  if (dofc != doff) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"DOF of DMDA do not match %D %D",dofc,doff);CHKERRQ(ierr);
  if (sc != sf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil width of DMDA do not match %D %D",sc,sf);CHKERRQ(ierr);
  if (bxc != bxf || byc != byf || bzc != bzf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Boundary type different in two DMDAs");CHKERRQ(ierr);
  if (stc != stf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil type different in two DMDAs");CHKERRQ(ierr);
  if (Mc < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in x direction");
  if (dimc > 1 && Nc < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in y direction");
  if (dimc > 2 && Pc < 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Coarse grid requires at least 2 points in z direction");

  if (dimc == 1){
    ierr = DMGetInjection_DA_1D(dac,daf,inject);CHKERRQ(ierr);
  } else if (dimc == 2) {
    ierr = DMGetInjection_DA_2D(dac,daf,inject);CHKERRQ(ierr);
  } else if (dimc == 3) {
    ierr = DMGetInjection_DA_3D(dac,daf,inject);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__  
#define __FUNCT__ "DMGetAggregates_DA"
PetscErrorCode  DMGetAggregates_DA(DM dac,DM daf,Mat *rest)
{
  PetscErrorCode   ierr;
  PetscInt         dimc,Mc,Nc,Pc,mc,nc,pc,dofc,sc;
  PetscInt         dimf,Mf,Nf,Pf,mf,nf,pf,doff,sf;
  DMDABoundaryType bxc,byc,bzc,bxf,byf,bzf;
  DMDAStencilType  stc,stf;
  PetscInt         i,j,l;
  PetscInt         i_start,j_start,l_start, m_f,n_f,p_f;
  PetscInt         i_start_ghost,j_start_ghost,l_start_ghost,m_ghost,n_ghost,p_ghost;
  PetscInt         *idx_f;
  PetscInt         i_c,j_c,l_c;
  PetscInt         i_start_c,j_start_c,l_start_c, m_c,n_c,p_c;
  PetscInt         i_start_ghost_c,j_start_ghost_c,l_start_ghost_c,m_ghost_c,n_ghost_c,p_ghost_c;
  PetscInt         *idx_c;
  PetscInt         d;
  PetscInt         a;
  PetscInt         max_agg_size;
  PetscInt         *fine_nodes;
  PetscScalar      *one_vec;
  PetscInt         fn_idx;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dac,DM_CLASSID,1);
  PetscValidHeaderSpecific(daf,DM_CLASSID,2);
  PetscValidPointer(rest,3);

  ierr = DMDAGetInfo(dac,&dimc,&Mc,&Nc,&Pc,&mc,&nc,&pc,&dofc,&sc,&bxc,&byc,&bzc,&stc);CHKERRQ(ierr);
  ierr = DMDAGetInfo(daf,&dimf,&Mf,&Nf,&Pf,&mf,&nf,&pf,&doff,&sf,&bxf,&byf,&bzf,&stf);CHKERRQ(ierr);
  if (dimc != dimf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Dimensions of DMDA do not match %D %D",dimc,dimf);CHKERRQ(ierr);
  if (dofc != doff) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"DOF of DMDA do not match %D %D",dofc,doff);CHKERRQ(ierr);
  if (sc != sf) SETERRQ2(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil width of DMDA do not match %D %D",sc,sf);CHKERRQ(ierr);
  if (bxc != bxf || byc != byf || bzc != bzf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Boundary type different in two DMDAs");CHKERRQ(ierr);
  if (stc != stf) SETERRQ(((PetscObject)daf)->comm,PETSC_ERR_ARG_INCOMP,"Stencil type different in two DMDAs");CHKERRQ(ierr);

  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);
  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);
  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);

  if (Pc < 0) Pc = 1;
  if (Pf < 0) Pf = 1;
  if (Nc < 0) Nc = 1;
  if (Nf < 0) Nf = 1;

  ierr = DMDAGetCorners(daf,&i_start,&j_start,&l_start,&m_f,&n_f,&p_f);CHKERRQ(ierr);
  ierr = DMDAGetGhostCorners(daf,&i_start_ghost,&j_start_ghost,&l_start_ghost,&m_ghost,&n_ghost,&p_ghost);CHKERRQ(ierr);
  ierr = DMDAGetGlobalIndices(daf,PETSC_NULL,&idx_f);CHKERRQ(ierr);

  ierr = DMDAGetCorners(dac,&i_start_c,&j_start_c,&l_start_c,&m_c,&n_c,&p_c);CHKERRQ(ierr);
  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);
  ierr = DMDAGetGlobalIndices(dac,PETSC_NULL,&idx_c);CHKERRQ(ierr);

  /* 
     Basic idea is as follows. Here's a 2D example, suppose r_x, r_y are the ratios
     for dimension 1 and 2 respectively.
     Let (i,j) be a coarse grid node. All the fine grid nodes between r_x*i and r_x*(i+1)
     and r_y*j and r_y*(j+1) will be grouped into the same coarse grid agregate.
     Each specific dof on the fine grid is mapped to one dof on the coarse grid.
  */

  max_agg_size = (Mf/Mc+1)*(Nf/Nc+1)*(Pf/Pc+1);

  /* create the matrix that will contain the restriction operator */
  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,
			  max_agg_size, PETSC_NULL, max_agg_size, PETSC_NULL, rest);CHKERRQ(ierr);

  /* store nodes in the fine grid here */
  ierr = PetscMalloc2(max_agg_size,PetscScalar, &one_vec,max_agg_size,PetscInt, &fine_nodes);CHKERRQ(ierr);
  for(i=0; i<max_agg_size; i++) one_vec[i] = 1.0;  
  
  /* loop over all coarse nodes */
  for (l_c=l_start_c; l_c<l_start_c+p_c; l_c++) {
    for (j_c=j_start_c; j_c<j_start_c+n_c; j_c++) {
      for (i_c=i_start_c; i_c<i_start_c+m_c; i_c++) {
	for(d=0; d<dofc; d++) {
	  /* convert to local "natural" numbering and then to PETSc global numbering */
	  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;

	  fn_idx = 0;
	  /* Corresponding fine points are all points (i_f, j_f, l_f) such that
	     i_c*Mf/Mc <= i_f < (i_c+1)*Mf/Mc
	     (same for other dimensions)
	  */
	  for (l=l_c*Pf/Pc; l<PetscMin((l_c+1)*Pf/Pc,Pf); l++) {
	    for (j=j_c*Nf/Nc; j<PetscMin((j_c+1)*Nf/Nc,Nf); j++) {
	      for (i=i_c*Mf/Mc; i<PetscMin((i_c+1)*Mf/Mc,Mf); i++) {
		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;
		fn_idx++;
	      }
	    }
	  }
	  /* add all these points to one aggregate */
	  ierr = MatSetValues(*rest, 1, &a, fn_idx, fine_nodes, one_vec, INSERT_VALUES);CHKERRQ(ierr);
	}
      }
    }
  }
  ierr = PetscFree2(one_vec,fine_nodes);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(*rest, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*rest, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}