xref: /petsc/src/dm/impls/da/da.c (revision 20f4b53cbb5e9bd9ef12b76a8697d60d197cda17)

#include <petsc/private/dmdaimpl.h> /*I   "petscdmda.h"   I*/

/*@
  DMDASetSizes - Sets the number of grid points in the three dimensional directions

  Logically Collective

  Input Parameters:
+ da - the `DMDA`
. M - the global X size
. N - the global Y size
- P - the global Z size

  Level: intermediate

  Developer Note:
  Since the dimension may not yet have been set the code cannot error check for non-positive Y and Z number of grid points

.seealso: `DM`, `DMDA`, `PetscSplitOwnership()`
@*/
PetscErrorCode DMDASetSizes(DM da, PetscInt M, PetscInt N, PetscInt P)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, M, 2);
  PetscValidLogicalCollectiveInt(da, N, 3);
  PetscValidLogicalCollectiveInt(da, P, 4);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  PetscCheck(M >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_SIZ, "Number of grid points in X direction must be positive");
  PetscCheck(N >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_SIZ, "Number of grid points in Y direction must be positive");
  PetscCheck(P >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_SIZ, "Number of grid points in Z direction must be positive");

  dd->M = M;
  dd->N = N;
  dd->P = P;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetNumProcs - Sets the number of processes in each dimension

  Logically Collective

  Input Parameters:
+ da - the `DMDA`
. m - the number of X procs (or `PETSC_DECIDE`)
. n - the number of Y procs (or `PETSC_DECIDE`)
- p - the number of Z procs (or `PETSC_DECIDE`)

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDASetSizes()`, `PetscSplitOwnership()`
@*/
PetscErrorCode DMDASetNumProcs(DM da, PetscInt m, PetscInt n, PetscInt p)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, m, 2);
  PetscValidLogicalCollectiveInt(da, n, 3);
  PetscValidLogicalCollectiveInt(da, p, 4);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  dd->m = m;
  dd->n = n;
  dd->p = p;
  if (da->dim == 2) {
    PetscMPIInt size;
    PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)da), &size));
    if ((dd->m > 0) && (dd->n < 0)) {
      dd->n = size / dd->m;
      PetscCheck(dd->n * dd->m == size, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_OUTOFRANGE, "%" PetscInt_FMT " processes in X direction not divisible into comm size %d", m, size);
    }
    if ((dd->n > 0) && (dd->m < 0)) {
      dd->m = size / dd->n;
      PetscCheck(dd->n * dd->m == size, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_OUTOFRANGE, "%" PetscInt_FMT " processes in Y direction not divisible into comm size %d", n, size);
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetBoundaryType - Sets the type of ghost nodes on domain boundaries.

  Not Collective

  Input Parameters:
+ da    - The `DMDA`
- bx,by,bz - One of `DM_BOUNDARY_NONE`, `DM_BOUNDARY_GHOSTED`, `DM_BOUNDARY_PERIODIC`

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDACreate()`, `DMDestroy()`, `DMBoundaryType`
@*/
PetscErrorCode DMDASetBoundaryType(DM da, DMBoundaryType bx, DMBoundaryType by, DMBoundaryType bz)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveEnum(da, bx, 2);
  PetscValidLogicalCollectiveEnum(da, by, 3);
  PetscValidLogicalCollectiveEnum(da, bz, 4);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  dd->bx = bx;
  dd->by = by;
  dd->bz = bz;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetDof - Sets the number of degrees of freedom per vertex

  Not Collective

  Input Parameters:
+ da  - The `DMDA`
- dof - Number of degrees of freedom

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDAGetDof()`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDASetDof(DM da, PetscInt dof)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, dof, 2);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  dd->w  = dof;
  da->bs = dof;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetDof - Gets the number of degrees of freedom per vertex

  Not Collective

  Input Parameter:
. da  - The `DMDA`

  Output Parameter:
. dof - Number of degrees of freedom

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDASetDof()`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDAGetDof(DM da, PetscInt *dof)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidIntPointer(dof, 2);
  *dof = dd->w;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetOverlap - Gets the size of the per-processor overlap.

  Not Collective

  Input Parameter:
. da  - The `DMDA`

  Output Parameters:
+ x   - Overlap in the x direction
. y   - Overlap in the y direction
- z   - Overlap in the z direction

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMCreateDomainDecomposition()`, `DMDASetOverlap()`
@*/
PetscErrorCode DMDAGetOverlap(DM da, PetscInt *x, PetscInt *y, PetscInt *z)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  if (x) *x = dd->xol;
  if (y) *y = dd->yol;
  if (z) *z = dd->zol;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetOverlap - Sets the size of the per-processor overlap.

  Not Collective

  Input Parameters:
+ da  - The `DMDA`
. x   - Overlap in the x direction
. y   - Overlap in the y direction
- z   - Overlap in the z direction

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMCreateDomainDecomposition()`, `DMDAGetOverlap()`
@*/
PetscErrorCode DMDASetOverlap(DM da, PetscInt x, PetscInt y, PetscInt z)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, x, 2);
  PetscValidLogicalCollectiveInt(da, y, 3);
  PetscValidLogicalCollectiveInt(da, z, 4);
  dd->xol = x;
  dd->yol = y;
  dd->zol = z;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetNumLocalSubDomains - Gets the number of local subdomains created upon decomposition.

  Not Collective

  Input Parameters:
. da  - The `DMDA`

  Output Parameters:
. Nsub   - Number of local subdomains created upon decomposition

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMCreateDomainDecomposition()`, `DMDASetNumLocalSubDomains()`
@*/
PetscErrorCode DMDAGetNumLocalSubDomains(DM da, PetscInt *Nsub)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  if (Nsub) *Nsub = dd->Nsub;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetNumLocalSubDomains - Sets the number of local subdomains created upon decomposition.

  Not Collective

  Input Parameters:
+ da  - The `DMDA`
- Nsub - The number of local subdomains requested

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMCreateDomainDecomposition()`, `DMDAGetNumLocalSubDomains()`
@*/
PetscErrorCode DMDASetNumLocalSubDomains(DM da, PetscInt Nsub)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, Nsub, 2);
  dd->Nsub = Nsub;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetOffset - Sets the index offset of the DA.

  Collective

  Input Parameters:
+ da  - The `DMDA`
. xo  - The offset in the x direction
. yo  - The offset in the y direction
- zo  - The offset in the z direction

  Level: intermediate

  Note:
    This is used primarily to overlap a computation on a local `DMDA` with that on a global `DMDA` without
  changing boundary conditions or subdomain features that depend upon the global offsets.

.seealso: `DM`, `DMDA`, `DMDAGetOffset()`, `DMDAVecGetArray()`
@*/
PetscErrorCode DMDASetOffset(DM da, PetscInt xo, PetscInt yo, PetscInt zo, PetscInt Mo, PetscInt No, PetscInt Po)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, xo, 2);
  PetscValidLogicalCollectiveInt(da, yo, 3);
  PetscValidLogicalCollectiveInt(da, zo, 4);
  PetscValidLogicalCollectiveInt(da, Mo, 5);
  PetscValidLogicalCollectiveInt(da, No, 6);
  PetscValidLogicalCollectiveInt(da, Po, 7);
  dd->xo = xo;
  dd->yo = yo;
  dd->zo = zo;
  dd->Mo = Mo;
  dd->No = No;
  dd->Po = Po;

  if (da->coordinates[0].dm) PetscCall(DMDASetOffset(da->coordinates[0].dm, xo, yo, zo, Mo, No, Po));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetOffset - Gets the index offset of the `DMDA`.

  Not Collective

  Input Parameter:
. da  - The `DMDA`

  Output Parameters:
+ xo  - The offset in the x direction
. yo  - The offset in the y direction
. zo  - The offset in the z direction
. Mo  - The global size in the x direction
. No  - The global size in the y direction
- Po  - The global size in the z direction

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDASetOffset()`, `DMDAVecGetArray()`
@*/
PetscErrorCode DMDAGetOffset(DM da, PetscInt *xo, PetscInt *yo, PetscInt *zo, PetscInt *Mo, PetscInt *No, PetscInt *Po)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  if (xo) *xo = dd->xo;
  if (yo) *yo = dd->yo;
  if (zo) *zo = dd->zo;
  if (Mo) *Mo = dd->Mo;
  if (No) *No = dd->No;
  if (Po) *Po = dd->Po;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetNonOverlappingRegion - Gets the indices of the nonoverlapping region of a subdomain `DM`.

  Not Collective

  Input Parameter:
. da  - The `DMDA`

  Output Parameters:
+ xs  - The start of the region in x
. ys  - The start of the region in y
. zs  - The start of the region in z
. xs  - The size of the region in x
. ys  - The size of the region in y
- zs  - The size of the region in z

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDAGetOffset()`, `DMDAVecGetArray()`
@*/
PetscErrorCode DMDAGetNonOverlappingRegion(DM da, PetscInt *xs, PetscInt *ys, PetscInt *zs, PetscInt *xm, PetscInt *ym, PetscInt *zm)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  if (xs) *xs = dd->nonxs;
  if (ys) *ys = dd->nonys;
  if (zs) *zs = dd->nonzs;
  if (xm) *xm = dd->nonxm;
  if (ym) *ym = dd->nonym;
  if (zm) *zm = dd->nonzm;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetNonOverlappingRegion - Sets the indices of the nonoverlapping region of a subdomain `DM`.

  Collective

  Input Parameters:
+ da  - The `DMDA`
. xs  - The start of the region in x
. ys  - The start of the region in y
. zs  - The start of the region in z
. xs  - The size of the region in x
. ys  - The size of the region in y
- zs  - The size of the region in z

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDAGetOffset()`, `DMDAVecGetArray()`
@*/
PetscErrorCode DMDASetNonOverlappingRegion(DM da, PetscInt xs, PetscInt ys, PetscInt zs, PetscInt xm, PetscInt ym, PetscInt zm)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, xs, 2);
  PetscValidLogicalCollectiveInt(da, ys, 3);
  PetscValidLogicalCollectiveInt(da, zs, 4);
  PetscValidLogicalCollectiveInt(da, xm, 5);
  PetscValidLogicalCollectiveInt(da, ym, 6);
  PetscValidLogicalCollectiveInt(da, zm, 7);
  dd->nonxs = xs;
  dd->nonys = ys;
  dd->nonzs = zs;
  dd->nonxm = xm;
  dd->nonym = ym;
  dd->nonzm = zm;

  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetStencilType - Sets the type of the communication stencil

  Logically Collective

  Input Parameters:
+ da    - The `DMDA`
- stype - The stencil type, use either `DMDA_STENCIL_BOX` or `DMDA_STENCIL_STAR`.

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDASetStencilType(DM da, DMDAStencilType stype)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveEnum(da, stype, 2);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  dd->stencil_type = stype;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetStencilType - Gets the type of the communication stencil

  Not Collective

  Input Parameter:
. da    - The `DMDA`

  Output Parameter:
. stype - The stencil type, use either `DMDA_STENCIL_BOX` or `DMDA_STENCIL_STAR`.

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDAGetStencilType(DM da, DMDAStencilType *stype)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidPointer(stype, 2);
  *stype = dd->stencil_type;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetStencilWidth - Sets the width of the communication stencil

  Logically Collective

  Input Parameters:
+ da    - The `DMDA`
- width - The stencil width

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDASetStencilWidth(DM da, PetscInt width)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, width, 2);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  dd->s = width;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDAGetStencilWidth - Gets the width of the communication stencil

  Not Collective

  Input Parameter:
. da    - The `DMDA`

  Output Parameter:
. width - The stencil width

  Level: intermediate

.seealso: `DM`, `DMDA`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDAGetStencilWidth(DM da, PetscInt *width)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidIntPointer(width, 2);
  *width = dd->s;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode DMDACheckOwnershipRanges_Private(DM da, PetscInt M, PetscInt m, const PetscInt lx[])
{
  PetscInt i, sum;

  PetscFunctionBegin;
  PetscCheck(M >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "Global dimension not set");
  for (i = sum = 0; i < m; i++) sum += lx[i];
  PetscCheck(sum == M, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_INCOMP, "Ownership ranges sum to %" PetscInt_FMT " but global dimension is %" PetscInt_FMT, sum, M);
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  DMDASetOwnershipRanges - Sets the number of nodes in each direction on each process

  Logically Collective

  Input Parameters:
+ da - The `DMDA`
. lx - array containing number of nodes in the X direction on each process, or NULL. If non-null, must be of length da->m
. ly - array containing number of nodes in the Y direction on each process, or NULL. If non-null, must be of length da->n
- lz - array containing number of nodes in the Z direction on each process, or NULL. If non-null, must be of length da->p.

  Level: intermediate

  Note: these numbers are NOT multiplied by the number of dof per node.

.seealso: `DM`, `DMDA`, `DMDACreate()`, `DMDestroy()`
@*/
PetscErrorCode DMDASetOwnershipRanges(DM da, const PetscInt lx[], const PetscInt ly[], const PetscInt lz[])
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscCheck(!da->setupcalled, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "This function must be called before DMSetUp()");
  if (lx) {
    PetscCheck(dd->m >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "Cannot set ownership ranges before setting number of procs");
    PetscCall(DMDACheckOwnershipRanges_Private(da, dd->M, dd->m, lx));
    if (!dd->lx) PetscCall(PetscMalloc1(dd->m, &dd->lx));
    PetscCall(PetscArraycpy(dd->lx, lx, dd->m));
  }
  if (ly) {
    PetscCheck(dd->n >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "Cannot set ownership ranges before setting number of procs");
    PetscCall(DMDACheckOwnershipRanges_Private(da, dd->N, dd->n, ly));
    if (!dd->ly) PetscCall(PetscMalloc1(dd->n, &dd->ly));
    PetscCall(PetscArraycpy(dd->ly, ly, dd->n));
  }
  if (lz) {
    PetscCheck(dd->p >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_WRONGSTATE, "Cannot set ownership ranges before setting number of procs");
    PetscCall(DMDACheckOwnershipRanges_Private(da, dd->P, dd->p, lz));
    if (!dd->lz) PetscCall(PetscMalloc1(dd->p, &dd->lz));
    PetscCall(PetscArraycpy(dd->lz, lz, dd->p));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
       DMDASetInterpolationType - Sets the type of interpolation that will be
          returned by `DMCreateInterpolation()`

   Logically Collective

   Input Parameters:
+  da - initial distributed array
-  ctype - `DMDA_Q1` and `DMDA_Q0` are currently the only supported forms

   Level: intermediate

   Note:
   You should call this on the coarser of the two `DMDA` you pass to `DMCreateInterpolation()`

.seealso: `DM`, `DMDA`, `DMDACreate1d()`, `DMDACreate2d()`, `DMDACreate3d()`, `DMDestroy()`, `DMDAInterpolationType`
@*/
PetscErrorCode DMDASetInterpolationType(DM da, DMDAInterpolationType ctype)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveEnum(da, ctype, 2);
  dd->interptype = ctype;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
       DMDAGetInterpolationType - Gets the type of interpolation that will be
          used by `DMCreateInterpolation()`

   Not Collective

   Input Parameter:
.  da - distributed array

   Output Parameter:
.  ctype - interpolation type (`DMDA_Q1` and `DMDA_Q0` are currently the only supported forms)

   Level: intermediate

.seealso: `DM`, `DMDA`, `DMDAInterpolationType`, `DMDASetInterpolationType()`, `DMCreateInterpolation()`
@*/
PetscErrorCode DMDAGetInterpolationType(DM da, DMDAInterpolationType *ctype)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidPointer(ctype, 2);
  *ctype = dd->interptype;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
      DMDAGetNeighbors - Gets an array containing the MPI rank of all the current
        processes neighbors.

    Not Collective

   Input Parameter:
.     da - the `DMDA` object

   Output Parameters:
.     ranks - the neighbors ranks, stored with the x index increasing most rapidly.
              this process itself is in the list

   Level: intermediate

   Notes:
   In 2d the array is of length 9, in 3d of length 27

   Not supported in 1d

   Do not free the array, it is freed when the `DMDA` is destroyed.

   Fortran Note:
    In fortran you must pass in an array of the appropriate length.

.seealso: `DMDA`, `DM`
@*/
PetscErrorCode DMDAGetNeighbors(DM da, const PetscMPIInt *ranks[])
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  *ranks = dd->neighbors;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
      DMDAGetOwnershipRanges - Gets the ranges of indices in the x, y and z direction that are owned by each process

    Not Collective

   Input Parameter:
.     da - the `DMDA` object

   Output Parameters:
+     lx - ownership along x direction (optional)
.     ly - ownership along y direction (optional)
-     lz - ownership along z direction (optional)

   Level: intermediate

    Note:
    These correspond to the optional final arguments passed to `DMDACreate()`, `DMDACreate2d()`, `DMDACreate3d()`

    In C you should not free these arrays, nor change the values in them. They will only have valid values while the
    `DMDA` they came from still exists (has not been destroyed).

    These numbers are NOT multiplied by the number of dof per node.

    Fortran Note:
    In Fortran one must pass in arrays `lx`, `ly`, and `lz` that are long enough to hold the values; the sixth, seventh and
    eighth arguments from `DMDAGetInfo()`

.seealso: `DM`, `DMDA`, `DMDAGetCorners()`, `DMDAGetGhostCorners()`, `DMDACreate()`, `DMDACreate1d()`, `DMDACreate2d()`, `DMDACreate3d()`, `VecGetOwnershipRanges()`
@*/
PetscErrorCode DMDAGetOwnershipRanges(DM da, const PetscInt *lx[], const PetscInt *ly[], const PetscInt *lz[])
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  if (lx) *lx = dd->lx;
  if (ly) *ly = dd->ly;
  if (lz) *lz = dd->lz;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
     DMDASetRefinementFactor - Set the ratios that the `DMDA` grid is refined

    Logically Collective

  Input Parameters:
+    da - the `DMDA` object
.    refine_x - ratio of fine grid to coarse in x direction (2 by default)
.    refine_y - ratio of fine grid to coarse in y direction (2 by default)
-    refine_z - ratio of fine grid to coarse in z direction (2 by default)

  Options Database Keys:
+  -da_refine_x refine_x - refinement ratio in x direction
.  -da_refine_y rafine_y - refinement ratio in y direction
.  -da_refine_z refine_z - refinement ratio in z direction
-  -da_refine <n> - refine the DMDA object n times when it is created.

  Level: intermediate

    Note:
    Pass `PETSC_IGNORE` to leave a value unchanged

.seealso: `DM`, `DMDA`, `DMRefine()`, `DMDAGetRefinementFactor()`
@*/
PetscErrorCode DMDASetRefinementFactor(DM da, PetscInt refine_x, PetscInt refine_y, PetscInt refine_z)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidLogicalCollectiveInt(da, refine_x, 2);
  PetscValidLogicalCollectiveInt(da, refine_y, 3);
  PetscValidLogicalCollectiveInt(da, refine_z, 4);

  if (refine_x > 0) dd->refine_x = refine_x;
  if (refine_y > 0) dd->refine_y = refine_y;
  if (refine_z > 0) dd->refine_z = refine_z;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
     DMDAGetRefinementFactor - Gets the ratios that the `DMDA` grid is refined

    Not Collective

  Input Parameter:
.    da - the `DMDA` object

  Output Parameters:
+    refine_x - ratio of fine grid to coarse in x direction (2 by default)
.    refine_y - ratio of fine grid to coarse in y direction (2 by default)
-    refine_z - ratio of fine grid to coarse in z direction (2 by default)

  Level: intermediate

    Note:
    Pass `NULL` for values you do not need

.seealso: `DM`, `DMDA`, `DMRefine()`, `DMDASetRefinementFactor()`
@*/
PetscErrorCode DMDAGetRefinementFactor(DM da, PetscInt *refine_x, PetscInt *refine_y, PetscInt *refine_z)
{
  DM_DA *dd = (DM_DA *)da->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  if (refine_x) *refine_x = dd->refine_x;
  if (refine_y) *refine_y = dd->refine_y;
  if (refine_z) *refine_z = dd->refine_z;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@C
     DMDASetGetMatrix - Sets the routine used by the `DMDA` to allocate a matrix.

    Logically Collective; No Fortran Support

  Input Parameters:
+    da - the `DMDA` object
-    f - the function that allocates the matrix for that specific DMDA

  Level: developer

   Note:
    See `DMDASetBlockFills()` that provides a simple way to provide the nonzero structure for
       the diagonal and off-diagonal blocks of the matrix

.seealso: `DM`, `DMDA`, `DMCreateMatrix()`, `DMDASetBlockFills()`
@*/
PetscErrorCode DMDASetGetMatrix(DM da, PetscErrorCode (*f)(DM, Mat *))
{
  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  da->ops->creatematrix = f;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
   DMDAMapMatStencilToGlobal - Map a list of `MatStencil` on a grid to global indices.

   Not Collective

   Input Parameters:
+  da - the `DMDA` object
.  m - number of MatStencils
-  idxm - grid points (and component number when dof > 1)

   Output Parameter:
.  gidxm - global row indices

   Level: intermediate

.seealso: `DM`, `DMDA`, `MatStencil`
@*/
PetscErrorCode DMDAMapMatStencilToGlobal(DM da, PetscInt m, const MatStencil idxm[], PetscInt gidxm[])
{
  const DM_DA           *dd  = (const DM_DA *)da->data;
  const PetscInt        *dxm = (const PetscInt *)idxm;
  PetscInt               i, j, sdim, tmp, dim;
  PetscInt               dims[4], starts[4], dims2[3], starts2[3], dof = dd->w;
  ISLocalToGlobalMapping ltog;

  PetscFunctionBegin;
  if (m <= 0) PetscFunctionReturn(PETSC_SUCCESS);

  /* Code adapted from DMDAGetGhostCorners() */
  starts2[0] = dd->Xs / dof + dd->xo;
  starts2[1] = dd->Ys + dd->yo;
  starts2[2] = dd->Zs + dd->zo;
  dims2[0]   = (dd->Xe - dd->Xs) / dof;
  dims2[1]   = (dd->Ye - dd->Ys);
  dims2[2]   = (dd->Ze - dd->Zs);

  /* As if we do MatSetStencil() to get dims[]/starts[] of mat->stencil */
  dim  = da->dim;                   /* DA dim: 1 to 3 */
  sdim = dim + (dof > 1 ? 1 : 0);   /* Dimensions in MatStencil's (k,j,i,c) view */
  for (i = 0; i < dim; i++) {       /* Reverse the order and also skip the unused dimensions */
    dims[i]   = dims2[dim - i - 1]; /* ex. dims/starts[] are in order of {i} for 1D, {j,i} for 2D and {k,j,i} for 3D */
    starts[i] = starts2[dim - i - 1];
  }
  starts[dim] = 0; /* Append the extra dim for dof (won't be used below if dof=1) */
  dims[dim]   = dof;

  /* Map stencils to local indices (code adapted from MatSetValuesStencil()) */
  for (i = 0; i < m; i++) {
    dxm += 3 - dim; /* Input is {k,j,i,c}; move the pointer to the first used index, e.g., j in 2D */
    tmp = 0;
    for (j = 0; j < sdim; j++) {                                                      /* Iter over, ex. j,i or j,i,c in 2D */
      if (tmp < 0 || dxm[j] < starts[j] || dxm[j] >= (starts[j] + dims[j])) tmp = -1; /* Beyond the ghost region, therefore ignored with negative indices */
      else tmp = tmp * dims[j] + (dxm[j] - starts[j]);
    }
    gidxm[i] = tmp;
    /* Move to the next MatStencil point */
    if (dof > 1) dxm += sdim; /* c is already counted in sdim */
    else dxm += sdim + 1;     /* skip the unused c */
  }

  /* Map local indices to global indices */
  PetscCall(DMGetLocalToGlobalMapping(da, &ltog));
  PetscCall(ISLocalToGlobalMappingApply(ltog, m, gidxm, gidxm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Creates "balanced" ownership ranges after refinement, constrained by the need for the
  fine grid boundaries to fall within one stencil width of the coarse partition.

  Uses a greedy algorithm to handle non-ideal layouts, could probably do something better.
*/
static PetscErrorCode DMDARefineOwnershipRanges(DM da, PetscBool periodic, PetscInt stencil_width, PetscInt ratio, PetscInt m, const PetscInt lc[], PetscInt lf[])
{
  PetscInt i, totalc = 0, remaining, startc = 0, startf = 0;

  PetscFunctionBegin;
  PetscCheck(ratio >= 1, PetscObjectComm((PetscObject)da), PETSC_ERR_USER, "Requested refinement ratio %" PetscInt_FMT " must be at least 1", ratio);
  if (ratio == 1) {
    PetscCall(PetscArraycpy(lf, lc, m));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  for (i = 0; i < m; i++) totalc += lc[i];
  remaining = (!periodic) + ratio * (totalc - (!periodic));
  for (i = 0; i < m; i++) {
    PetscInt want = remaining / (m - i) + !!(remaining % (m - i));
    if (i == m - 1) lf[i] = want;
    else {
      const PetscInt nextc = startc + lc[i];
      /* Move the first fine node of the next subdomain to the right until the coarse node on its left is within one
       * coarse stencil width of the first coarse node in the next subdomain. */
      while ((startf + want) / ratio < nextc - stencil_width) want++;
      /* Move the last fine node in the current subdomain to the left until the coarse node on its right is within one
       * coarse stencil width of the last coarse node in the current subdomain. */
      while ((startf + want - 1 + ratio - 1) / ratio > nextc - 1 + stencil_width) want--;
      /* Make sure all constraints are satisfied */
      if (want < 0 || want > remaining || ((startf + want) / ratio < nextc - stencil_width) || ((startf + want - 1 + ratio - 1) / ratio > nextc - 1 + stencil_width))
        SETERRQ(PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_SIZ, "Could not find a compatible refined ownership range");
    }
    lf[i] = want;
    startc += lc[i];
    startf += lf[i];
    remaining -= lf[i];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Creates "balanced" ownership ranges after coarsening, constrained by the need for the
  fine grid boundaries to fall within one stencil width of the coarse partition.

  Uses a greedy algorithm to handle non-ideal layouts, could probably do something better.
*/
static PetscErrorCode DMDACoarsenOwnershipRanges(DM da, PetscBool periodic, PetscInt stencil_width, PetscInt ratio, PetscInt m, const PetscInt lf[], PetscInt lc[])
{
  PetscInt i, totalf, remaining, startc, startf;

  PetscFunctionBegin;
  PetscCheck(ratio >= 1, PetscObjectComm((PetscObject)da), PETSC_ERR_USER, "Requested refinement ratio %" PetscInt_FMT " must be at least 1", ratio);
  if (ratio == 1) {
    PetscCall(PetscArraycpy(lc, lf, m));
    PetscFunctionReturn(PETSC_SUCCESS);
  }
  for (i = 0, totalf = 0; i < m; i++) totalf += lf[i];
  remaining = (!periodic) + (totalf - (!periodic)) / ratio;
  for (i = 0, startc = 0, startf = 0; i < m; i++) {
    PetscInt want = remaining / (m - i) + !!(remaining % (m - i));
    if (i == m - 1) lc[i] = want;
    else {
      const PetscInt nextf = startf + lf[i];
      /* Slide first coarse node of next subdomain to the left until the coarse node to the left of the first fine
       * node is within one stencil width. */
      while (nextf / ratio < startc + want - stencil_width) want--;
      /* Slide the last coarse node of the current subdomain to the right until the coarse node to the right of the last
       * fine node is within one stencil width. */
      while ((nextf - 1 + ratio - 1) / ratio > startc + want - 1 + stencil_width) want++;
      if (want < 0 || want > remaining || (nextf / ratio < startc + want - stencil_width) || ((nextf - 1 + ratio - 1) / ratio > startc + want - 1 + stencil_width))
        SETERRQ(PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_SIZ, "Could not find a compatible coarsened ownership range");
    }
    lc[i] = want;
    startc += lc[i];
    startf += lf[i];
    remaining -= lc[i];
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMRefine_DA(DM da, MPI_Comm comm, DM *daref)
{
  PetscInt M, N, P, i, dim;
  Vec      coordsc, coordsf;
  DM       da2;
  DM_DA   *dd = (DM_DA *)da->data, *dd2;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(da, DM_CLASSID, 1, DMDA);
  PetscValidPointer(daref, 3);

  PetscCall(DMGetDimension(da, &dim));
  if (dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0) {
    M = dd->refine_x * dd->M;
  } else {
    M = 1 + dd->refine_x * (dd->M - 1);
  }
  if (dd->by == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0) {
    if (dim > 1) {
      N = dd->refine_y * dd->N;
    } else {
      N = 1;
    }
  } else {
    N = 1 + dd->refine_y * (dd->N - 1);
  }
  if (dd->bz == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0) {
    if (dim > 2) {
      P = dd->refine_z * dd->P;
    } else {
      P = 1;
    }
  } else {
    P = 1 + dd->refine_z * (dd->P - 1);
  }
  PetscCall(DMDACreate(PetscObjectComm((PetscObject)da), &da2));
  PetscCall(DMSetOptionsPrefix(da2, ((PetscObject)da)->prefix));
  PetscCall(DMSetDimension(da2, dim));
  PetscCall(DMDASetSizes(da2, M, N, P));
  PetscCall(DMDASetNumProcs(da2, dd->m, dd->n, dd->p));
  PetscCall(DMDASetBoundaryType(da2, dd->bx, dd->by, dd->bz));
  PetscCall(DMDASetDof(da2, dd->w));
  PetscCall(DMDASetStencilType(da2, dd->stencil_type));
  PetscCall(DMDASetStencilWidth(da2, dd->s));
  if (dim == 3) {
    PetscInt *lx, *ly, *lz;
    PetscCall(PetscMalloc3(dd->m, &lx, dd->n, &ly, dd->p, &lz));
    PetscCall(DMDARefineOwnershipRanges(da, (PetscBool)(dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->refine_x, dd->m, dd->lx, lx));
    PetscCall(DMDARefineOwnershipRanges(da, (PetscBool)(dd->by == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->refine_y, dd->n, dd->ly, ly));
    PetscCall(DMDARefineOwnershipRanges(da, (PetscBool)(dd->bz == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->refine_z, dd->p, dd->lz, lz));
    PetscCall(DMDASetOwnershipRanges(da2, lx, ly, lz));
    PetscCall(PetscFree3(lx, ly, lz));
  } else if (dim == 2) {
    PetscInt *lx, *ly;
    PetscCall(PetscMalloc2(dd->m, &lx, dd->n, &ly));
    PetscCall(DMDARefineOwnershipRanges(da, (PetscBool)(dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->refine_x, dd->m, dd->lx, lx));
    PetscCall(DMDARefineOwnershipRanges(da, (PetscBool)(dd->by == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->refine_y, dd->n, dd->ly, ly));
    PetscCall(DMDASetOwnershipRanges(da2, lx, ly, NULL));
    PetscCall(PetscFree2(lx, ly));
  } else if (dim == 1) {
    PetscInt *lx;
    PetscCall(PetscMalloc1(dd->m, &lx));
    PetscCall(DMDARefineOwnershipRanges(da, (PetscBool)(dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->refine_x, dd->m, dd->lx, lx));
    PetscCall(DMDASetOwnershipRanges(da2, lx, NULL, NULL));
    PetscCall(PetscFree(lx));
  }
  dd2 = (DM_DA *)da2->data;

  /* allow overloaded (user replaced) operations to be inherited by refinement clones */
  da2->ops->creatematrix = da->ops->creatematrix;
  /* da2->ops->createinterpolation = da->ops->createinterpolation; this causes problem with SNESVI */
  da2->ops->getcoloring = da->ops->getcoloring;
  dd2->interptype       = dd->interptype;

  /* copy fill information if given */
  if (dd->dfill) {
    PetscCall(PetscMalloc1(dd->dfill[dd->w] + dd->w + 1, &dd2->dfill));
    PetscCall(PetscArraycpy(dd2->dfill, dd->dfill, dd->dfill[dd->w] + dd->w + 1));
  }
  if (dd->ofill) {
    PetscCall(PetscMalloc1(dd->ofill[dd->w] + dd->w + 1, &dd2->ofill));
    PetscCall(PetscArraycpy(dd2->ofill, dd->ofill, dd->ofill[dd->w] + dd->w + 1));
  }
  /* copy the refine information */
  dd2->coarsen_x = dd2->refine_x = dd->refine_x;
  dd2->coarsen_y = dd2->refine_y = dd->refine_y;
  dd2->coarsen_z = dd2->refine_z = dd->refine_z;

  if (dd->refine_z_hier) {
    if (da->levelup - da->leveldown + 1 > -1 && da->levelup - da->leveldown + 1 < dd->refine_z_hier_n) dd2->refine_z = dd->refine_z_hier[da->levelup - da->leveldown + 1];
    if (da->levelup - da->leveldown > -1 && da->levelup - da->leveldown < dd->refine_z_hier_n) dd2->coarsen_z = dd->refine_z_hier[da->levelup - da->leveldown];
    dd2->refine_z_hier_n = dd->refine_z_hier_n;
    PetscCall(PetscMalloc1(dd2->refine_z_hier_n, &dd2->refine_z_hier));
    PetscCall(PetscArraycpy(dd2->refine_z_hier, dd->refine_z_hier, dd2->refine_z_hier_n));
  }
  if (dd->refine_y_hier) {
    if (da->levelup - da->leveldown + 1 > -1 && da->levelup - da->leveldown + 1 < dd->refine_y_hier_n) dd2->refine_y = dd->refine_y_hier[da->levelup - da->leveldown + 1];
    if (da->levelup - da->leveldown > -1 && da->levelup - da->leveldown < dd->refine_y_hier_n) dd2->coarsen_y = dd->refine_y_hier[da->levelup - da->leveldown];
    dd2->refine_y_hier_n = dd->refine_y_hier_n;
    PetscCall(PetscMalloc1(dd2->refine_y_hier_n, &dd2->refine_y_hier));
    PetscCall(PetscArraycpy(dd2->refine_y_hier, dd->refine_y_hier, dd2->refine_y_hier_n));
  }
  if (dd->refine_x_hier) {
    if (da->levelup - da->leveldown + 1 > -1 && da->levelup - da->leveldown + 1 < dd->refine_x_hier_n) dd2->refine_x = dd->refine_x_hier[da->levelup - da->leveldown + 1];
    if (da->levelup - da->leveldown > -1 && da->levelup - da->leveldown < dd->refine_x_hier_n) dd2->coarsen_x = dd->refine_x_hier[da->levelup - da->leveldown];
    dd2->refine_x_hier_n = dd->refine_x_hier_n;
    PetscCall(PetscMalloc1(dd2->refine_x_hier_n, &dd2->refine_x_hier));
    PetscCall(PetscArraycpy(dd2->refine_x_hier, dd->refine_x_hier, dd2->refine_x_hier_n));
  }

  /* copy vector type information */
  PetscCall(DMSetVecType(da2, da->vectype));

  dd2->lf = dd->lf;
  dd2->lj = dd->lj;

  da2->leveldown = da->leveldown;
  da2->levelup   = da->levelup + 1;

  PetscCall(DMSetUp(da2));

  /* interpolate coordinates if they are set on the coarse grid */
  PetscCall(DMGetCoordinates(da, &coordsc));
  if (coordsc) {
    DM  cdaf, cdac;
    Mat II;

    PetscCall(DMGetCoordinateDM(da, &cdac));
    PetscCall(DMGetCoordinateDM(da2, &cdaf));
    /* force creation of the coordinate vector */
    PetscCall(DMDASetUniformCoordinates(da2, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
    PetscCall(DMGetCoordinates(da2, &coordsf));
    PetscCall(DMCreateInterpolation(cdac, cdaf, &II, NULL));
    PetscCall(MatInterpolate(II, coordsc, coordsf));
    PetscCall(MatDestroy(&II));
  }

  for (i = 0; i < da->bs; i++) {
    const char *fieldname;
    PetscCall(DMDAGetFieldName(da, i, &fieldname));
    PetscCall(DMDASetFieldName(da2, i, fieldname));
  }

  *daref = da2;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCoarsen_DA(DM dmf, MPI_Comm comm, DM *dmc)
{
  PetscInt M, N, P, i, dim;
  Vec      coordsc, coordsf;
  DM       dmc2;
  DM_DA   *dd = (DM_DA *)dmf->data, *dd2;

  PetscFunctionBegin;
  PetscValidHeaderSpecificType(dmf, DM_CLASSID, 1, DMDA);
  PetscValidPointer(dmc, 3);

  PetscCall(DMGetDimension(dmf, &dim));
  if (dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0) {
    M = dd->M / dd->coarsen_x;
  } else {
    M = 1 + (dd->M - 1) / dd->coarsen_x;
  }
  if (dd->by == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0) {
    if (dim > 1) {
      N = dd->N / dd->coarsen_y;
    } else {
      N = 1;
    }
  } else {
    N = 1 + (dd->N - 1) / dd->coarsen_y;
  }
  if (dd->bz == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0) {
    if (dim > 2) {
      P = dd->P / dd->coarsen_z;
    } else {
      P = 1;
    }
  } else {
    P = 1 + (dd->P - 1) / dd->coarsen_z;
  }
  PetscCall(DMDACreate(PetscObjectComm((PetscObject)dmf), &dmc2));
  PetscCall(DMSetOptionsPrefix(dmc2, ((PetscObject)dmf)->prefix));
  PetscCall(DMSetDimension(dmc2, dim));
  PetscCall(DMDASetSizes(dmc2, M, N, P));
  PetscCall(DMDASetNumProcs(dmc2, dd->m, dd->n, dd->p));
  PetscCall(DMDASetBoundaryType(dmc2, dd->bx, dd->by, dd->bz));
  PetscCall(DMDASetDof(dmc2, dd->w));
  PetscCall(DMDASetStencilType(dmc2, dd->stencil_type));
  PetscCall(DMDASetStencilWidth(dmc2, dd->s));
  if (dim == 3) {
    PetscInt *lx, *ly, *lz;
    PetscCall(PetscMalloc3(dd->m, &lx, dd->n, &ly, dd->p, &lz));
    PetscCall(DMDACoarsenOwnershipRanges(dmf, (PetscBool)(dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->coarsen_x, dd->m, dd->lx, lx));
    PetscCall(DMDACoarsenOwnershipRanges(dmf, (PetscBool)(dd->by == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->coarsen_y, dd->n, dd->ly, ly));
    PetscCall(DMDACoarsenOwnershipRanges(dmf, (PetscBool)(dd->bz == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->coarsen_z, dd->p, dd->lz, lz));
    PetscCall(DMDASetOwnershipRanges(dmc2, lx, ly, lz));
    PetscCall(PetscFree3(lx, ly, lz));
  } else if (dim == 2) {
    PetscInt *lx, *ly;
    PetscCall(PetscMalloc2(dd->m, &lx, dd->n, &ly));
    PetscCall(DMDACoarsenOwnershipRanges(dmf, (PetscBool)(dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->coarsen_x, dd->m, dd->lx, lx));
    PetscCall(DMDACoarsenOwnershipRanges(dmf, (PetscBool)(dd->by == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->coarsen_y, dd->n, dd->ly, ly));
    PetscCall(DMDASetOwnershipRanges(dmc2, lx, ly, NULL));
    PetscCall(PetscFree2(lx, ly));
  } else if (dim == 1) {
    PetscInt *lx;
    PetscCall(PetscMalloc1(dd->m, &lx));
    PetscCall(DMDACoarsenOwnershipRanges(dmf, (PetscBool)(dd->bx == DM_BOUNDARY_PERIODIC || dd->interptype == DMDA_Q0), dd->s, dd->coarsen_x, dd->m, dd->lx, lx));
    PetscCall(DMDASetOwnershipRanges(dmc2, lx, NULL, NULL));
    PetscCall(PetscFree(lx));
  }
  dd2 = (DM_DA *)dmc2->data;

  /* allow overloaded (user replaced) operations to be inherited by refinement clones; why are only some inherited and not all? */
  /* dmc2->ops->createinterpolation = dmf->ops->createinterpolation; copying this one causes trouble for DMSetVI */
  dmc2->ops->creatematrix = dmf->ops->creatematrix;
  dmc2->ops->getcoloring  = dmf->ops->getcoloring;
  dd2->interptype         = dd->interptype;

  /* copy fill information if given */
  if (dd->dfill) {
    PetscCall(PetscMalloc1(dd->dfill[dd->w] + dd->w + 1, &dd2->dfill));
    PetscCall(PetscArraycpy(dd2->dfill, dd->dfill, dd->dfill[dd->w] + dd->w + 1));
  }
  if (dd->ofill) {
    PetscCall(PetscMalloc1(dd->ofill[dd->w] + dd->w + 1, &dd2->ofill));
    PetscCall(PetscArraycpy(dd2->ofill, dd->ofill, dd->ofill[dd->w] + dd->w + 1));
  }
  /* copy the refine information */
  dd2->coarsen_x = dd2->refine_x = dd->coarsen_x;
  dd2->coarsen_y = dd2->refine_y = dd->coarsen_y;
  dd2->coarsen_z = dd2->refine_z = dd->coarsen_z;

  if (dd->refine_z_hier) {
    if (dmf->levelup - dmf->leveldown - 1 > -1 && dmf->levelup - dmf->leveldown - 1 < dd->refine_z_hier_n) dd2->refine_z = dd->refine_z_hier[dmf->levelup - dmf->leveldown - 1];
    if (dmf->levelup - dmf->leveldown - 2 > -1 && dmf->levelup - dmf->leveldown - 2 < dd->refine_z_hier_n) dd2->coarsen_z = dd->refine_z_hier[dmf->levelup - dmf->leveldown - 2];
    dd2->refine_z_hier_n = dd->refine_z_hier_n;
    PetscCall(PetscMalloc1(dd2->refine_z_hier_n, &dd2->refine_z_hier));
    PetscCall(PetscArraycpy(dd2->refine_z_hier, dd->refine_z_hier, dd2->refine_z_hier_n));
  }
  if (dd->refine_y_hier) {
    if (dmf->levelup - dmf->leveldown - 1 > -1 && dmf->levelup - dmf->leveldown - 1 < dd->refine_y_hier_n) dd2->refine_y = dd->refine_y_hier[dmf->levelup - dmf->leveldown - 1];
    if (dmf->levelup - dmf->leveldown - 2 > -1 && dmf->levelup - dmf->leveldown - 2 < dd->refine_y_hier_n) dd2->coarsen_y = dd->refine_y_hier[dmf->levelup - dmf->leveldown - 2];
    dd2->refine_y_hier_n = dd->refine_y_hier_n;
    PetscCall(PetscMalloc1(dd2->refine_y_hier_n, &dd2->refine_y_hier));
    PetscCall(PetscArraycpy(dd2->refine_y_hier, dd->refine_y_hier, dd2->refine_y_hier_n));
  }
  if (dd->refine_x_hier) {
    if (dmf->levelup - dmf->leveldown - 1 > -1 && dmf->levelup - dmf->leveldown - 1 < dd->refine_x_hier_n) dd2->refine_x = dd->refine_x_hier[dmf->levelup - dmf->leveldown - 1];
    if (dmf->levelup - dmf->leveldown - 2 > -1 && dmf->levelup - dmf->leveldown - 2 < dd->refine_x_hier_n) dd2->coarsen_x = dd->refine_x_hier[dmf->levelup - dmf->leveldown - 2];
    dd2->refine_x_hier_n = dd->refine_x_hier_n;
    PetscCall(PetscMalloc1(dd2->refine_x_hier_n, &dd2->refine_x_hier));
    PetscCall(PetscArraycpy(dd2->refine_x_hier, dd->refine_x_hier, dd2->refine_x_hier_n));
  }

  /* copy vector type information */
  PetscCall(DMSetVecType(dmc2, dmf->vectype));

  dd2->lf = dd->lf;
  dd2->lj = dd->lj;

  dmc2->leveldown = dmf->leveldown + 1;
  dmc2->levelup   = dmf->levelup;

  PetscCall(DMSetUp(dmc2));

  /* inject coordinates if they are set on the fine grid */
  PetscCall(DMGetCoordinates(dmf, &coordsf));
  if (coordsf) {
    DM         cdaf, cdac;
    Mat        inject;
    VecScatter vscat;

    PetscCall(DMGetCoordinateDM(dmf, &cdaf));
    PetscCall(DMGetCoordinateDM(dmc2, &cdac));
    /* force creation of the coordinate vector */
    PetscCall(DMDASetUniformCoordinates(dmc2, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
    PetscCall(DMGetCoordinates(dmc2, &coordsc));

    PetscCall(DMCreateInjection(cdac, cdaf, &inject));
    PetscCall(MatScatterGetVecScatter(inject, &vscat));
    PetscCall(VecScatterBegin(vscat, coordsf, coordsc, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(VecScatterEnd(vscat, coordsf, coordsc, INSERT_VALUES, SCATTER_FORWARD));
    PetscCall(MatDestroy(&inject));
  }

  for (i = 0; i < dmf->bs; i++) {
    const char *fieldname;
    PetscCall(DMDAGetFieldName(dmf, i, &fieldname));
    PetscCall(DMDASetFieldName(dmc2, i, fieldname));
  }

  *dmc = dmc2;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMRefineHierarchy_DA(DM da, PetscInt nlevels, DM daf[])
{
  PetscInt i, n, *refx, *refy, *refz;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(da, DM_CLASSID, 1);
  PetscCheck(nlevels >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_OUTOFRANGE, "nlevels cannot be negative");
  if (nlevels == 0) PetscFunctionReturn(PETSC_SUCCESS);
  PetscValidPointer(daf, 3);

  /* Get refinement factors, defaults taken from the coarse DMDA */
  PetscCall(PetscMalloc3(nlevels, &refx, nlevels, &refy, nlevels, &refz));
  for (i = 0; i < nlevels; i++) PetscCall(DMDAGetRefinementFactor(da, &refx[i], &refy[i], &refz[i]));
  n = nlevels;
  PetscCall(PetscOptionsGetIntArray(((PetscObject)da)->options, ((PetscObject)da)->prefix, "-da_refine_hierarchy_x", refx, &n, NULL));
  n = nlevels;
  PetscCall(PetscOptionsGetIntArray(((PetscObject)da)->options, ((PetscObject)da)->prefix, "-da_refine_hierarchy_y", refy, &n, NULL));
  n = nlevels;
  PetscCall(PetscOptionsGetIntArray(((PetscObject)da)->options, ((PetscObject)da)->prefix, "-da_refine_hierarchy_z", refz, &n, NULL));

  PetscCall(DMDASetRefinementFactor(da, refx[0], refy[0], refz[0]));
  PetscCall(DMRefine(da, PetscObjectComm((PetscObject)da), &daf[0]));
  for (i = 1; i < nlevels; i++) {
    PetscCall(DMDASetRefinementFactor(daf[i - 1], refx[i], refy[i], refz[i]));
    PetscCall(DMRefine(daf[i - 1], PetscObjectComm((PetscObject)da), &daf[i]));
  }
  PetscCall(PetscFree3(refx, refy, refz));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMCoarsenHierarchy_DA(DM da, PetscInt nlevels, DM dac[])
{
  PetscInt i;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(da, DM_CLASSID, 1);
  PetscCheck(nlevels >= 0, PetscObjectComm((PetscObject)da), PETSC_ERR_ARG_OUTOFRANGE, "nlevels cannot be negative");
  if (nlevels == 0) PetscFunctionReturn(PETSC_SUCCESS);
  PetscValidPointer(dac, 3);
  PetscCall(DMCoarsen(da, PetscObjectComm((PetscObject)da), &dac[0]));
  for (i = 1; i < nlevels; i++) PetscCall(DMCoarsen(dac[i - 1], PetscObjectComm((PetscObject)da), &dac[i]));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode DMDASetGLLCoordinates_1d(DM dm, PetscInt n, PetscReal *nodes)
{
  PetscInt     i, j, xs, xn, q;
  PetscScalar *xx;
  PetscReal    h;
  Vec          x;
  DM_DA       *da = (DM_DA *)dm->data;

  PetscFunctionBegin;
  if (da->bx != DM_BOUNDARY_PERIODIC) {
    PetscCall(DMDAGetInfo(dm, NULL, &q, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL));
    q = (q - 1) / (n - 1); /* number of spectral elements */
    h = 2.0 / q;
    PetscCall(DMDAGetCorners(dm, &xs, NULL, NULL, &xn, NULL, NULL));
    xs = xs / (n - 1);
    xn = xn / (n - 1);
    PetscCall(DMDASetUniformCoordinates(dm, -1., 1., 0., 0., 0., 0.));
    PetscCall(DMGetCoordinates(dm, &x));
    PetscCall(DMDAVecGetArray(dm, x, &xx));

    /* loop over local spectral elements */
    for (j = xs; j < xs + xn; j++) {
      /*
       Except for the first process, each process starts on the second GLL point of the first element on that process
       */
      for (i = (j == xs && xs > 0) ? 1 : 0; i < n; i++) xx[j * (n - 1) + i] = -1.0 + h * j + h * (nodes[i] + 1.0) / 2.;
    }
    PetscCall(DMDAVecRestoreArray(dm, x, &xx));
  } else SETERRQ(PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Not yet implemented for periodic");
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@

     DMDASetGLLCoordinates - Sets the global coordinates from -1 to 1 to the GLL points of as many GLL elements that fit the number of grid points

   Collective

   Input Parameters:
+   da - the `DMDA` object
-   n - the number of GLL nodes
-   nodes - the GLL nodes

   Level: advanced

   Note:
   The parallel decomposition of grid points must correspond to the degree of the GLL. That is, the number of grid points
   on each process much be divisible by the number of GLL elements needed per process. This depends on whether the `DM` is
   periodic or not.

.seealso: `DM`, `DMDA`, `DMDACreate()`, `PetscDTGaussLobattoLegendreQuadrature()`, `DMGetCoordinates()`
@*/
PetscErrorCode DMDASetGLLCoordinates(DM da, PetscInt n, PetscReal *nodes)
{
  PetscFunctionBegin;
  if (da->dim == 1) {
    PetscCall(DMDASetGLLCoordinates_1d(da, n, nodes));
  } else SETERRQ(PetscObjectComm((PetscObject)da), PETSC_ERR_SUP, "Not yet implemented for 2 or 3d");
  PetscFunctionReturn(PETSC_SUCCESS);
}

PETSC_INTERN PetscErrorCode DMGetCompatibility_DA(DM da1, DM dm2, PetscBool *compatible, PetscBool *set)
{
  DM_DA    *dd1 = (DM_DA *)da1->data, *dd2;
  DM        da2;
  DMType    dmtype2;
  PetscBool isda, compatibleLocal;
  PetscInt  i;

  PetscFunctionBegin;
  PetscCheck(da1->setupcalled, PetscObjectComm((PetscObject)da1), PETSC_ERR_ARG_WRONGSTATE, "DMSetUp() must be called on first DM before DMGetCompatibility()");
  PetscCall(DMGetType(dm2, &dmtype2));
  PetscCall(PetscStrcmp(dmtype2, DMDA, &isda));
  if (isda) {
    da2 = dm2;
    dd2 = (DM_DA *)da2->data;
    PetscCheck(da2->setupcalled, PetscObjectComm((PetscObject)da2), PETSC_ERR_ARG_WRONGSTATE, "DMSetUp() must be called on second DM before DMGetCompatibility()");
    compatibleLocal = (PetscBool)(da1->dim == da2->dim);
    if (compatibleLocal) compatibleLocal = (PetscBool)(compatibleLocal && (dd1->s == dd2->s)); /* Stencil width */
    /*                                                                           Global size              ranks               Boundary type */
    if (compatibleLocal) compatibleLocal = (PetscBool)(compatibleLocal && (dd1->M == dd2->M) && (dd1->m == dd2->m) && (dd1->bx == dd2->bx));
    if (compatibleLocal && da1->dim > 1) compatibleLocal = (PetscBool)(compatibleLocal && (dd1->N == dd2->N) && (dd1->n == dd2->n) && (dd1->by == dd2->by));
    if (compatibleLocal && da1->dim > 2) compatibleLocal = (PetscBool)(compatibleLocal && (dd1->P == dd2->P) && (dd1->p == dd2->p) && (dd1->bz == dd2->bz));
    if (compatibleLocal) {
      for (i = 0; i < dd1->m; ++i) { compatibleLocal = (PetscBool)(compatibleLocal && (dd1->lx[i] == dd2->lx[i])); /* Local size     */ }
    }
    if (compatibleLocal && da1->dim > 1) {
      for (i = 0; i < dd1->n; ++i) compatibleLocal = (PetscBool)(compatibleLocal && (dd1->ly[i] == dd2->ly[i]));
    }
    if (compatibleLocal && da1->dim > 2) {
      for (i = 0; i < dd1->p; ++i) compatibleLocal = (PetscBool)(compatibleLocal && (dd1->lz[i] == dd2->lz[i]));
    }
    *compatible = compatibleLocal;
    *set        = PETSC_TRUE;
  } else {
    /* Decline to determine compatibility with other DM types */
    *set = PETSC_FALSE;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}