xref: /petsc/src/snes/utils/dmplexsnes.c (revision f5af7f232b71b4a723423f52797ae8ea7ad3f041)

#include <petscdmplex.h> /*I "petscdmplex.h" I*/
#include <petscsnes.h>      /*I "petscsnes.h" I*/

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationCreate"
PetscErrorCode DMInterpolationCreate(MPI_Comm comm, DMInterpolationInfo *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(ctx, 2);
  ierr = PetscMalloc(sizeof(struct _DMInterpolationInfo), ctx);CHKERRQ(ierr);

  (*ctx)->comm   = comm;
  (*ctx)->dim    = -1;
  (*ctx)->nInput = 0;
  (*ctx)->points = PETSC_NULL;
  (*ctx)->cells  = PETSC_NULL;
  (*ctx)->n      = -1;
  (*ctx)->coords = PETSC_NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationSetDim"
PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo ctx, PetscInt dim)
{
  PetscFunctionBegin;
  if ((dim < 1) || (dim > 3)) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid dimension for points: %d", dim);
  ctx->dim = dim;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationGetDim"
PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo ctx, PetscInt *dim)
{
  PetscFunctionBegin;
  PetscValidIntPointer(dim, 2);
  *dim = ctx->dim;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationSetDof"
PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo ctx, PetscInt dof)
{
  PetscFunctionBegin;
  if (dof < 1) SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Invalid number of components: %d", dof);
  ctx->dof = dof;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationGetDof"
PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo ctx, PetscInt *dof)
{
  PetscFunctionBegin;
  PetscValidIntPointer(dof, 2);
  *dof = ctx->dof;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationAddPoints"
PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo ctx, PetscInt n, PetscReal points[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (ctx->dim < 0) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
  if (ctx->points)  SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "Cannot add points multiple times yet");
  ctx->nInput = n;

  ierr = PetscMalloc(n*ctx->dim * sizeof(PetscReal), &ctx->points);CHKERRQ(ierr);
  ierr = PetscMemcpy(ctx->points, points, n*ctx->dim * sizeof(PetscReal));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationSetUp"
PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo ctx, DM dm, PetscBool redundantPoints)
{
  MPI_Comm       comm = ctx->comm;
  PetscScalar    *a;
  PetscInt       p, q, i;
  PetscMPIInt    rank, size;
  PetscErrorCode ierr;
  Vec            pointVec;
  IS             cellIS;
  PetscLayout    layout;
  PetscReal      *globalPoints;
  PetscScalar    *globalPointsScalar;
  const PetscInt *ranges;
  PetscMPIInt    *counts, *displs;
  const PetscInt *foundCells;
  PetscMPIInt    *foundProcs, *globalProcs;
  PetscInt       n, N;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  if (ctx->dim < 0) SETERRQ(comm, PETSC_ERR_ARG_WRONGSTATE, "The spatial dimension has not been set");
  /* Locate points */
  n = ctx->nInput;
  if (!redundantPoints) {
    ierr = PetscLayoutCreate(comm, &layout);CHKERRQ(ierr);
    ierr = PetscLayoutSetBlockSize(layout, 1);CHKERRQ(ierr);
    ierr = PetscLayoutSetLocalSize(layout, n);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(layout);CHKERRQ(ierr);
    ierr = PetscLayoutGetSize(layout, &N);CHKERRQ(ierr);
    /* Communicate all points to all processes */
    ierr = PetscMalloc3(N*ctx->dim,PetscReal,&globalPoints,size,PetscMPIInt,&counts,size,PetscMPIInt,&displs);CHKERRQ(ierr);
    ierr = PetscLayoutGetRanges(layout, &ranges);CHKERRQ(ierr);
    for (p = 0; p < size; ++p) {
      counts[p] = (ranges[p+1] - ranges[p])*ctx->dim;
      displs[p] = ranges[p]*ctx->dim;
    }
    ierr = MPI_Allgatherv(ctx->points, n*ctx->dim, MPIU_REAL, globalPoints, counts, displs, MPIU_REAL, comm);CHKERRQ(ierr);
  } else {
    N = n;

    globalPoints = ctx->points;
  }
#if 0
  ierr = PetscMalloc3(N,PetscInt,&foundCells,N,PetscMPIInt,&foundProcs,N,PetscMPIInt,&globalProcs);CHKERRQ(ierr);
  /* foundCells[p] = m->locatePoint(&globalPoints[p*ctx->dim]); */
#else
#if defined(PETSC_USE_COMPLEX)
  ierr = PetscMalloc(N*sizeof(PetscScalar),&globalPointsScalar);CHKERRQ(ierr);
  for (i=0; i<N; i++) globalPointsScalar[i] = globalPoints[i];
#else
  globalPointsScalar = globalPoints;
#endif
  ierr = VecCreateSeqWithArray(PETSC_COMM_SELF, ctx->dim, N*ctx->dim, globalPointsScalar, &pointVec);CHKERRQ(ierr);
  ierr = PetscMalloc2(N,PetscMPIInt,&foundProcs,N,PetscMPIInt,&globalProcs);CHKERRQ(ierr);
  ierr = DMLocatePoints(dm, pointVec, &cellIS);CHKERRQ(ierr);
  ierr = ISGetIndices(cellIS, &foundCells);CHKERRQ(ierr);
#endif
  for (p = 0; p < N; ++p) {
    if (foundCells[p] >= 0) foundProcs[p] = rank;
    else foundProcs[p] = size;
  }
  /* Let the lowest rank process own each point */
  ierr   = MPI_Allreduce(foundProcs, globalProcs, N, MPI_INT, MPI_MIN, comm);CHKERRQ(ierr);
  ctx->n = 0;
  for (p = 0; p < N; ++p) {
    if (globalProcs[p] == size) SETERRQ4(comm, PETSC_ERR_PLIB, "Point %d: %g %g %g not located in mesh", p, globalPoints[p*ctx->dim+0], ctx->dim > 1 ? globalPoints[p*ctx->dim+1] : 0.0, ctx->dim > 2 ? globalPoints[p*ctx->dim+2] : 0.0);
    else if (globalProcs[p] == rank) ctx->n++;
  }
  /* Create coordinates vector and array of owned cells */
  ierr = PetscMalloc(ctx->n * sizeof(PetscInt), &ctx->cells);CHKERRQ(ierr);
  ierr = VecCreate(comm, &ctx->coords);CHKERRQ(ierr);
  ierr = VecSetSizes(ctx->coords, ctx->n*ctx->dim, PETSC_DECIDE);CHKERRQ(ierr);
  ierr = VecSetBlockSize(ctx->coords, ctx->dim);CHKERRQ(ierr);
  ierr = VecSetFromOptions(ctx->coords);CHKERRQ(ierr);
  ierr = VecGetArray(ctx->coords, &a);CHKERRQ(ierr);
  for (p = 0, q = 0, i = 0; p < N; ++p) {
    if (globalProcs[p] == rank) {
      PetscInt d;

      for (d = 0; d < ctx->dim; ++d, ++i) a[i] = globalPoints[p*ctx->dim+d];
      ctx->cells[q++] = foundCells[p];
    }
  }
  ierr = VecRestoreArray(ctx->coords, &a);CHKERRQ(ierr);
#if 0
  ierr = PetscFree3(foundCells,foundProcs,globalProcs);CHKERRQ(ierr);
#else
  ierr = PetscFree2(foundProcs,globalProcs);CHKERRQ(ierr);
  ierr = ISRestoreIndices(cellIS, &foundCells);CHKERRQ(ierr);
  ierr = ISDestroy(&cellIS);CHKERRQ(ierr);
  ierr = VecDestroy(&pointVec);CHKERRQ(ierr);
#endif
  if ((void*)globalPointsScalar != (void*)globalPoints) {ierr = PetscFree(globalPointsScalar);CHKERRQ(ierr);}
  if (!redundantPoints) {
    ierr = PetscFree3(globalPoints,counts,displs);CHKERRQ(ierr);
    ierr = PetscLayoutDestroy(&layout);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationGetCoordinates"
PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo ctx, Vec *coordinates)
{
  PetscFunctionBegin;
  PetscValidPointer(coordinates, 2);
  if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
  *coordinates = ctx->coords;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationGetVector"
PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo ctx, Vec *v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(v, 2);
  if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
  ierr = VecCreate(ctx->comm, v);CHKERRQ(ierr);
  ierr = VecSetSizes(*v, ctx->n*ctx->dof, PETSC_DECIDE);CHKERRQ(ierr);
  ierr = VecSetBlockSize(*v, ctx->dof);CHKERRQ(ierr);
  ierr = VecSetFromOptions(*v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationRestoreVector"
PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo ctx, Vec *v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(v, 2);
  if (!ctx->coords) SETERRQ(ctx->comm, PETSC_ERR_ARG_WRONGSTATE, "The interpolation context has not been setup.");
  ierr = VecDestroy(v);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolate_Simplex_Private"
PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Simplex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
{
  PetscReal      *v0, *J, *invJ, detJ;
  PetscScalar    *a, *coords;
  PetscInt       p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscMalloc3(ctx->dim,PetscReal,&v0,ctx->dim*ctx->dim,PetscReal,&J,ctx->dim*ctx->dim,PetscReal,&invJ);CHKERRQ(ierr);
  ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
  ierr = VecGetArray(v, &a);CHKERRQ(ierr);
  for (p = 0; p < ctx->n; ++p) {
    PetscInt          c = ctx->cells[p];
    const PetscScalar *x;
    PetscReal         xi[4];
    PetscInt          d, f, comp;

    ierr = DMPlexComputeCellGeometry(dm, c, v0, J, invJ, &detJ);CHKERRQ(ierr);
    if (detJ <= 0.0) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Invalid determinant %g for element %d", detJ, c);
    ierr = DMPlexVecGetClosure(dm, PETSC_NULL, xLocal, c, PETSC_NULL, &x);CHKERRQ(ierr);
    for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp];

    for (d = 0; d < ctx->dim; ++d) {
      xi[d] = 0.0;
      for (f = 0; f < ctx->dim; ++f) xi[d] += invJ[d*ctx->dim+f]*0.5*PetscRealPart(coords[p*ctx->dim+f] - v0[f]);
      for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] += PetscRealPart(x[(d+1)*ctx->dof+comp] - x[0*ctx->dof+comp])*xi[d];
    }
    ierr = DMPlexVecRestoreClosure(dm, PETSC_NULL, xLocal, c, PETSC_NULL, &x);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
  ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);
  ierr = PetscFree3(v0, J, invJ);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "QuadMap_Private"
PETSC_STATIC_INLINE PetscErrorCode QuadMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
{
  const PetscScalar *vertices = (const PetscScalar*) ctx;
  const PetscScalar x0        = vertices[0];
  const PetscScalar y0        = vertices[1];
  const PetscScalar x1        = vertices[2];
  const PetscScalar y1        = vertices[3];
  const PetscScalar x2        = vertices[4];
  const PetscScalar y2        = vertices[5];
  const PetscScalar x3        = vertices[6];
  const PetscScalar y3        = vertices[7];
  const PetscScalar f_1       = x1 - x0;
  const PetscScalar g_1       = y1 - y0;
  const PetscScalar f_3       = x3 - x0;
  const PetscScalar g_3       = y3 - y0;
  const PetscScalar f_01      = x2 - x1 - x3 + x0;
  const PetscScalar g_01      = y2 - y1 - y3 + y0;
  PetscScalar       *ref, *real;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
  ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
  {
    const PetscScalar p0 = ref[0];
    const PetscScalar p1 = ref[1];

    real[0] = x0 + f_1 * p0 + f_3 * p1 + f_01 * p0 * p1;
    real[1] = y0 + g_1 * p0 + g_3 * p1 + g_01 * p0 * p1;
  }
  ierr = PetscLogFlops(28);CHKERRQ(ierr);
  ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
  ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "QuadJacobian_Private"
PETSC_STATIC_INLINE PetscErrorCode QuadJacobian_Private(SNES snes, Vec Xref, Mat *J, Mat *M, MatStructure *flag, void *ctx)
{
  const PetscScalar *vertices = (const PetscScalar*) ctx;
  const PetscScalar x0        = vertices[0];
  const PetscScalar y0        = vertices[1];
  const PetscScalar x1        = vertices[2];
  const PetscScalar y1        = vertices[3];
  const PetscScalar x2        = vertices[4];
  const PetscScalar y2        = vertices[5];
  const PetscScalar x3        = vertices[6];
  const PetscScalar y3        = vertices[7];
  const PetscScalar f_01      = x2 - x1 - x3 + x0;
  const PetscScalar g_01      = y2 - y1 - y3 + y0;
  PetscScalar       *ref;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
  {
    const PetscScalar x       = ref[0];
    const PetscScalar y       = ref[1];
    const PetscInt    rows[2] = {0, 1};
    PetscScalar       values[4];

    values[0] = (x1 - x0 + f_01*y) * 0.5; values[1] = (x3 - x0 + f_01*x) * 0.5;
    values[2] = (y1 - y0 + g_01*y) * 0.5; values[3] = (y3 - y0 + g_01*x) * 0.5;
    ierr      = MatSetValues(*J, 2, rows, 2, rows, values, INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscLogFlops(30);CHKERRQ(ierr);
  ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(*J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolate_Quad_Private"
PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Quad_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
{
  DM             dmCoord;
  SNES           snes;
  KSP            ksp;
  PC             pc;
  Vec            coordsLocal, r, ref, real;
  Mat            J;
  PetscScalar    *a, *coords;
  PetscInt       p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
  ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
  ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
  ierr = SNESSetOptionsPrefix(snes, "quad_interp_");CHKERRQ(ierr);
  ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
  ierr = VecSetSizes(r, 2, 2);CHKERRQ(ierr);
  ierr = VecSetFromOptions(r);CHKERRQ(ierr);
  ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
  ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
  ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
  ierr = MatSetSizes(J, 2, 2, 2, 2);CHKERRQ(ierr);
  ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
  ierr = MatSetUp(J);CHKERRQ(ierr);
  ierr = SNESSetFunction(snes, r, QuadMap_Private, PETSC_NULL);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes, J, J, QuadJacobian_Private, PETSC_NULL);CHKERRQ(ierr);
  ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
  ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);

  ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
  ierr = VecGetArray(v, &a);CHKERRQ(ierr);
  for (p = 0; p < ctx->n; ++p) {
    const PetscScalar *x, *vertices;
    PetscScalar       *xi;
    PetscReal         xir[2];
    PetscInt          c = ctx->cells[p], comp, coordSize, xSize;

    /* Can make this do all points at once */
    ierr = DMPlexVecGetClosure(dmCoord, PETSC_NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
    if (4*2 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 4*2);
    ierr = DMPlexVecGetClosure(dm, PETSC_NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
    if (4*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 4*ctx->dof);
    ierr   = SNESSetFunction(snes, PETSC_NULL, PETSC_NULL, (void*) vertices);CHKERRQ(ierr);
    ierr   = SNESSetJacobian(snes, PETSC_NULL, PETSC_NULL, PETSC_NULL, (void*) vertices);CHKERRQ(ierr);
    ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
    xi[0]  = coords[p*ctx->dim+0];
    xi[1]  = coords[p*ctx->dim+1];
    ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
    ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
    ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
    xir[0] = PetscRealPart(xi[0]);
    xir[1] = PetscRealPart(xi[1]);
    for (comp = 0; comp < ctx->dof; ++comp) a[p*ctx->dof+comp] = x[0*ctx->dof+comp]*(1 - xir[0])*(1 - xir[1]) + x[1*ctx->dof+comp]*xir[0]*(1 - xir[1]) + x[2*ctx->dof+comp]*xir[0]*xir[1] + x[3*ctx->dof+comp]*(1 - xir[0])*xir[1];

    ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
    ierr = DMPlexVecRestoreClosure(dmCoord, PETSC_NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
    ierr = DMPlexVecRestoreClosure(dm, PETSC_NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
  ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);

  ierr = SNESDestroy(&snes);CHKERRQ(ierr);
  ierr = VecDestroy(&r);CHKERRQ(ierr);
  ierr = VecDestroy(&ref);CHKERRQ(ierr);
  ierr = VecDestroy(&real);CHKERRQ(ierr);
  ierr = MatDestroy(&J);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "HexMap_Private"
PETSC_STATIC_INLINE PetscErrorCode HexMap_Private(SNES snes, Vec Xref, Vec Xreal, void *ctx)
{
  const PetscScalar *vertices = (const PetscScalar*) ctx;
  const PetscScalar x0        = vertices[0];
  const PetscScalar y0        = vertices[1];
  const PetscScalar z0        = vertices[2];
  const PetscScalar x1        = vertices[3];
  const PetscScalar y1        = vertices[4];
  const PetscScalar z1        = vertices[5];
  const PetscScalar x2        = vertices[6];
  const PetscScalar y2        = vertices[7];
  const PetscScalar z2        = vertices[8];
  const PetscScalar x3        = vertices[9];
  const PetscScalar y3        = vertices[10];
  const PetscScalar z3        = vertices[11];
  const PetscScalar x4        = vertices[12];
  const PetscScalar y4        = vertices[13];
  const PetscScalar z4        = vertices[14];
  const PetscScalar x5        = vertices[15];
  const PetscScalar y5        = vertices[16];
  const PetscScalar z5        = vertices[17];
  const PetscScalar x6        = vertices[18];
  const PetscScalar y6        = vertices[19];
  const PetscScalar z6        = vertices[20];
  const PetscScalar x7        = vertices[21];
  const PetscScalar y7        = vertices[22];
  const PetscScalar z7        = vertices[23];
  const PetscScalar f_1       = x1 - x0;
  const PetscScalar g_1       = y1 - y0;
  const PetscScalar h_1       = z1 - z0;
  const PetscScalar f_3       = x3 - x0;
  const PetscScalar g_3       = y3 - y0;
  const PetscScalar h_3       = z3 - z0;
  const PetscScalar f_4       = x4 - x0;
  const PetscScalar g_4       = y4 - y0;
  const PetscScalar h_4       = z4 - z0;
  const PetscScalar f_01      = x2 - x1 - x3 + x0;
  const PetscScalar g_01      = y2 - y1 - y3 + y0;
  const PetscScalar h_01      = z2 - z1 - z3 + z0;
  const PetscScalar f_12      = x7 - x3 - x4 + x0;
  const PetscScalar g_12      = y7 - y3 - y4 + y0;
  const PetscScalar h_12      = z7 - z3 - z4 + z0;
  const PetscScalar f_02      = x5 - x1 - x4 + x0;
  const PetscScalar g_02      = y5 - y1 - y4 + y0;
  const PetscScalar h_02      = z5 - z1 - z4 + z0;
  const PetscScalar f_012     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
  const PetscScalar g_012     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
  const PetscScalar h_012     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
  PetscScalar       *ref, *real;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
  ierr = VecGetArray(Xreal, &real);CHKERRQ(ierr);
  {
    const PetscScalar p0 = ref[0];
    const PetscScalar p1 = ref[1];
    const PetscScalar p2 = ref[2];

    real[0] = x0 + f_1*p0 + f_3*p1 + f_4*p2 + f_01*p0*p1 + f_12*p1*p2 + f_02*p0*p2 + f_012*p0*p1*p2;
    real[1] = y0 + g_1*p0 + g_3*p1 + g_4*p2 + g_01*p0*p1 + g_01*p0*p1 + g_12*p1*p2 + g_02*p0*p2 + g_012*p0*p1*p2;
    real[2] = z0 + h_1*p0 + h_3*p1 + h_4*p2 + h_01*p0*p1 + h_01*p0*p1 + h_12*p1*p2 + h_02*p0*p2 + h_012*p0*p1*p2;
  }
  ierr = PetscLogFlops(114);CHKERRQ(ierr);
  ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
  ierr = VecRestoreArray(Xreal, &real);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "HexJacobian_Private"
PETSC_STATIC_INLINE PetscErrorCode HexJacobian_Private(SNES snes, Vec Xref, Mat *J, Mat *M, MatStructure *flag, void *ctx)
{
  const PetscScalar *vertices = (const PetscScalar*) ctx;
  const PetscScalar x0        = vertices[0];
  const PetscScalar y0        = vertices[1];
  const PetscScalar z0        = vertices[2];
  const PetscScalar x1        = vertices[3];
  const PetscScalar y1        = vertices[4];
  const PetscScalar z1        = vertices[5];
  const PetscScalar x2        = vertices[6];
  const PetscScalar y2        = vertices[7];
  const PetscScalar z2        = vertices[8];
  const PetscScalar x3        = vertices[9];
  const PetscScalar y3        = vertices[10];
  const PetscScalar z3        = vertices[11];
  const PetscScalar x4        = vertices[12];
  const PetscScalar y4        = vertices[13];
  const PetscScalar z4        = vertices[14];
  const PetscScalar x5        = vertices[15];
  const PetscScalar y5        = vertices[16];
  const PetscScalar z5        = vertices[17];
  const PetscScalar x6        = vertices[18];
  const PetscScalar y6        = vertices[19];
  const PetscScalar z6        = vertices[20];
  const PetscScalar x7        = vertices[21];
  const PetscScalar y7        = vertices[22];
  const PetscScalar z7        = vertices[23];
  const PetscScalar f_xy      = x2 - x1 - x3 + x0;
  const PetscScalar g_xy      = y2 - y1 - y3 + y0;
  const PetscScalar h_xy      = z2 - z1 - z3 + z0;
  const PetscScalar f_yz      = x7 - x3 - x4 + x0;
  const PetscScalar g_yz      = y7 - y3 - y4 + y0;
  const PetscScalar h_yz      = z7 - z3 - z4 + z0;
  const PetscScalar f_xz      = x5 - x1 - x4 + x0;
  const PetscScalar g_xz      = y5 - y1 - y4 + y0;
  const PetscScalar h_xz      = z5 - z1 - z4 + z0;
  const PetscScalar f_xyz     = x6 - x0 + x1 - x2 + x3 + x4 - x5 - x7;
  const PetscScalar g_xyz     = y6 - y0 + y1 - y2 + y3 + y4 - y5 - y7;
  const PetscScalar h_xyz     = z6 - z0 + z1 - z2 + z3 + z4 - z5 - z7;
  PetscScalar       *ref;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = VecGetArray(Xref,  &ref);CHKERRQ(ierr);
  {
    const PetscScalar x       = ref[0];
    const PetscScalar y       = ref[1];
    const PetscScalar z       = ref[2];
    const PetscInt    rows[3] = {0, 1, 2};
    PetscScalar       values[9];

    values[0] = (x1 - x0 + f_xy*y + f_xz*z + f_xyz*y*z) / 2.0;
    values[1] = (x3 - x0 + f_xy*x + f_yz*z + f_xyz*x*z) / 2.0;
    values[2] = (x4 - x0 + f_yz*y + f_xz*x + f_xyz*x*y) / 2.0;
    values[3] = (y1 - y0 + g_xy*y + g_xz*z + g_xyz*y*z) / 2.0;
    values[4] = (y3 - y0 + g_xy*x + g_yz*z + g_xyz*x*z) / 2.0;
    values[5] = (y4 - y0 + g_yz*y + g_xz*x + g_xyz*x*y) / 2.0;
    values[6] = (z1 - z0 + h_xy*y + h_xz*z + h_xyz*y*z) / 2.0;
    values[7] = (z3 - z0 + h_xy*x + h_yz*z + h_xyz*x*z) / 2.0;
    values[8] = (z4 - z0 + h_yz*y + h_xz*x + h_xyz*x*y) / 2.0;

    ierr = MatSetValues(*J, 3, rows, 3, rows, values, INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = PetscLogFlops(152);CHKERRQ(ierr);
  ierr = VecRestoreArray(Xref,  &ref);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(*J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*J, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolate_Hex_Private"
PETSC_STATIC_INLINE PetscErrorCode DMInterpolate_Hex_Private(DMInterpolationInfo ctx, DM dm, Vec xLocal, Vec v)
{
  DM             dmCoord;
  SNES           snes;
  KSP            ksp;
  PC             pc;
  Vec            coordsLocal, r, ref, real;
  Mat            J;
  PetscScalar    *a, *coords;
  PetscInt       p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetCoordinatesLocal(dm, &coordsLocal);CHKERRQ(ierr);
  ierr = DMGetCoordinateDM(dm, &dmCoord);CHKERRQ(ierr);
  ierr = SNESCreate(PETSC_COMM_SELF, &snes);CHKERRQ(ierr);
  ierr = SNESSetOptionsPrefix(snes, "hex_interp_");CHKERRQ(ierr);
  ierr = VecCreate(PETSC_COMM_SELF, &r);CHKERRQ(ierr);
  ierr = VecSetSizes(r, 3, 3);CHKERRQ(ierr);
  ierr = VecSetFromOptions(r);CHKERRQ(ierr);
  ierr = VecDuplicate(r, &ref);CHKERRQ(ierr);
  ierr = VecDuplicate(r, &real);CHKERRQ(ierr);
  ierr = MatCreate(PETSC_COMM_SELF, &J);CHKERRQ(ierr);
  ierr = MatSetSizes(J, 3, 3, 3, 3);CHKERRQ(ierr);
  ierr = MatSetType(J, MATSEQDENSE);CHKERRQ(ierr);
  ierr = MatSetUp(J);CHKERRQ(ierr);
  ierr = SNESSetFunction(snes, r, HexMap_Private, PETSC_NULL);CHKERRQ(ierr);
  ierr = SNESSetJacobian(snes, J, J, HexJacobian_Private, PETSC_NULL);CHKERRQ(ierr);
  ierr = SNESGetKSP(snes, &ksp);CHKERRQ(ierr);
  ierr = KSPGetPC(ksp, &pc);CHKERRQ(ierr);
  ierr = PCSetType(pc, PCLU);CHKERRQ(ierr);
  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);

  ierr = VecGetArray(ctx->coords, &coords);CHKERRQ(ierr);
  ierr = VecGetArray(v, &a);CHKERRQ(ierr);
  for (p = 0; p < ctx->n; ++p) {
    const PetscScalar *x, *vertices;
    PetscScalar       *xi;
    PetscReal         xir[3];
    PetscInt          c = ctx->cells[p], comp, coordSize, xSize;

    /* Can make this do all points at once */
    ierr = DMPlexVecGetClosure(dmCoord, PETSC_NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
    if (8*3 != coordSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", coordSize, 8*3);
    ierr = DMPlexVecGetClosure(dm, PETSC_NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
    if (8*ctx->dof != xSize) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid closure size %d should be %d", xSize, 8*ctx->dof);
    ierr   = SNESSetFunction(snes, PETSC_NULL, PETSC_NULL, (void*) vertices);CHKERRQ(ierr);
    ierr   = SNESSetJacobian(snes, PETSC_NULL, PETSC_NULL, PETSC_NULL, (void*) vertices);CHKERRQ(ierr);
    ierr   = VecGetArray(real, &xi);CHKERRQ(ierr);
    xi[0]  = coords[p*ctx->dim+0];
    xi[1]  = coords[p*ctx->dim+1];
    xi[2]  = coords[p*ctx->dim+2];
    ierr   = VecRestoreArray(real, &xi);CHKERRQ(ierr);
    ierr   = SNESSolve(snes, real, ref);CHKERRQ(ierr);
    ierr   = VecGetArray(ref, &xi);CHKERRQ(ierr);
    xir[0] = PetscRealPart(xi[0]);
    xir[1] = PetscRealPart(xi[1]);
    xir[2] = PetscRealPart(xi[2]);
    for (comp = 0; comp < ctx->dof; ++comp) {
      a[p*ctx->dof+comp] =
        x[0*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*(1-xir[2]) +
        x[1*ctx->dof+comp]*    xir[0]*(1-xir[1])*(1-xir[2]) +
        x[2*ctx->dof+comp]*    xir[0]*    xir[1]*(1-xir[2]) +
        x[3*ctx->dof+comp]*(1-xir[0])*    xir[1]*(1-xir[2]) +
        x[4*ctx->dof+comp]*(1-xir[0])*(1-xir[1])*   xir[2] +
        x[5*ctx->dof+comp]*    xir[0]*(1-xir[1])*   xir[2] +
        x[6*ctx->dof+comp]*    xir[0]*    xir[1]*   xir[2] +
        x[7*ctx->dof+comp]*(1-xir[0])*    xir[1]*   xir[2];
    }
    ierr = VecRestoreArray(ref, &xi);CHKERRQ(ierr);
    ierr = DMPlexVecRestoreClosure(dmCoord, PETSC_NULL, coordsLocal, c, &coordSize, &vertices);CHKERRQ(ierr);
    ierr = DMPlexVecRestoreClosure(dm, PETSC_NULL, xLocal, c, &xSize, &x);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(v, &a);CHKERRQ(ierr);
  ierr = VecRestoreArray(ctx->coords, &coords);CHKERRQ(ierr);

  ierr = SNESDestroy(&snes);CHKERRQ(ierr);
  ierr = VecDestroy(&r);CHKERRQ(ierr);
  ierr = VecDestroy(&ref);CHKERRQ(ierr);
  ierr = VecDestroy(&real);CHKERRQ(ierr);
  ierr = MatDestroy(&J);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationEvaluate"
/*
  Input Parameters:
+ ctx - The DMInterpolationInfo context
. dm  - The DM
- x   - The local vector containing the field to be interpolated

  Output Parameters:
. v   - The vector containing the interpolated values
*/
PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo ctx, DM dm, Vec x, Vec v)
{
  PetscInt       dim, coneSize, n;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
  PetscValidHeaderSpecific(x, VEC_CLASSID, 3);
  PetscValidHeaderSpecific(v, VEC_CLASSID, 4);
  ierr = VecGetLocalSize(v, &n);CHKERRQ(ierr);
  if (n != ctx->n*ctx->dof) SETERRQ2(ctx->comm, PETSC_ERR_ARG_SIZ, "Invalid input vector size %d should be %d", n, ctx->n*ctx->dof);
  if (n) {
    ierr = DMPlexGetDimension(dm, &dim);CHKERRQ(ierr);
    ierr = DMPlexGetConeSize(dm, ctx->cells[0], &coneSize);CHKERRQ(ierr);
    if (dim == 2) {
      if (coneSize == 3) {
        ierr = DMInterpolate_Simplex_Private(ctx, dm, x, v);CHKERRQ(ierr);
      } else if (coneSize == 4) {
        ierr = DMInterpolate_Quad_Private(ctx, dm, x, v);CHKERRQ(ierr);
      } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
    } else if (dim == 3) {
      if (coneSize == 4) {
        ierr = DMInterpolate_Simplex_Private(ctx, dm, x, v);CHKERRQ(ierr);
      } else {
        ierr = DMInterpolate_Hex_Private(ctx, dm, x, v);CHKERRQ(ierr);
      }
    } else SETERRQ1(ctx->comm, PETSC_ERR_ARG_OUTOFRANGE, "Unsupported dimension %d for point interpolation", dim);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMInterpolationDestroy"
PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *ctx)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidPointer(ctx, 2);
  ierr = VecDestroy(&(*ctx)->coords);CHKERRQ(ierr);
  ierr = PetscFree((*ctx)->points);CHKERRQ(ierr);
  ierr = PetscFree((*ctx)->cells);CHKERRQ(ierr);
  ierr = PetscFree(*ctx);CHKERRQ(ierr);
  *ctx = PETSC_NULL;
  PetscFunctionReturn(0);
}