xref: /petsc/src/dm/dt/space/impls/wxy/spacewxy.c (revision 69cc43acf904673348835f1e68d7a5ddf92b44cb)

#include <petsc/private/petscfeimpl.h> /*I "petscfe.h" I*/

static PetscErrorCode PetscSpaceSetFromOptions_WXY(PetscOptionItems *PetscOptionsObject,PetscSpace sp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscOptionsHead(PetscOptionsObject,"PetscSpace WXY options");CHKERRQ(ierr);
  ierr = PetscOptionsTail();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpacePolynomialView_Ascii(PetscSpace sp, PetscViewer v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscViewerASCIIPrintf(v, "WXY space of degree %" PetscInt_FMT "\n", sp->degree);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpaceView_WXY(PetscSpace sp, PetscViewer viewer)
{
  PetscBool      iascii;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
  if (iascii) {ierr = PetscSpacePolynomialView_Ascii(sp, viewer);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpaceDestroy_WXY(PetscSpace sp)
{
  PetscSpace_WXY *wxy = (PetscSpace_WXY *) sp->data;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  ierr = PetscFree(wxy);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpaceSetUp_WXY(PetscSpace sp)
{
  PetscSpace_WXY *wxy = (PetscSpace_WXY *) sp->data;

  PetscFunctionBegin;
  if (wxy->setupCalled) PetscFunctionReturn(0);
  PetscCheck(sp->degree >= 0, PetscObjectComm((PetscObject)sp), PETSC_ERR_ARG_OUTOFRANGE, "Negative degree %" PetscInt_FMT " invalid\n", sp->degree);
  sp->maxDegree = sp->degree;
  wxy->setupCalled = PETSC_TRUE;
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpaceGetDimension_WXY(PetscSpace sp, PetscInt *dim)
{
  PetscFunctionBegin;
  *dim = 6;
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpaceEvaluate_WXY(PetscSpace sp, PetscInt npoints, const PetscReal points[], PetscReal B[], PetscReal D[], PetscReal H[])
{
  PetscSpace_WXY *wxy = (PetscSpace_WXY *) sp->data;
  PetscInt        dim = sp->Nv;
  PetscInt        Nb  = 6;
  PetscInt        Nc  = 3;

  PetscFunctionBegin;
  if (!wxy->setupCalled) {
    PetscErrorCode ierr;
    ierr = PetscSpaceSetUp(sp);CHKERRQ(ierr);
    ierr = PetscSpaceEvaluate(sp, npoints, points, B, D, H);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  PetscCheck((sp->Nc == 3) && (sp->Nv == 3), PETSC_COMM_SELF, PETSC_ERR_PLIB, "WXY space must have 3 variables and 3 components");
  if (B) {
    PetscInt p_inc = Nb*Nc;
    PetscInt b_inc = Nc;
    PetscInt c_inc = 1;

    for (PetscInt p = 0; p < npoints; p++) {
      const PetscReal x = points[p*dim+0];
      const PetscReal y = points[p*dim+1];
      const PetscReal z = points[p*dim+2];

      /* {2 y z, 0, 0} */
      B[p*p_inc + 0*b_inc + 0*c_inc] = 2.*y*z;
      B[p*p_inc + 0*b_inc + 1*c_inc] = 0.;
      B[p*p_inc + 0*b_inc + 2*c_inc] = 0.;
      /* {0, 2 x z, 0} */
      B[p*p_inc + 1*b_inc + 0*c_inc] = 0.;
      B[p*p_inc + 1*b_inc + 1*c_inc] = 2.*x*z;
      B[p*p_inc + 1*b_inc + 2*c_inc] = 0.;
      /* {0, 2 y z, -z^2} */
      B[p*p_inc + 2*b_inc + 0*c_inc] = 0.;
      B[p*p_inc + 2*b_inc + 1*c_inc] = 2.*y*z;
      B[p*p_inc + 2*b_inc + 2*c_inc] = -z*z;
      /* {2 x z, 0, -z^2} */
      B[p*p_inc + 3*b_inc + 0*c_inc] = 2.*x*z;
      B[p*p_inc + 3*b_inc + 1*c_inc] = 0.;
      B[p*p_inc + 3*b_inc + 2*c_inc] = -z*z;
      /* {x^2, x y, -3 x z} */
      B[p*p_inc + 4*b_inc + 0*c_inc] = x*x;
      B[p*p_inc + 4*b_inc + 1*c_inc] = x*y;
      B[p*p_inc + 4*b_inc + 2*c_inc] = -3.*x*z;
      /* {x y, y^2, -3 y z} */
      B[p*p_inc + 5*b_inc + 0*c_inc] = x*y;
      B[p*p_inc + 5*b_inc + 1*c_inc] = y*y;
      B[p*p_inc + 5*b_inc + 2*c_inc] = -3.*y*z;
    }
  }
  if (D) {
    PetscInt p_inc = Nb*Nc*dim;
    PetscInt b_inc = Nc*dim;
    PetscInt c_inc = dim;

    for (PetscInt p = 0; p < npoints; p++) {
      const PetscReal x = points[p*dim+0];
      const PetscReal y = points[p*dim+1];
      const PetscReal z = points[p*dim+2];

      /* {2 y z, 0, 0} */
      D[p*p_inc + 0*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 1] = 2.*z;
      D[p*p_inc + 0*b_inc + 0*c_inc + 2] = 2.*y;
      D[p*p_inc + 0*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 2] = 0.;
      /* {0, 2 x z, 0} */
      D[p*p_inc + 1*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 0] = 2.*z;
      D[p*p_inc + 1*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 2] = 2.*x;
      D[p*p_inc + 1*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 2] = 0.;
      /* {0, 2 y z, -z^2} */
      D[p*p_inc + 2*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 1] = 2.*z;
      D[p*p_inc + 2*b_inc + 1*c_inc + 2] = 2.*y;
      D[p*p_inc + 2*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 2] = -2.*z;
      /* {2 x z, 0, -z^2} */
      D[p*p_inc + 3*b_inc + 0*c_inc + 0] = 2.*z;
      D[p*p_inc + 3*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 2] = 2.*x;
      D[p*p_inc + 3*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 2] = -2.*z;
      /* {x^2, x y, -3 x z} */
      D[p*p_inc + 4*b_inc + 0*c_inc + 0] = 2.*x;
      D[p*p_inc + 4*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 0] = y;
      D[p*p_inc + 4*b_inc + 1*c_inc + 1] = x;
      D[p*p_inc + 4*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 0] = -3.*z;
      D[p*p_inc + 4*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 2] = -3.*x;
      /* {x y, y^2, -3 y z} */
      D[p*p_inc + 5*b_inc + 0*c_inc + 0] = y;
      D[p*p_inc + 5*b_inc + 0*c_inc + 1] = x;
      D[p*p_inc + 5*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 5*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 5*b_inc + 1*c_inc + 1] = 2.*y;
      D[p*p_inc + 5*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 5*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 5*b_inc + 2*c_inc + 1] = -3.*z;
      D[p*p_inc + 5*b_inc + 2*c_inc + 2] = -3.*y;
    }
  }
  if (H) {
    PetscInt p_inc = Nb*Nc*dim*dim;
    PetscInt b_inc = Nc*dim*dim;
    PetscInt c_inc = dim*dim;

    for (PetscInt p = 0; p < npoints; p++) {
      /* {2 y z, 0, 0} */
      D[p*p_inc + 0*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 3] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 4] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 5] = 2.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 6] = 0.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 7] = 2.;
      D[p*p_inc + 0*b_inc + 0*c_inc + 8] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 3] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 4] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 5] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 6] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 7] = 0.;
      D[p*p_inc + 0*b_inc + 1*c_inc + 8] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 2] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 3] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 4] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 5] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 6] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 7] = 0.;
      D[p*p_inc + 0*b_inc + 2*c_inc + 8] = 0.;
      /* {0, 2 x z, 0} */
      D[p*p_inc + 1*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 3] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 4] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 5] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 6] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 7] = 0.;
      D[p*p_inc + 1*b_inc + 0*c_inc + 8] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 2] = 2.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 3] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 4] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 5] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 6] = 2.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 7] = 0.;
      D[p*p_inc + 1*b_inc + 1*c_inc + 8] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 2] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 3] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 4] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 5] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 6] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 7] = 0.;
      D[p*p_inc + 1*b_inc + 2*c_inc + 8] = 0.;
      /* {0, 2 y z, -z^2} */
      D[p*p_inc + 2*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 3] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 4] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 5] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 6] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 7] = 0.;
      D[p*p_inc + 2*b_inc + 0*c_inc + 8] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 3] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 4] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 5] = 2.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 6] = 0.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 7] = 2.;
      D[p*p_inc + 2*b_inc + 1*c_inc + 8] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 2] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 3] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 4] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 5] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 6] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 7] = 0.;
      D[p*p_inc + 2*b_inc + 2*c_inc + 8] = -2.;
      /* {2 x z, 0, -z^2} */
      D[p*p_inc + 3*b_inc + 0*c_inc + 0] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 2] = 2.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 3] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 4] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 5] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 6] = 2.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 7] = 0.;
      D[p*p_inc + 3*b_inc + 0*c_inc + 8] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 1] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 3] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 4] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 5] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 6] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 7] = 0.;
      D[p*p_inc + 3*b_inc + 1*c_inc + 8] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 2] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 3] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 4] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 5] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 6] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 7] = 0.;
      D[p*p_inc + 3*b_inc + 2*c_inc + 8] = -2.;
      /* {x^2, x y, -3 x z} */
      D[p*p_inc + 4*b_inc + 0*c_inc + 0] = 2.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 3] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 4] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 5] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 6] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 7] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 8] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 1] = 1.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 3] = 1.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 4] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 5] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 6] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 7] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 8] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 2] = -3.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 3] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 4] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 5] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 6] = -3.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 7] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 8] = 0.;
      /* {x y, y^2, -3 y z} */
      D[p*p_inc + 4*b_inc + 0*c_inc + 0] = 2.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 1] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 2] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 3] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 4] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 5] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 6] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 7] = 0.;
      D[p*p_inc + 4*b_inc + 0*c_inc + 8] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 0] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 1] = 1.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 2] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 3] = 1.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 4] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 5] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 6] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 7] = 0.;
      D[p*p_inc + 4*b_inc + 1*c_inc + 8] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 0] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 1] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 2] = -3.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 3] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 4] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 5] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 6] = -3.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 7] = 0.;
      D[p*p_inc + 4*b_inc + 2*c_inc + 8] = 0.;
    }
  }
  PetscFunctionReturn(0);
}

static PetscErrorCode PetscSpaceGetHeightSubspace_WXY(PetscSpace sp, PetscInt height, PetscSpace *subsp)
{
  SETERRQ(PetscObjectComm((PetscObject) sp), PETSC_ERR_SUP, "Do not know how to do this");
}

static PetscErrorCode PetscSpaceInitialize_WXY(PetscSpace sp)
{
  PetscFunctionBegin;
  sp->ops->setfromoptions    = PetscSpaceSetFromOptions_WXY;
  sp->ops->setup             = PetscSpaceSetUp_WXY;
  sp->ops->view              = PetscSpaceView_WXY;
  sp->ops->destroy           = PetscSpaceDestroy_WXY;
  sp->ops->getdimension      = PetscSpaceGetDimension_WXY;
  sp->ops->evaluate          = PetscSpaceEvaluate_WXY;
  sp->ops->getheightsubspace = PetscSpaceGetHeightSubspace_WXY;
  PetscFunctionReturn(0);
}

/*MC
  PETSCSPACEWXY = "wxy" - A PetscSpace object that encapsulates the Wheeler-Xu-Yotov enrichments.
$ curl {{0, 0, y^2 z}, {x z^2, 0, 0}, {y z^2, 0, 0}, {0, -x z^2, 0}, {0, -3/2 x^2 z, -1/2 x^2 y}, {3/2 y^2 z, 0, 1/2 y^2 x}}
$ = {{2 y z, 0, 0}, {0, 2 x z, 0}, {0, 2 y z, -z^2}, {2 x z, 0, -z^2}, {x^2, x y, -3 x z}, {x y, y^2, -3 y z}}

  Level: intermediate

.seealso: PetscSpaceType, PetscSpaceCreate(), PetscSpaceSetType()
M*/

PETSC_EXTERN PetscErrorCode PetscSpaceCreate_WXY(PetscSpace sp)
{
  PetscSpace_WXY *wxy;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(sp, PETSCSPACE_CLASSID, 1);
  ierr     = PetscNewLog(sp,&wxy);CHKERRQ(ierr);
  sp->data = wxy;
  sp->degree = 2;

  ierr = PetscSpaceInitialize_WXY(sp);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}