xref: /petsc/src/dm/tests/ex36.c (revision 327415f76d85372a4417cf1aaa14db707d4d6c04)

static char help[] = "Checks the functionality of DMGetInterpolation() on deformed grids.\n\n";

#include <petscdm.h>
#include <petscdmda.h>

typedef struct _n_CCmplx CCmplx;
struct _n_CCmplx {
  PetscReal real;
  PetscReal imag;
};

CCmplx CCmplxPow(CCmplx a,PetscReal n)
{
  CCmplx b;
  PetscReal r,theta;
  r      = PetscSqrtReal(a.real*a.real + a.imag*a.imag);
  theta  = PetscAtan2Real(a.imag,a.real);
  b.real = PetscPowReal(r,n) * PetscCosReal(n*theta);
  b.imag = PetscPowReal(r,n) * PetscSinReal(n*theta);
  return b;
}
CCmplx CCmplxExp(CCmplx a)
{
  CCmplx b;
  b.real = PetscExpReal(a.real) * PetscCosReal(a.imag);
  b.imag = PetscExpReal(a.real) * PetscSinReal(a.imag);
  return b;
}
CCmplx CCmplxSqrt(CCmplx a)
{
  CCmplx b;
  PetscReal r,theta;
  r      = PetscSqrtReal(a.real*a.real + a.imag*a.imag);
  theta  = PetscAtan2Real(a.imag,a.real);
  b.real = PetscSqrtReal(r) * PetscCosReal(0.5*theta);
  b.imag = PetscSqrtReal(r) * PetscSinReal(0.5*theta);
  return b;
}
CCmplx CCmplxAdd(CCmplx a,CCmplx c)
{
  CCmplx b;
  b.real = a.real +c.real;
  b.imag = a.imag +c.imag;
  return b;
}
PetscScalar CCmplxRe(CCmplx a)
{
  return (PetscScalar)a.real;
}
PetscScalar CCmplxIm(CCmplx a)
{
  return (PetscScalar)a.imag;
}

PetscErrorCode DAApplyConformalMapping(DM da,PetscInt idx)
{
  PetscInt       i,n;
  PetscInt       sx,nx,sy,ny,sz,nz,dim;
  Vec            Gcoords;
  PetscScalar    *XX;
  PetscScalar    xx,yy,zz;
  DM             cda;

  PetscFunctionBeginUser;
  if (idx==0) {
    PetscFunctionReturn(0);
  } else if (idx==1) { /* dam break */
    PetscCall(DMDASetUniformCoordinates(da, -1.0,1.0, -1.0,1.0, -1.0,1.0));
  } else if (idx==2) { /* stagnation in a corner */
    PetscCall(DMDASetUniformCoordinates(da, -1.0,1.0, 0.0,1.0, -1.0,1.0));
  } else if (idx==3) { /* nautilis */
    PetscCall(DMDASetUniformCoordinates(da, -1.0,1.0, -1.0,1.0, -1.0,1.0));
  } else if (idx==4) PetscCall(DMDASetUniformCoordinates(da, -1.0,1.0, -1.0,1.0, -1.0,1.0));

  PetscCall(DMGetCoordinateDM(da,&cda));
  PetscCall(DMGetCoordinates(da,&Gcoords));

  PetscCall(VecGetArray(Gcoords,&XX));
  PetscCall(DMDAGetCorners(da,&sx,&sy,&sz,&nx,&ny,&nz));
  PetscCall(DMDAGetInfo(da, &dim, 0,0,0, 0,0,0, 0,0,0,0,0,0));
  PetscCall(VecGetLocalSize(Gcoords,&n));
  n    = n / dim;

  for (i=0; i<n; i++) {
    if ((dim==3) && (idx!=2)) {
      PetscScalar Ni[8];
      PetscScalar xi   = XX[dim*i];
      PetscScalar eta  = XX[dim*i+1];
      PetscScalar zeta = XX[dim*i+2];
      PetscScalar xn[] = {-1.0,1.0,-1.0,1.0,   -1.0,1.0,-1.0,1.0  };
      PetscScalar yn[] = {-1.0,-1.0,1.0,1.0,   -1.0,-1.0,1.0,1.0  };
      PetscScalar zn[] = {-0.1,-4.0,-0.2,-1.0,  0.1,4.0,0.2,1.0  };
      PetscInt    p;

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

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

      xx = yy = zz = 0.0;
      for (p=0; p<8; p++) {
        xx += Ni[p]*xn[p];
        yy += Ni[p]*yn[p];
        zz += Ni[p]*zn[p];
      }
      XX[dim*i]   = xx;
      XX[dim*i+1] = yy;
      XX[dim*i+2] = zz;
    }

    if (idx==1) {
      CCmplx zeta,t1,t2;

      xx = XX[dim*i]   - 0.8;
      yy = XX[dim*i+1] + 1.5;

      zeta.real = PetscRealPart(xx);
      zeta.imag = PetscRealPart(yy);

      t1 = CCmplxPow(zeta,-1.0);
      t2 = CCmplxAdd(zeta,t1);

      XX[dim*i]   = CCmplxRe(t2);
      XX[dim*i+1] = CCmplxIm(t2);
    } else if (idx==2) {
      CCmplx zeta,t1;

      xx = XX[dim*i];
      yy = XX[dim*i+1];
      zeta.real = PetscRealPart(xx);
      zeta.imag = PetscRealPart(yy);

      t1 = CCmplxSqrt(zeta);
      XX[dim*i]   = CCmplxRe(t1);
      XX[dim*i+1] = CCmplxIm(t1);
    } else if (idx==3) {
      CCmplx zeta,t1,t2;

      xx = XX[dim*i]   - 0.8;
      yy = XX[dim*i+1] + 1.5;

      zeta.real   = PetscRealPart(xx);
      zeta.imag   = PetscRealPart(yy);
      t1          = CCmplxPow(zeta,-1.0);
      t2          = CCmplxAdd(zeta,t1);
      XX[dim*i]   = CCmplxRe(t2);
      XX[dim*i+1] = CCmplxIm(t2);

      xx          = XX[dim*i];
      yy          = XX[dim*i+1];
      zeta.real   = PetscRealPart(xx);
      zeta.imag   = PetscRealPart(yy);
      t1          = CCmplxExp(zeta);
      XX[dim*i]   = CCmplxRe(t1);
      XX[dim*i+1] = CCmplxIm(t1);

      xx          = XX[dim*i] + 0.4;
      yy          = XX[dim*i+1];
      zeta.real   = PetscRealPart(xx);
      zeta.imag   = PetscRealPart(yy);
      t1          = CCmplxPow(zeta,2.0);
      XX[dim*i]   = CCmplxRe(t1);
      XX[dim*i+1] = CCmplxIm(t1);
    } else if (idx==4) {
      PetscScalar Ni[4];
      PetscScalar xi   = XX[dim*i];
      PetscScalar eta  = XX[dim*i+1];
      PetscScalar xn[] = {0.0,2.0,0.2,3.5};
      PetscScalar yn[] = {-1.3,0.0,2.0,4.0};
      PetscInt    p;

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

      xx = yy = 0.0;
      for (p=0; p<4; p++) {
        xx += Ni[p]*xn[p];
        yy += Ni[p]*yn[p];
      }
      XX[dim*i]   = xx;
      XX[dim*i+1] = yy;
    }
  }
  PetscCall(VecRestoreArray(Gcoords,&XX));
  PetscFunctionReturn(0);
}

PetscErrorCode DAApplyTrilinearMapping(DM da)
{
  PetscInt       i,j,k;
  PetscInt       sx,nx,sy,ny,sz,nz;
  Vec            Gcoords;
  DMDACoor3d     ***XX;
  PetscScalar    xx,yy,zz;
  DM             cda;

  PetscFunctionBeginUser;
  PetscCall(DMDASetUniformCoordinates(da, -1.0,1.0, -1.0,1.0, -1.0,1.0));
  PetscCall(DMGetCoordinateDM(da,&cda));
  PetscCall(DMGetCoordinates(da,&Gcoords));

  PetscCall(DMDAVecGetArrayRead(cda,Gcoords,&XX));
  PetscCall(DMDAGetCorners(da,&sx,&sy,&sz,&nx,&ny,&nz));

  for (i=sx; i<sx+nx; i++) {
    for (j=sy; j<sy+ny; j++) {
      for (k=sz; k<sz+nz; k++) {
        PetscScalar Ni[8];
        PetscScalar xi   = XX[k][j][i].x;
        PetscScalar eta  = XX[k][j][i].y;
        PetscScalar zeta = XX[k][j][i].z;
        PetscScalar xn[] = {0.0,2.0,0.2,3.5,   0.0,2.1,0.23,3.125  };
        PetscScalar yn[] = {-1.3,0.0,2.0,4.0,  -1.45,-0.1,2.24,3.79  };
        PetscScalar zn[] = {0.0,0.3,-0.1,0.123,  0.956,1.32,1.12,0.798  };
        PetscInt    p;

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

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

        xx = yy = zz = 0.0;
        for (p=0; p<8; p++) {
          xx += Ni[p]*xn[p];
          yy += Ni[p]*yn[p];
          zz += Ni[p]*zn[p];
        }
        XX[k][j][i].x = xx;
        XX[k][j][i].y = yy;
        XX[k][j][i].z = zz;
      }
    }
  }
  PetscCall(DMDAVecRestoreArrayRead(cda,Gcoords,&XX));
  PetscFunctionReturn(0);
}

PetscErrorCode DADefineXLinearField2D(DM da,Vec field)
{
  PetscInt       i,j;
  PetscInt       sx,nx,sy,ny;
  Vec            Gcoords;
  DMDACoor2d     **XX;
  PetscScalar    **FF;
  DM             cda;

  PetscFunctionBeginUser;
  PetscCall(DMGetCoordinateDM(da,&cda));
  PetscCall(DMGetCoordinates(da,&Gcoords));

  PetscCall(DMDAVecGetArrayRead(cda,Gcoords,&XX));
  PetscCall(DMDAVecGetArray(da,field,&FF));

  PetscCall(DMDAGetCorners(da,&sx,&sy,0,&nx,&ny,0));

  for (i=sx; i<sx+nx; i++) {
    for (j=sy; j<sy+ny; j++) {
      FF[j][i] = 10.0 + 3.0 * XX[j][i].x + 5.5 * XX[j][i].y + 8.003 * XX[j][i].x * XX[j][i].y;
    }
  }

  PetscCall(DMDAVecRestoreArray(da,field,&FF));
  PetscCall(DMDAVecRestoreArrayRead(cda,Gcoords,&XX));
  PetscFunctionReturn(0);
}

PetscErrorCode DADefineXLinearField3D(DM da,Vec field)
{
  PetscInt       i,j,k;
  PetscInt       sx,nx,sy,ny,sz,nz;
  Vec            Gcoords;
  DMDACoor3d     ***XX;
  PetscScalar    ***FF;
  DM             cda;

  PetscFunctionBeginUser;
  PetscCall(DMGetCoordinateDM(da,&cda));
  PetscCall(DMGetCoordinates(da,&Gcoords));

  PetscCall(DMDAVecGetArrayRead(cda,Gcoords,&XX));
  PetscCall(DMDAVecGetArray(da,field,&FF));

  PetscCall(DMDAGetCorners(da,&sx,&sy,&sz,&nx,&ny,&nz));

  for (k=sz; k<sz+nz; k++) {
    for (j=sy; j<sy+ny; j++) {
      for (i=sx; i<sx+nx; i++) {
        FF[k][j][i] = 10.0
                + 4.05 * XX[k][j][i].x
                + 5.50 * XX[k][j][i].y
                + 1.33 * XX[k][j][i].z
                + 2.03 * XX[k][j][i].x * XX[k][j][i].y
                + 0.03 * XX[k][j][i].x * XX[k][j][i].z
                + 0.83 * XX[k][j][i].y * XX[k][j][i].z
                + 3.79 * XX[k][j][i].x * XX[k][j][i].y * XX[k][j][i].z;
      }
    }
  }

  PetscCall(DMDAVecRestoreArray(da,field,&FF));
  PetscCall(DMDAVecRestoreArrayRead(cda,Gcoords,&XX));
  PetscFunctionReturn(0);
}

PetscErrorCode da_test_RefineCoords1D(PetscInt mx)
{
  DM             dac,daf;
  PetscViewer    vv;
  Vec            ac,af;
  PetscInt       Mx;
  Mat            II,INTERP;
  Vec            scale;
  PetscBool      output = PETSC_FALSE;

  PetscFunctionBeginUser;
  PetscCall(DMDACreate1d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE,mx+1,1, /* 1 dof */1, /* stencil = 1 */NULL,&dac));
  PetscCall(DMSetFromOptions(dac));
  PetscCall(DMSetUp(dac));

  PetscCall(DMRefine(dac,MPI_COMM_NULL,&daf));
  PetscCall(DMDAGetInfo(daf,0,&Mx,0,0,0,0,0,0,0,0,0,0,0));
  Mx--;

  PetscCall(DMDASetUniformCoordinates(dac, -1.0,1.0, PETSC_DECIDE,PETSC_DECIDE, PETSC_DECIDE,PETSC_DECIDE));
  PetscCall(DMDASetUniformCoordinates(daf, -1.0,1.0, PETSC_DECIDE,PETSC_DECIDE, PETSC_DECIDE,PETSC_DECIDE));

  {
    DM  cdaf,cdac;
    Vec coordsc,coordsf;

    PetscCall(DMGetCoordinateDM(dac,&cdac));
    PetscCall(DMGetCoordinateDM(daf,&cdaf));

    PetscCall(DMGetCoordinates(dac,&coordsc));
    PetscCall(DMGetCoordinates(daf,&coordsf));

    PetscCall(DMCreateInterpolation(cdac,cdaf,&II,&scale));
    PetscCall(MatInterpolate(II,coordsc,coordsf));
    PetscCall(MatDestroy(&II));
    PetscCall(VecDestroy(&scale));
  }

  PetscCall(DMCreateInterpolation(dac,daf,&INTERP,NULL));

  PetscCall(DMCreateGlobalVector(dac,&ac));
  PetscCall(VecSet(ac,66.99));

  PetscCall(DMCreateGlobalVector(daf,&af));

  PetscCall(MatMult(INTERP,ac, af));

  {
    Vec       afexact;
    PetscReal nrm;
    PetscInt  N;

    PetscCall(DMCreateGlobalVector(daf,&afexact));
    PetscCall(VecSet(afexact,66.99));
    PetscCall(VecAXPY(afexact,-1.0,af)); /* af <= af - afinterp */
    PetscCall(VecNorm(afexact,NORM_2,&nrm));
    PetscCall(VecGetSize(afexact,&N));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%" PetscInt_FMT "=>%" PetscInt_FMT ", interp err = %1.4e\n",mx,Mx,(double)(nrm/PetscSqrtReal((PetscReal)N))));
    PetscCall(VecDestroy(&afexact));
  }

  PetscCall(PetscOptionsGetBool(NULL,NULL,"-output",&output,NULL));
  if (output) {
    PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "dac_1D.vtr", &vv));
    PetscCall(VecView(ac, vv));
    PetscCall(PetscViewerDestroy(&vv));

    PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "daf_1D.vtr", &vv));
    PetscCall(VecView(af, vv));
    PetscCall(PetscViewerDestroy(&vv));
  }

  PetscCall(MatDestroy(&INTERP));
  PetscCall(DMDestroy(&dac));
  PetscCall(DMDestroy(&daf));
  PetscCall(VecDestroy(&ac));
  PetscCall(VecDestroy(&af));
  PetscFunctionReturn(0);
}

PetscErrorCode da_test_RefineCoords2D(PetscInt mx,PetscInt my)
{
  DM             dac,daf;
  PetscViewer    vv;
  Vec            ac,af;
  PetscInt       map_id,Mx,My;
  Mat            II,INTERP;
  Vec            scale;
  PetscBool      output = PETSC_FALSE;

  PetscFunctionBeginUser;
  PetscCall(DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX,mx+1,my+1,PETSC_DECIDE, PETSC_DECIDE,1, /* 1 dof */1, /* stencil = 1 */NULL, NULL,&dac));
  PetscCall(DMSetFromOptions(dac));
  PetscCall(DMSetUp(dac));

  PetscCall(DMRefine(dac,MPI_COMM_NULL,&daf));
  PetscCall(DMDAGetInfo(daf,0,&Mx,&My,0,0,0,0,0,0,0,0,0,0));
  Mx--; My--;

  PetscCall(DMDASetUniformCoordinates(dac, -1.0,1.0, -1.0,1.0, PETSC_DECIDE,PETSC_DECIDE));
  PetscCall(DMDASetUniformCoordinates(daf, -1.0,1.0, -1.0,1.0, PETSC_DECIDE,PETSC_DECIDE));

  /* apply conformal mappings */
  map_id = 0;
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-cmap", &map_id,NULL));
  if (map_id >= 1) {
    PetscCall(DAApplyConformalMapping(dac,map_id));
  }

  {
    DM  cdaf,cdac;
    Vec coordsc,coordsf;

    PetscCall(DMGetCoordinateDM(dac,&cdac));
    PetscCall(DMGetCoordinateDM(daf,&cdaf));

    PetscCall(DMGetCoordinates(dac,&coordsc));
    PetscCall(DMGetCoordinates(daf,&coordsf));

    PetscCall(DMCreateInterpolation(cdac,cdaf,&II,&scale));
    PetscCall(MatInterpolate(II,coordsc,coordsf));
    PetscCall(MatDestroy(&II));
    PetscCall(VecDestroy(&scale));
  }

  PetscCall(DMCreateInterpolation(dac,daf,&INTERP,NULL));

  PetscCall(DMCreateGlobalVector(dac,&ac));
  PetscCall(DADefineXLinearField2D(dac,ac));

  PetscCall(DMCreateGlobalVector(daf,&af));
  PetscCall(MatMult(INTERP,ac, af));

  {
    Vec       afexact;
    PetscReal nrm;
    PetscInt  N;

    PetscCall(DMCreateGlobalVector(daf,&afexact));
    PetscCall(VecZeroEntries(afexact));
    PetscCall(DADefineXLinearField2D(daf,afexact));
    PetscCall(VecAXPY(afexact,-1.0,af)); /* af <= af - afinterp */
    PetscCall(VecNorm(afexact,NORM_2,&nrm));
    PetscCall(VecGetSize(afexact,&N));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%" PetscInt_FMT " x %" PetscInt_FMT "]=>[%" PetscInt_FMT " x %" PetscInt_FMT "], interp err = %1.4e\n",mx,my,Mx,My,(double)(nrm/PetscSqrtReal((PetscReal)N))));
    PetscCall(VecDestroy(&afexact));
  }

  PetscCall(PetscOptionsGetBool(NULL,NULL,"-output",&output,NULL));
  if (output) {
    PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "dac_2D.vtr", &vv));
    PetscCall(VecView(ac, vv));
    PetscCall(PetscViewerDestroy(&vv));

    PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "daf_2D.vtr", &vv));
    PetscCall(VecView(af, vv));
    PetscCall(PetscViewerDestroy(&vv));
  }

  PetscCall(MatDestroy(&INTERP));
  PetscCall(DMDestroy(&dac));
  PetscCall(DMDestroy(&daf));
  PetscCall(VecDestroy(&ac));
  PetscCall(VecDestroy(&af));
  PetscFunctionReturn(0);
}

PetscErrorCode da_test_RefineCoords3D(PetscInt mx,PetscInt my,PetscInt mz)
{
  DM             dac,daf;
  PetscViewer    vv;
  Vec            ac,af;
  PetscInt       map_id,Mx,My,Mz;
  Mat            II,INTERP;
  Vec            scale;
  PetscBool      output = PETSC_FALSE;

  PetscFunctionBeginUser;
  PetscCall(DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx+1, my+1,mz+1,PETSC_DECIDE, PETSC_DECIDE,PETSC_DECIDE,1, /* 1 dof */
                         1, /* stencil = 1 */NULL,NULL,NULL,&dac));
  PetscCall(DMSetFromOptions(dac));
  PetscCall(DMSetUp(dac));

  PetscCall(DMRefine(dac,MPI_COMM_NULL,&daf));
  PetscCall(DMDAGetInfo(daf,0,&Mx,&My,&Mz,0,0,0,0,0,0,0,0,0));
  Mx--; My--; Mz--;

  PetscCall(DMDASetUniformCoordinates(dac, -1.0,1.0, -1.0,1.0, -1.0,1.0));
  PetscCall(DMDASetUniformCoordinates(daf, -1.0,1.0, -1.0,1.0, -1.0,1.0));

  /* apply trilinear mappings */
  /*PetscCall(DAApplyTrilinearMapping(dac));*/
  /* apply conformal mappings */
  map_id = 0;
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-cmap", &map_id,NULL));
  if (map_id >= 1) {
    PetscCall(DAApplyConformalMapping(dac,map_id));
  }

  {
    DM  cdaf,cdac;
    Vec coordsc,coordsf;

    PetscCall(DMGetCoordinateDM(dac,&cdac));
    PetscCall(DMGetCoordinateDM(daf,&cdaf));

    PetscCall(DMGetCoordinates(dac,&coordsc));
    PetscCall(DMGetCoordinates(daf,&coordsf));

    PetscCall(DMCreateInterpolation(cdac,cdaf,&II,&scale));
    PetscCall(MatInterpolate(II,coordsc,coordsf));
    PetscCall(MatDestroy(&II));
    PetscCall(VecDestroy(&scale));
  }

  PetscCall(DMCreateInterpolation(dac,daf,&INTERP,NULL));

  PetscCall(DMCreateGlobalVector(dac,&ac));
  PetscCall(VecZeroEntries(ac));
  PetscCall(DADefineXLinearField3D(dac,ac));

  PetscCall(DMCreateGlobalVector(daf,&af));
  PetscCall(VecZeroEntries(af));

  PetscCall(MatMult(INTERP,ac, af));

  {
    Vec       afexact;
    PetscReal nrm;
    PetscInt  N;

    PetscCall(DMCreateGlobalVector(daf,&afexact));
    PetscCall(VecZeroEntries(afexact));
    PetscCall(DADefineXLinearField3D(daf,afexact));
    PetscCall(VecAXPY(afexact,-1.0,af)); /* af <= af - afinterp */
    PetscCall(VecNorm(afexact,NORM_2,&nrm));
    PetscCall(VecGetSize(afexact,&N));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"[%" PetscInt_FMT " x %" PetscInt_FMT " x %" PetscInt_FMT "]=>[%" PetscInt_FMT " x %" PetscInt_FMT " x %" PetscInt_FMT "], interp err = %1.4e\n",mx,my,mz,Mx,My,Mz,(double)(nrm/PetscSqrtReal((PetscReal)N))));
    PetscCall(VecDestroy(&afexact));
  }

  PetscCall(PetscOptionsGetBool(NULL,NULL,"-output",&output,NULL));
  if (output) {
    PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "dac_3D.vtr", &vv));
    PetscCall(VecView(ac, vv));
    PetscCall(PetscViewerDestroy(&vv));

    PetscCall(PetscViewerASCIIOpen(PETSC_COMM_WORLD, "daf_3D.vtr", &vv));
    PetscCall(VecView(af, vv));
    PetscCall(PetscViewerDestroy(&vv));
  }

  PetscCall(MatDestroy(&INTERP));
  PetscCall(DMDestroy(&dac));
  PetscCall(DMDestroy(&daf));
  PetscCall(VecDestroy(&ac));
  PetscCall(VecDestroy(&af));
  PetscFunctionReturn(0);
}

int main(int argc,char **argv)
{
  PetscInt       mx = 2,my = 2,mz = 2,l,nl,dim;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc,&argv,0,help));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-mx", &mx, 0));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-my", &my, 0));
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-mz", &mz, 0));
  nl = 1;
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-nl", &nl, 0));
  dim = 2;
  PetscCall(PetscOptionsGetInt(NULL,NULL,"-dim", &dim, 0));

  for (l=0; l<nl; l++) {
    if (dim==1) PetscCall(da_test_RefineCoords1D(mx));
    else if (dim==2) PetscCall(da_test_RefineCoords2D(mx,my));
    else if (dim==3) PetscCall(da_test_RefineCoords3D(mx,my,mz));
    mx = mx * 2;
    my = my * 2;
    mz = mz * 2;
  }
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

   test:
      suffix: 1d
      args: -mx 10 -nl 6 -dim 1

   test:
      suffix: 2d
      output_file: output/ex36_2d.out
      args: -mx 10 -my 10 -nl 6 -dim 2 -cmap {{0 1 2 3}}

   test:
      suffix: 2dp1
      nsize: 8
      args: -mx 10 -my 10 -nl 4 -dim 2 -cmap 3 -da_refine_x 3 -da_refine_y 4
      timeoutfactor: 2

   test:
      suffix: 2dp2
      nsize: 8
      args: -mx 10 -my 10 -nl 4 -dim 2 -cmap 3 -da_refine_x 3 -da_refine_y 1
      timeoutfactor: 2

   test:
      suffix: 3d
      args: -mx 5 -my 5 -mz 5 -nl 4 -dim 3 -cmap 3

   test:
      suffix: 3dp1
      nsize: 32
      args: -mx 5 -my 5 -mz 5 -nl 3 -dim 3 -cmap 1 -da_refine_x 1 -da_refine_y 3 -da_refine_z 4

TEST*/