plex/tests/ex3.c

static char help[] = "Check that a DM can accurately represent and interpolate functions of a given polynomial order\n\n";

#include <petscdmplex.h>
#include <petscdm.h>
#include <petscdmda.h>
#include <petscfe.h>
#include <petscds.h>
#include <petscksp.h>
#include <petscsnes.h>
#include <petscsf.h>

typedef struct {
  /* Domain and mesh definition */
  PetscBool useDA;           /* Flag DMDA tensor product mesh */
  PetscBool shearCoords;     /* Flag for shear transform */
  PetscBool nonaffineCoords; /* Flag for non-affine transform */
  /* Element definition */
  PetscInt qorder;        /* Order of the quadrature */
  PetscInt numComponents; /* Number of field components */
  PetscFE  fe;            /* The finite element */
  /* Testing space */
  PetscInt  porder;         /* Order of polynomials to test */
  PetscBool convergence;    /* Test for order of convergence */
  PetscBool convRefine;     /* Test for convergence using refinement, otherwise use coarsening */
  PetscBool constraints;    /* Test local constraints */
  PetscBool tree;           /* Test tree routines */
  PetscBool testFEjacobian; /* Test finite element Jacobian assembly */
  PetscBool testFVgrad;     /* Test finite difference gradient routine */
  PetscBool testInjector;   /* Test finite element injection routines */
  PetscInt  treeCell;       /* Cell to refine in tree test */
  PetscReal constants[3];   /* Constant values for each dimension */
} AppCtx;

/* u = 1 */
PetscErrorCode constant(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  AppCtx  *user = (AppCtx *)ctx;
  PetscInt d;
  for (d = 0; d < dim; ++d) u[d] = user->constants[d];
  return PETSC_SUCCESS;
}
PetscErrorCode constantDer(PetscInt dim, PetscReal time, const PetscReal coords[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  PetscInt d;
  for (d = 0; d < dim; ++d) u[d] = 0.0;
  return PETSC_SUCCESS;
}

/* u = x */
PetscErrorCode linear(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  PetscInt d;
  for (d = 0; d < dim; ++d) u[d] = coords[d];
  return PETSC_SUCCESS;
}
PetscErrorCode linearDer(PetscInt dim, PetscReal time, const PetscReal coords[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  PetscInt d, e;
  for (d = 0; d < dim; ++d) {
    u[d] = 0.0;
    for (e = 0; e < dim; ++e) u[d] += (d == e ? 1.0 : 0.0) * n[e];
  }
  return PETSC_SUCCESS;
}

/* u = x^2 or u = (x^2, xy) or u = (xy, yz, zx) */
PetscErrorCode quadratic(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  if (dim > 2) {
    u[0] = coords[0] * coords[1];
    u[1] = coords[1] * coords[2];
    u[2] = coords[2] * coords[0];
  } else if (dim > 1) {
    u[0] = coords[0] * coords[0];
    u[1] = coords[0] * coords[1];
  } else if (dim > 0) {
    u[0] = coords[0] * coords[0];
  }
  return PETSC_SUCCESS;
}
PetscErrorCode quadraticDer(PetscInt dim, PetscReal time, const PetscReal coords[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  if (dim > 2) {
    u[0] = coords[1] * n[0] + coords[0] * n[1];
    u[1] = coords[2] * n[1] + coords[1] * n[2];
    u[2] = coords[2] * n[0] + coords[0] * n[2];
  } else if (dim > 1) {
    u[0] = 2.0 * coords[0] * n[0];
    u[1] = coords[1] * n[0] + coords[0] * n[1];
  } else if (dim > 0) {
    u[0] = 2.0 * coords[0] * n[0];
  }
  return PETSC_SUCCESS;
}

/* u = x^3 or u = (x^3, x^2y) or u = (x^2y, y^2z, z^2x) */
PetscErrorCode cubic(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  if (dim > 2) {
    u[0] = coords[0] * coords[0] * coords[1];
    u[1] = coords[1] * coords[1] * coords[2];
    u[2] = coords[2] * coords[2] * coords[0];
  } else if (dim > 1) {
    u[0] = coords[0] * coords[0] * coords[0];
    u[1] = coords[0] * coords[0] * coords[1];
  } else if (dim > 0) {
    u[0] = coords[0] * coords[0] * coords[0];
  }
  return PETSC_SUCCESS;
}
PetscErrorCode cubicDer(PetscInt dim, PetscReal time, const PetscReal coords[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  if (dim > 2) {
    u[0] = 2.0 * coords[0] * coords[1] * n[0] + coords[0] * coords[0] * n[1];
    u[1] = 2.0 * coords[1] * coords[2] * n[1] + coords[1] * coords[1] * n[2];
    u[2] = 2.0 * coords[2] * coords[0] * n[2] + coords[2] * coords[2] * n[0];
  } else if (dim > 1) {
    u[0] = 3.0 * coords[0] * coords[0] * n[0];
    u[1] = 2.0 * coords[0] * coords[1] * n[0] + coords[0] * coords[0] * n[1];
  } else if (dim > 0) {
    u[0] = 3.0 * coords[0] * coords[0] * n[0];
  }
  return PETSC_SUCCESS;
}

/* u = tanh(x) */
PetscErrorCode trig(PetscInt dim, PetscReal time, const PetscReal coords[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  PetscInt d;
  for (d = 0; d < dim; ++d) u[d] = PetscTanhReal(coords[d] - 0.5);
  return PETSC_SUCCESS;
}
PetscErrorCode trigDer(PetscInt dim, PetscReal time, const PetscReal coords[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  PetscInt d;
  for (d = 0; d < dim; ++d) u[d] = 1.0 / PetscSqr(PetscCoshReal(coords[d] - 0.5)) * n[d];
  return PETSC_SUCCESS;
}

static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
{
  PetscInt n = 3;

  PetscFunctionBeginUser;
  options->useDA           = PETSC_FALSE;
  options->shearCoords     = PETSC_FALSE;
  options->nonaffineCoords = PETSC_FALSE;
  options->qorder          = 0;
  options->numComponents   = PETSC_DEFAULT;
  options->porder          = 0;
  options->convergence     = PETSC_FALSE;
  options->convRefine      = PETSC_TRUE;
  options->constraints     = PETSC_FALSE;
  options->tree            = PETSC_FALSE;
  options->treeCell        = 0;
  options->testFEjacobian  = PETSC_FALSE;
  options->testFVgrad      = PETSC_FALSE;
  options->testInjector    = PETSC_FALSE;
  options->constants[0]    = 1.0;
  options->constants[1]    = 2.0;
  options->constants[2]    = 3.0;

  PetscOptionsBegin(comm, "", "Projection Test Options", "DMPlex");
  PetscCall(PetscOptionsBool("-use_da", "Flag for DMDA mesh", "ex3.c", options->useDA, &options->useDA, NULL));
  PetscCall(PetscOptionsBool("-shear_coords", "Transform coordinates with a shear", "ex3.c", options->shearCoords, &options->shearCoords, NULL));
  PetscCall(PetscOptionsBool("-non_affine_coords", "Transform coordinates with a non-affine transform", "ex3.c", options->nonaffineCoords, &options->nonaffineCoords, NULL));
  PetscCall(PetscOptionsBoundedInt("-qorder", "The quadrature order", "ex3.c", options->qorder, &options->qorder, NULL, 0));
  PetscCall(PetscOptionsBoundedInt("-num_comp", "The number of field components", "ex3.c", options->numComponents, &options->numComponents, NULL, PETSC_DEFAULT));
  PetscCall(PetscOptionsBoundedInt("-porder", "The order of polynomials to test", "ex3.c", options->porder, &options->porder, NULL, 0));
  PetscCall(PetscOptionsBool("-convergence", "Check the convergence rate", "ex3.c", options->convergence, &options->convergence, NULL));
  PetscCall(PetscOptionsBool("-conv_refine", "Use refinement for the convergence rate", "ex3.c", options->convRefine, &options->convRefine, NULL));
  PetscCall(PetscOptionsBool("-constraints", "Test local constraints (serial only)", "ex3.c", options->constraints, &options->constraints, NULL));
  PetscCall(PetscOptionsBool("-tree", "Test tree routines", "ex3.c", options->tree, &options->tree, NULL));
  PetscCall(PetscOptionsBoundedInt("-tree_cell", "cell to refine in tree test", "ex3.c", options->treeCell, &options->treeCell, NULL, 0));
  PetscCall(PetscOptionsBool("-test_fe_jacobian", "Test finite element Jacobian assembly", "ex3.c", options->testFEjacobian, &options->testFEjacobian, NULL));
  PetscCall(PetscOptionsBool("-test_fv_grad", "Test finite volume gradient reconstruction", "ex3.c", options->testFVgrad, &options->testFVgrad, NULL));
  PetscCall(PetscOptionsBool("-test_injector", "Test finite element injection", "ex3.c", options->testInjector, &options->testInjector, NULL));
  PetscCall(PetscOptionsRealArray("-constants", "Set the constant values", "ex3.c", options->constants, &n, NULL));
  PetscOptionsEnd();
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TransformCoordinates(DM dm, AppCtx *user)
{
  PetscSection coordSection;
  Vec          coordinates;
  PetscScalar *coords;
  PetscInt     vStart, vEnd, v;

  PetscFunctionBeginUser;
  if (user->nonaffineCoords) {
    /* x' = r^(1/p) (x/r), y' = r^(1/p) (y/r), z' = z */
    PetscCall(DMGetCoordinateSection(dm, &coordSection));
    PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    PetscCall(VecGetArray(coordinates, &coords));
    for (v = vStart; v < vEnd; ++v) {
      PetscInt  dof, off;
      PetscReal p = 4.0, r;

      PetscCall(PetscSectionGetDof(coordSection, v, &dof));
      PetscCall(PetscSectionGetOffset(coordSection, v, &off));
      switch (dof) {
      case 2:
        r               = PetscSqr(PetscRealPart(coords[off + 0])) + PetscSqr(PetscRealPart(coords[off + 1]));
        coords[off + 0] = r == 0.0 ? 0.0 : PetscPowReal(r, (1 - p) / (2 * p)) * coords[off + 0];
        coords[off + 1] = r == 0.0 ? 0.0 : PetscPowReal(r, (1 - p) / (2 * p)) * coords[off + 1];
        break;
      case 3:
        r               = PetscSqr(PetscRealPart(coords[off + 0])) + PetscSqr(PetscRealPart(coords[off + 1]));
        coords[off + 0] = r == 0.0 ? 0.0 : PetscPowReal(r, (1 - p) / (2 * p)) * coords[off + 0];
        coords[off + 1] = r == 0.0 ? 0.0 : PetscPowReal(r, (1 - p) / (2 * p)) * coords[off + 1];
        coords[off + 2] = coords[off + 2];
        break;
      }
    }
    PetscCall(VecRestoreArray(coordinates, &coords));
  }
  if (user->shearCoords) {
    /* x' = x + m y + m z, y' = y + m z,  z' = z */
    PetscCall(DMGetCoordinateSection(dm, &coordSection));
    PetscCall(DMGetCoordinatesLocal(dm, &coordinates));
    PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    PetscCall(VecGetArray(coordinates, &coords));
    for (v = vStart; v < vEnd; ++v) {
      PetscInt  dof, off;
      PetscReal m = 1.0;

      PetscCall(PetscSectionGetDof(coordSection, v, &dof));
      PetscCall(PetscSectionGetOffset(coordSection, v, &off));
      switch (dof) {
      case 2:
        coords[off + 0] = coords[off + 0] + m * coords[off + 1];
        coords[off + 1] = coords[off + 1];
        break;
      case 3:
        coords[off + 0] = coords[off + 0] + m * coords[off + 1] + m * coords[off + 2];
        coords[off + 1] = coords[off + 1] + m * coords[off + 2];
        coords[off + 2] = coords[off + 2];
        break;
      }
    }
    PetscCall(VecRestoreArray(coordinates, &coords));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
{
  PetscInt  dim = 2;
  PetscBool simplex;

  PetscFunctionBeginUser;
  if (user->useDA) {
    switch (dim) {
    case 2:
      PetscCall(DMDACreate2d(comm, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DMDA_STENCIL_BOX, 2, 2, PETSC_DETERMINE, PETSC_DETERMINE, 1, 1, NULL, NULL, dm));
      PetscCall(DMSetFromOptions(*dm));
      PetscCall(DMSetUp(*dm));
      PetscCall(DMDASetVertexCoordinates(*dm, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
      break;
    default:
      SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Cannot create structured mesh of dimension %" PetscInt_FMT, dim);
    }
    PetscCall(PetscObjectSetName((PetscObject)*dm, "Hexahedral Mesh"));
  } else {
    PetscCall(DMCreate(comm, dm));
    PetscCall(DMSetType(*dm, DMPLEX));
    PetscCall(DMPlexDistributeSetDefault(*dm, PETSC_FALSE));
    PetscCall(DMSetFromOptions(*dm));

    PetscCall(DMGetDimension(*dm, &dim));
    PetscCall(DMPlexIsSimplex(*dm, &simplex));
    PetscCallMPI(MPI_Bcast(&simplex, 1, MPIU_BOOL, 0, comm));
    if (user->tree) {
      DM refTree, ncdm = NULL;

      PetscCall(DMPlexCreateDefaultReferenceTree(comm, dim, simplex, &refTree));
      PetscCall(DMViewFromOptions(refTree, NULL, "-reftree_dm_view"));
      PetscCall(DMPlexSetReferenceTree(*dm, refTree));
      PetscCall(DMDestroy(&refTree));
      PetscCall(DMPlexTreeRefineCell(*dm, user->treeCell, &ncdm));
      if (ncdm) {
        PetscCall(DMDestroy(dm));
        *dm = ncdm;
        PetscCall(DMPlexSetRefinementUniform(*dm, PETSC_FALSE));
      }
      PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*dm, "tree_"));
      PetscCall(DMPlexDistributeSetDefault(*dm, PETSC_FALSE));
      PetscCall(DMSetFromOptions(*dm));
      PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
    } else {
      PetscCall(DMPlexSetRefinementUniform(*dm, PETSC_TRUE));
    }
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*dm, "dist_"));
    PetscCall(DMPlexDistributeSetDefault(*dm, PETSC_FALSE));
    PetscCall(DMSetFromOptions(*dm));
    PetscCall(PetscObjectSetOptionsPrefix((PetscObject)*dm, NULL));
    if (simplex) PetscCall(PetscObjectSetName((PetscObject)*dm, "Simplicial Mesh"));
    else PetscCall(PetscObjectSetName((PetscObject)*dm, "Hexahedral Mesh"));
  }
  PetscCall(DMSetFromOptions(*dm));
  PetscCall(TransformCoordinates(*dm, user));
  PetscCall(DMViewFromOptions(*dm, NULL, "-dm_view"));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static void simple_mass(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar g0[])
{
  PetscInt d, e;
  for (d = 0, e = 0; d < dim; d++, e += dim + 1) g0[e] = 1.;
}

/* < \nabla v, 1/2(\nabla u + {\nabla u}^T) > */
static void symmetric_gradient_inner_product(PetscInt dim, PetscInt Nf, PetscInt NfAux, const PetscInt uOff[], const PetscInt uOff_x[], const PetscScalar u[], const PetscScalar u_t[], const PetscScalar u_x[], const PetscInt aOff[], const PetscInt aOff_x[], const PetscScalar a[], const PetscScalar a_t[], const PetscScalar a_x[], PetscReal t, PetscReal u_tShift, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar C[])
{
  PetscInt compI, compJ, d, e;

  for (compI = 0; compI < dim; ++compI) {
    for (compJ = 0; compJ < dim; ++compJ) {
      for (d = 0; d < dim; ++d) {
        for (e = 0; e < dim; e++) {
          if (d == e && d == compI && d == compJ) {
            C[((compI * dim + compJ) * dim + d) * dim + e] = 1.0;
          } else if ((d == compJ && e == compI) || (d == e && compI == compJ)) {
            C[((compI * dim + compJ) * dim + d) * dim + e] = 0.5;
          } else {
            C[((compI * dim + compJ) * dim + d) * dim + e] = 0.0;
          }
        }
      }
    }
  }
}

static PetscErrorCode SetupSection(DM dm, AppCtx *user)
{
  PetscFunctionBeginUser;
  if (user->constraints) {
    /* test local constraints */
    DM           coordDM;
    PetscInt     fStart, fEnd, f, vStart, vEnd, v;
    PetscInt     edgesx = 2, vertsx;
    PetscInt     edgesy = 2, vertsy;
    PetscMPIInt  size;
    PetscInt     numConst;
    PetscSection aSec;
    PetscInt    *anchors;
    PetscInt     offset;
    IS           aIS;
    MPI_Comm     comm = PetscObjectComm((PetscObject)dm);

    PetscCallMPI(MPI_Comm_size(comm, &size));
    PetscCheck(size <= 1, comm, PETSC_ERR_SUP, "Local constraint test can only be performed in serial");

    /* we are going to test constraints by using them to enforce periodicity
     * in one direction, and comparing to the existing method of enforcing
     * periodicity */

    /* first create the coordinate section so that it does not clone the
     * constraints */
    PetscCall(DMGetCoordinateDM(dm, &coordDM));

    /* create the constrained-to-anchor section */
    PetscCall(DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd));
    PetscCall(DMPlexGetDepthStratum(dm, 1, &fStart, &fEnd));
    PetscCall(PetscSectionCreate(PETSC_COMM_SELF, &aSec));
    PetscCall(PetscSectionSetChart(aSec, PetscMin(fStart, vStart), PetscMax(fEnd, vEnd)));

    /* define the constraints */
    PetscCall(PetscOptionsGetInt(NULL, NULL, "-da_grid_x", &edgesx, NULL));
    PetscCall(PetscOptionsGetInt(NULL, NULL, "-da_grid_y", &edgesy, NULL));
    vertsx   = edgesx + 1;
    vertsy   = edgesy + 1;
    numConst = vertsy + edgesy;
    PetscCall(PetscMalloc1(numConst, &anchors));
    offset = 0;
    for (v = vStart + edgesx; v < vEnd; v += vertsx) {
      PetscCall(PetscSectionSetDof(aSec, v, 1));
      anchors[offset++] = v - edgesx;
    }
    for (f = fStart + edgesx * vertsy + edgesx * edgesy; f < fEnd; f++) {
      PetscCall(PetscSectionSetDof(aSec, f, 1));
      anchors[offset++] = f - edgesx * edgesy;
    }
    PetscCall(PetscSectionSetUp(aSec));
    PetscCall(ISCreateGeneral(PETSC_COMM_SELF, numConst, anchors, PETSC_OWN_POINTER, &aIS));

    PetscCall(DMPlexSetAnchors(dm, aSec, aIS));
    PetscCall(PetscSectionDestroy(&aSec));
    PetscCall(ISDestroy(&aIS));
  }
  PetscCall(DMSetNumFields(dm, 1));
  PetscCall(DMSetField(dm, 0, NULL, (PetscObject)user->fe));
  PetscCall(DMCreateDS(dm));
  if (user->constraints) {
    /* test getting local constraint matrix that matches section */
    PetscSection aSec;
    IS           aIS;

    PetscCall(DMPlexGetAnchors(dm, &aSec, &aIS));
    if (aSec) {
      PetscDS         ds;
      PetscSection    cSec, section;
      PetscInt        cStart, cEnd, c, numComp;
      Mat             cMat, mass;
      Vec             local;
      const PetscInt *anchors;

      PetscCall(DMGetLocalSection(dm, &section));
      /* this creates the matrix and preallocates the matrix structure: we
       * just have to fill in the values */
      PetscCall(DMGetDefaultConstraints(dm, &cSec, &cMat, NULL));
      PetscCall(PetscSectionGetChart(cSec, &cStart, &cEnd));
      PetscCall(ISGetIndices(aIS, &anchors));
      PetscCall(PetscFEGetNumComponents(user->fe, &numComp));
      for (c = cStart; c < cEnd; c++) {
        PetscInt cDof;

        /* is this point constrained? (does it have an anchor?) */
        PetscCall(PetscSectionGetDof(aSec, c, &cDof));
        if (cDof) {
          PetscInt cOff, a, aDof, aOff, j;
          PetscCheck(cDof == 1, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Found %" PetscInt_FMT " anchor points: should be just one", cDof);

          /* find the anchor point */
          PetscCall(PetscSectionGetOffset(aSec, c, &cOff));
          a = anchors[cOff];

          /* find the constrained dofs (row in constraint matrix) */
          PetscCall(PetscSectionGetDof(cSec, c, &cDof));
          PetscCall(PetscSectionGetOffset(cSec, c, &cOff));

          /* find the anchor dofs (column in constraint matrix) */
          PetscCall(PetscSectionGetDof(section, a, &aDof));
          PetscCall(PetscSectionGetOffset(section, a, &aOff));

          PetscCheck(cDof == aDof, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point and anchor have different number of dofs: %" PetscInt_FMT ", %" PetscInt_FMT, cDof, aDof);
          PetscCheck(cDof % numComp == 0, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Point dofs not divisible by field components: %" PetscInt_FMT ", %" PetscInt_FMT, cDof, numComp);

          /* put in a simple equality constraint */
          for (j = 0; j < cDof; j++) PetscCall(MatSetValue(cMat, cOff + j, aOff + j, 1., INSERT_VALUES));
        }
      }
      PetscCall(MatAssemblyBegin(cMat, MAT_FINAL_ASSEMBLY));
      PetscCall(MatAssemblyEnd(cMat, MAT_FINAL_ASSEMBLY));
      PetscCall(ISRestoreIndices(aIS, &anchors));

      /* Now that we have constructed the constraint matrix, any FE matrix
       * that we construct will apply the constraints during construction */

      PetscCall(DMCreateMatrix(dm, &mass));
      /* get a dummy local variable to serve as the solution */
      PetscCall(DMGetLocalVector(dm, &local));
      PetscCall(DMGetDS(dm, &ds));
      /* set the jacobian to be the mass matrix */
      PetscCall(PetscDSSetJacobian(ds, 0, 0, simple_mass, NULL, NULL, NULL));
      /* build the mass matrix */
      PetscCall(DMPlexSNESComputeJacobianFEM(dm, local, mass, mass, NULL));
      PetscCall(MatView(mass, PETSC_VIEWER_STDOUT_WORLD));
      PetscCall(MatDestroy(&mass));
      PetscCall(DMRestoreLocalVector(dm, &local));
    }
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TestFEJacobian(DM dm, AppCtx *user)
{
  PetscFunctionBeginUser;
  if (!user->useDA) {
    Vec          local;
    const Vec   *vecs;
    Mat          E;
    MatNullSpace sp;
    PetscBool    isNullSpace, hasConst;
    PetscInt     dim, n, i;
    Vec          res = NULL, localX, localRes;
    PetscDS      ds;

    PetscCall(DMGetDimension(dm, &dim));
    PetscCheck(user->numComponents == dim, PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_OUTOFRANGE, "The number of components %" PetscInt_FMT " must be equal to the dimension %" PetscInt_FMT " for this test", user->numComponents, dim);
    PetscCall(DMGetDS(dm, &ds));
    PetscCall(PetscDSSetJacobian(ds, 0, 0, NULL, NULL, NULL, symmetric_gradient_inner_product));
    PetscCall(DMCreateMatrix(dm, &E));
    PetscCall(DMGetLocalVector(dm, &local));
    PetscCall(DMPlexSNESComputeJacobianFEM(dm, local, E, E, NULL));
    PetscCall(DMPlexCreateRigidBody(dm, 0, &sp));
    PetscCall(MatNullSpaceGetVecs(sp, &hasConst, &n, &vecs));
    if (n) PetscCall(VecDuplicate(vecs[0], &res));
    PetscCall(DMCreateLocalVector(dm, &localX));
    PetscCall(DMCreateLocalVector(dm, &localRes));
    for (i = 0; i < n; i++) { /* also test via matrix-free Jacobian application */
      PetscReal resNorm;

      PetscCall(VecSet(localRes, 0.));
      PetscCall(VecSet(localX, 0.));
      PetscCall(VecSet(local, 0.));
      PetscCall(VecSet(res, 0.));
      PetscCall(DMGlobalToLocalBegin(dm, vecs[i], INSERT_VALUES, localX));
      PetscCall(DMGlobalToLocalEnd(dm, vecs[i], INSERT_VALUES, localX));
      PetscCall(DMSNESComputeJacobianAction(dm, local, localX, localRes, NULL));
      PetscCall(DMLocalToGlobalBegin(dm, localRes, ADD_VALUES, res));
      PetscCall(DMLocalToGlobalEnd(dm, localRes, ADD_VALUES, res));
      PetscCall(VecNorm(res, NORM_2, &resNorm));
      if (resNorm > PETSC_SMALL) PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Symmetric gradient action null space vector %" PetscInt_FMT " residual: %E\n", i, (double)resNorm));
    }
    PetscCall(VecDestroy(&localRes));
    PetscCall(VecDestroy(&localX));
    PetscCall(VecDestroy(&res));
    PetscCall(MatNullSpaceTest(sp, E, &isNullSpace));
    if (isNullSpace) {
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Symmetric gradient null space: PASS\n"));
    } else {
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Symmetric gradient null space: FAIL\n"));
    }
    PetscCall(MatNullSpaceDestroy(&sp));
    PetscCall(MatDestroy(&E));
    PetscCall(DMRestoreLocalVector(dm, &local));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TestInjector(DM dm, AppCtx *user)
{
  DM          refTree;
  PetscMPIInt rank;

  PetscFunctionBegin;
  PetscCall(DMPlexGetReferenceTree(dm, &refTree));
  if (refTree) {
    Mat inj;

    PetscCall(DMPlexComputeInjectorReferenceTree(refTree, &inj));
    PetscCall(PetscObjectSetName((PetscObject)inj, "Reference Tree Injector"));
    PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank));
    if (rank == 0) PetscCall(MatView(inj, PETSC_VIEWER_STDOUT_SELF));
    PetscCall(MatDestroy(&inj));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode TestFVGrad(DM dm, AppCtx *user)
{
  MPI_Comm           comm;
  DM                 dmRedist, dmfv, dmgrad, dmCell, refTree;
  PetscFV            fv;
  PetscInt           dim, nvecs, v, cStart, cEnd, cEndInterior;
  PetscMPIInt        size;
  Vec                cellgeom, grad, locGrad;
  const PetscScalar *cgeom;
  PetscReal          allVecMaxDiff = 0., fvTol = 100. * PETSC_MACHINE_EPSILON;

  PetscFunctionBeginUser;
  comm = PetscObjectComm((PetscObject)dm);
  PetscCall(DMGetDimension(dm, &dim));
  /* duplicate DM, give dup. a FV discretization */
  PetscCall(DMSetBasicAdjacency(dm, PETSC_TRUE, PETSC_FALSE));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  dmRedist = NULL;
  if (size > 1) PetscCall(DMPlexDistributeOverlap(dm, 1, NULL, &dmRedist));
  if (!dmRedist) {
    dmRedist = dm;
    PetscCall(PetscObjectReference((PetscObject)dmRedist));
  }
  PetscCall(PetscFVCreate(comm, &fv));
  PetscCall(PetscFVSetType(fv, PETSCFVLEASTSQUARES));
  PetscCall(PetscFVSetNumComponents(fv, user->numComponents));
  PetscCall(PetscFVSetSpatialDimension(fv, dim));
  PetscCall(PetscFVSetFromOptions(fv));
  PetscCall(PetscFVSetUp(fv));
  {
    PetscSF pointSF;
    DMLabel label;

    PetscCall(DMCreateLabel(dmRedist, "Face Sets"));
    PetscCall(DMGetLabel(dmRedist, "Face Sets", &label));
    PetscCall(DMGetPointSF(dmRedist, &pointSF));
    PetscCall(PetscObjectReference((PetscObject)pointSF));
    PetscCall(DMSetPointSF(dmRedist, NULL));
    PetscCall(DMPlexMarkBoundaryFaces(dmRedist, 1, label));
    PetscCall(DMSetPointSF(dmRedist, pointSF));
    PetscCall(PetscSFDestroy(&pointSF));
  }
  PetscCall(DMPlexConstructGhostCells(dmRedist, NULL, NULL, &dmfv));
  PetscCall(DMDestroy(&dmRedist));
  PetscCall(DMSetNumFields(dmfv, 1));
  PetscCall(DMSetField(dmfv, 0, NULL, (PetscObject)fv));
  PetscCall(DMCreateDS(dmfv));
  PetscCall(DMPlexGetReferenceTree(dm, &refTree));
  if (refTree) PetscCall(DMCopyDisc(dmfv, refTree));
  PetscCall(DMPlexGetGradientDM(dmfv, fv, &dmgrad));
  PetscCall(DMPlexGetHeightStratum(dmfv, 0, &cStart, &cEnd));
  nvecs = dim * (dim + 1) / 2;
  PetscCall(DMPlexGetGeometryFVM(dmfv, NULL, &cellgeom, NULL));
  PetscCall(VecGetDM(cellgeom, &dmCell));
  PetscCall(VecGetArrayRead(cellgeom, &cgeom));
  PetscCall(DMGetGlobalVector(dmgrad, &grad));
  PetscCall(DMGetLocalVector(dmgrad, &locGrad));
  PetscCall(DMPlexGetCellTypeStratum(dmgrad, DM_POLYTOPE_FV_GHOST, &cEndInterior, NULL));
  cEndInterior = (cEndInterior < 0) ? cEnd : cEndInterior;
  for (v = 0; v < nvecs; v++) {
    Vec                locX;
    PetscInt           c;
    PetscScalar        trueGrad[3][3] = {{0.}};
    const PetscScalar *gradArray;
    PetscReal          maxDiff, maxDiffGlob;

    PetscCall(DMGetLocalVector(dmfv, &locX));
    /* get the local projection of the rigid body mode */
    for (c = cStart; c < cEnd; c++) {
      PetscFVCellGeom *cg;
      PetscScalar      cx[3] = {0., 0., 0.};

      PetscCall(DMPlexPointLocalRead(dmCell, c, cgeom, &cg));
      if (v < dim) {
        cx[v] = 1.;
      } else {
        PetscInt w = v - dim;

        cx[(w + 1) % dim] = cg->centroid[(w + 2) % dim];
        cx[(w + 2) % dim] = -cg->centroid[(w + 1) % dim];
      }
      PetscCall(DMPlexVecSetClosure(dmfv, NULL, locX, c, cx, INSERT_ALL_VALUES));
    }
    /* TODO: this isn't in any header */
    PetscCall(DMPlexReconstructGradientsFVM(dmfv, locX, grad));
    PetscCall(DMGlobalToLocalBegin(dmgrad, grad, INSERT_VALUES, locGrad));
    PetscCall(DMGlobalToLocalEnd(dmgrad, grad, INSERT_VALUES, locGrad));
    PetscCall(VecGetArrayRead(locGrad, &gradArray));
    /* compare computed gradient to exact gradient */
    if (v >= dim) {
      PetscInt w = v - dim;

      trueGrad[(w + 1) % dim][(w + 2) % dim] = 1.;
      trueGrad[(w + 2) % dim][(w + 1) % dim] = -1.;
    }
    maxDiff = 0.;
    for (c = cStart; c < cEndInterior; c++) {
      PetscScalar *compGrad;
      PetscInt     i, j, k;
      PetscReal    FrobDiff = 0.;

      PetscCall(DMPlexPointLocalRead(dmgrad, c, gradArray, &compGrad));

      for (i = 0, k = 0; i < dim; i++) {
        for (j = 0; j < dim; j++, k++) {
          PetscScalar diff = compGrad[k] - trueGrad[i][j];
          FrobDiff += PetscRealPart(diff * PetscConj(diff));
        }
      }
      FrobDiff = PetscSqrtReal(FrobDiff);
      maxDiff  = PetscMax(maxDiff, FrobDiff);
    }
    PetscCall(MPIU_Allreduce(&maxDiff, &maxDiffGlob, 1, MPIU_REAL, MPIU_MAX, comm));
    allVecMaxDiff = PetscMax(allVecMaxDiff, maxDiffGlob);
    PetscCall(VecRestoreArrayRead(locGrad, &gradArray));
    PetscCall(DMRestoreLocalVector(dmfv, &locX));
  }
  if (allVecMaxDiff < fvTol) {
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Finite volume gradient reconstruction: PASS\n"));
  } else {
    PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Finite volume gradient reconstruction: FAIL at tolerance %g with max difference %g\n", (double)fvTol, (double)allVecMaxDiff));
  }
  PetscCall(DMRestoreLocalVector(dmgrad, &locGrad));
  PetscCall(DMRestoreGlobalVector(dmgrad, &grad));
  PetscCall(VecRestoreArrayRead(cellgeom, &cgeom));
  PetscCall(DMDestroy(&dmfv));
  PetscCall(PetscFVDestroy(&fv));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode ComputeError(DM dm, PetscErrorCode (**exactFuncs)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), PetscErrorCode (**exactFuncDers)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **exactCtxs, PetscReal *error, PetscReal *errorDer, AppCtx *user)
{
  Vec       u;
  PetscReal n[3] = {1.0, 1.0, 1.0};

  PetscFunctionBeginUser;
  PetscCall(DMGetGlobalVector(dm, &u));
  /* Project function into FE function space */
  PetscCall(DMProjectFunction(dm, 0.0, exactFuncs, exactCtxs, INSERT_ALL_VALUES, u));
  PetscCall(VecViewFromOptions(u, NULL, "-projection_view"));
  /* Compare approximation to exact in L_2 */
  PetscCall(DMComputeL2Diff(dm, 0.0, exactFuncs, exactCtxs, u, error));
  PetscCall(DMComputeL2GradientDiff(dm, 0.0, exactFuncDers, exactCtxs, u, n, errorDer));
  PetscCall(DMRestoreGlobalVector(dm, &u));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CheckFunctions(DM dm, PetscInt order, AppCtx *user)
{
  PetscErrorCode (*exactFuncs[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
  PetscErrorCode (*exactFuncDers[1])(PetscInt dim, PetscReal time, const PetscReal x[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx);
  void     *exactCtxs[3];
  MPI_Comm  comm;
  PetscReal error, errorDer, tol = PETSC_SMALL;

  PetscFunctionBeginUser;
  exactCtxs[0] = user;
  exactCtxs[1] = user;
  exactCtxs[2] = user;
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  /* Setup functions to approximate */
  switch (order) {
  case 0:
    exactFuncs[0]    = constant;
    exactFuncDers[0] = constantDer;
    break;
  case 1:
    exactFuncs[0]    = linear;
    exactFuncDers[0] = linearDer;
    break;
  case 2:
    exactFuncs[0]    = quadratic;
    exactFuncDers[0] = quadraticDer;
    break;
  case 3:
    exactFuncs[0]    = cubic;
    exactFuncDers[0] = cubicDer;
    break;
  default:
    SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Could not determine functions to test for order %" PetscInt_FMT, order);
  }
  PetscCall(ComputeError(dm, exactFuncs, exactFuncDers, exactCtxs, &error, &errorDer, user));
  /* Report result */
  if (error > tol) PetscCall(PetscPrintf(comm, "Function tests FAIL for order %" PetscInt_FMT " at tolerance %g error %g\n", order, (double)tol, (double)error));
  else PetscCall(PetscPrintf(comm, "Function tests pass for order %" PetscInt_FMT " at tolerance %g\n", order, (double)tol));
  if (errorDer > tol) PetscCall(PetscPrintf(comm, "Function tests FAIL for order %" PetscInt_FMT " derivatives at tolerance %g error %g\n", order, (double)tol, (double)errorDer));
  else PetscCall(PetscPrintf(comm, "Function tests pass for order %" PetscInt_FMT " derivatives at tolerance %g\n", order, (double)tol));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CheckInterpolation(DM dm, PetscBool checkRestrict, PetscInt order, AppCtx *user)
{
  PetscErrorCode (*exactFuncs[1])(PetscInt, PetscReal, const PetscReal x[], PetscInt, PetscScalar *u, void *ctx);
  PetscErrorCode (*exactFuncDers[1])(PetscInt, PetscReal, const PetscReal x[], const PetscReal n[], PetscInt, PetscScalar *u, void *ctx);
  PetscReal n[3] = {1.0, 1.0, 1.0};
  void     *exactCtxs[3];
  DM        rdm, idm, fdm;
  Mat       Interp;
  Vec       iu, fu, scaling;
  MPI_Comm  comm;
  PetscInt  dim;
  PetscReal error, errorDer, tol = PETSC_SMALL;

  PetscFunctionBeginUser;
  exactCtxs[0] = user;
  exactCtxs[1] = user;
  exactCtxs[2] = user;
  PetscCall(PetscObjectGetComm((PetscObject)dm, &comm));
  PetscCall(DMGetDimension(dm, &dim));
  PetscCall(DMRefine(dm, comm, &rdm));
  PetscCall(DMSetCoarseDM(rdm, dm));
  PetscCall(DMPlexSetRegularRefinement(rdm, user->convRefine));
  if (user->tree) {
    DM refTree;
    PetscCall(DMPlexGetReferenceTree(dm, &refTree));
    PetscCall(DMPlexSetReferenceTree(rdm, refTree));
  }
  if (user->useDA) PetscCall(DMDASetVertexCoordinates(rdm, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
  PetscCall(SetupSection(rdm, user));
  /* Setup functions to approximate */
  switch (order) {
  case 0:
    exactFuncs[0]    = constant;
    exactFuncDers[0] = constantDer;
    break;
  case 1:
    exactFuncs[0]    = linear;
    exactFuncDers[0] = linearDer;
    break;
  case 2:
    exactFuncs[0]    = quadratic;
    exactFuncDers[0] = quadraticDer;
    break;
  case 3:
    exactFuncs[0]    = cubic;
    exactFuncDers[0] = cubicDer;
    break;
  default:
    SETERRQ(comm, PETSC_ERR_ARG_OUTOFRANGE, "Could not determine functions to test for dimension %" PetscInt_FMT " order %" PetscInt_FMT, dim, order);
  }
  idm = checkRestrict ? rdm : dm;
  fdm = checkRestrict ? dm : rdm;
  PetscCall(DMGetGlobalVector(idm, &iu));
  PetscCall(DMGetGlobalVector(fdm, &fu));
  PetscCall(DMSetApplicationContext(dm, user));
  PetscCall(DMSetApplicationContext(rdm, user));
  PetscCall(DMCreateInterpolation(dm, rdm, &Interp, &scaling));
  /* Project function into initial FE function space */
  PetscCall(DMProjectFunction(idm, 0.0, exactFuncs, exactCtxs, INSERT_ALL_VALUES, iu));
  /* Interpolate function into final FE function space */
  if (checkRestrict) {
    PetscCall(MatRestrict(Interp, iu, fu));
    PetscCall(VecPointwiseMult(fu, scaling, fu));
  } else PetscCall(MatInterpolate(Interp, iu, fu));
  /* Compare approximation to exact in L_2 */
  PetscCall(DMComputeL2Diff(fdm, 0.0, exactFuncs, exactCtxs, fu, &error));
  PetscCall(DMComputeL2GradientDiff(fdm, 0.0, exactFuncDers, exactCtxs, fu, n, &errorDer));
  /* Report result */
  if (error > tol) PetscCall(PetscPrintf(comm, "Interpolation tests FAIL for order %" PetscInt_FMT " at tolerance %g error %g\n", order, (double)tol, (double)error));
  else PetscCall(PetscPrintf(comm, "Interpolation tests pass for order %" PetscInt_FMT " at tolerance %g\n", order, (double)tol));
  if (errorDer > tol) PetscCall(PetscPrintf(comm, "Interpolation tests FAIL for order %" PetscInt_FMT " derivatives at tolerance %g error %g\n", order, (double)tol, (double)errorDer));
  else PetscCall(PetscPrintf(comm, "Interpolation tests pass for order %" PetscInt_FMT " derivatives at tolerance %g\n", order, (double)tol));
  PetscCall(DMRestoreGlobalVector(idm, &iu));
  PetscCall(DMRestoreGlobalVector(fdm, &fu));
  PetscCall(MatDestroy(&Interp));
  PetscCall(VecDestroy(&scaling));
  PetscCall(DMDestroy(&rdm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode CheckConvergence(DM dm, PetscInt Nr, AppCtx *user)
{
  DM odm = dm, rdm = NULL, cdm = NULL;
  PetscErrorCode (*exactFuncs[1])(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx)                         = {trig};
  PetscErrorCode (*exactFuncDers[1])(PetscInt dim, PetscReal time, const PetscReal x[], const PetscReal n[], PetscInt Nf, PetscScalar *u, void *ctx) = {trigDer};
  void     *exactCtxs[3];
  PetscInt  r, c, cStart, cEnd;
  PetscReal errorOld, errorDerOld, error, errorDer, rel, len, lenOld;
  double    p;

  PetscFunctionBeginUser;
  if (!user->convergence) PetscFunctionReturn(PETSC_SUCCESS);
  exactCtxs[0] = user;
  exactCtxs[1] = user;
  exactCtxs[2] = user;
  PetscCall(PetscObjectReference((PetscObject)odm));
  if (!user->convRefine) {
    for (r = 0; r < Nr; ++r) {
      PetscCall(DMRefine(odm, PetscObjectComm((PetscObject)dm), &rdm));
      PetscCall(DMDestroy(&odm));
      odm = rdm;
    }
    PetscCall(SetupSection(odm, user));
  }
  PetscCall(ComputeError(odm, exactFuncs, exactFuncDers, exactCtxs, &errorOld, &errorDerOld, user));
  if (user->convRefine) {
    for (r = 0; r < Nr; ++r) {
      PetscCall(DMRefine(odm, PetscObjectComm((PetscObject)dm), &rdm));
      if (user->useDA) PetscCall(DMDASetVertexCoordinates(rdm, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
      PetscCall(SetupSection(rdm, user));
      PetscCall(ComputeError(rdm, exactFuncs, exactFuncDers, exactCtxs, &error, &errorDer, user));
      p = PetscLog2Real(errorOld / error);
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Function   convergence rate at refinement %" PetscInt_FMT ": %.2f\n", r, (double)p));
      p = PetscLog2Real(errorDerOld / errorDer);
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Derivative convergence rate at refinement %" PetscInt_FMT ": %.2f\n", r, (double)p));
      PetscCall(DMDestroy(&odm));
      odm         = rdm;
      errorOld    = error;
      errorDerOld = errorDer;
    }
  } else {
    /* PetscCall(ComputeLongestEdge(dm, &lenOld)); */
    PetscCall(DMPlexGetHeightStratum(odm, 0, &cStart, &cEnd));
    lenOld = cEnd - cStart;
    for (c = 0; c < Nr; ++c) {
      PetscCall(DMCoarsen(odm, PetscObjectComm((PetscObject)dm), &cdm));
      if (user->useDA) PetscCall(DMDASetVertexCoordinates(cdm, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0));
      PetscCall(SetupSection(cdm, user));
      PetscCall(ComputeError(cdm, exactFuncs, exactFuncDers, exactCtxs, &error, &errorDer, user));
      /* PetscCall(ComputeLongestEdge(cdm, &len)); */
      PetscCall(DMPlexGetHeightStratum(cdm, 0, &cStart, &cEnd));
      len = cEnd - cStart;
      rel = error / errorOld;
      p   = PetscLogReal(rel) / PetscLogReal(lenOld / len);
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Function   convergence rate at coarsening %" PetscInt_FMT ": %.2f\n", c, (double)p));
      rel = errorDer / errorDerOld;
      p   = PetscLogReal(rel) / PetscLogReal(lenOld / len);
      PetscCall(PetscPrintf(PetscObjectComm((PetscObject)dm), "Derivative convergence rate at coarsening %" PetscInt_FMT ": %.2f\n", c, (double)p));
      PetscCall(DMDestroy(&odm));
      odm         = cdm;
      errorOld    = error;
      errorDerOld = errorDer;
      lenOld      = len;
    }
  }
  PetscCall(DMDestroy(&odm));
  PetscFunctionReturn(PETSC_SUCCESS);
}

int main(int argc, char **argv)
{
  DM        dm;
  AppCtx    user; /* user-defined work context */
  PetscInt  dim     = 2;
  PetscBool simplex = PETSC_FALSE;

  PetscFunctionBeginUser;
  PetscCall(PetscInitialize(&argc, &argv, NULL, help));
  PetscCall(ProcessOptions(PETSC_COMM_WORLD, &user));
  PetscCall(CreateMesh(PETSC_COMM_WORLD, &user, &dm));
  if (!user.useDA) {
    PetscCall(DMGetDimension(dm, &dim));
    PetscCall(DMPlexIsSimplex(dm, &simplex));
  }
  PetscCall(DMPlexMetricSetFromOptions(dm));
  user.numComponents = user.numComponents < 0 ? dim : user.numComponents;
  PetscCall(PetscFECreateDefault(PETSC_COMM_WORLD, dim, user.numComponents, simplex, NULL, user.qorder, &user.fe));
  PetscCall(SetupSection(dm, &user));
  if (user.testFEjacobian) PetscCall(TestFEJacobian(dm, &user));
  if (user.testFVgrad) PetscCall(TestFVGrad(dm, &user));
  if (user.testInjector) PetscCall(TestInjector(dm, &user));
  PetscCall(CheckFunctions(dm, user.porder, &user));
  {
    PetscDualSpace dsp;
    PetscInt       k;

    PetscCall(PetscFEGetDualSpace(user.fe, &dsp));
    PetscCall(PetscDualSpaceGetDeRahm(dsp, &k));
    if (dim == 2 && simplex == PETSC_TRUE && user.tree == PETSC_FALSE && k == 0) {
      PetscCall(CheckInterpolation(dm, PETSC_FALSE, user.porder, &user));
      PetscCall(CheckInterpolation(dm, PETSC_TRUE, user.porder, &user));
    }
  }
  PetscCall(CheckConvergence(dm, 3, &user));
  PetscCall(PetscFEDestroy(&user.fe));
  PetscCall(DMDestroy(&dm));
  PetscCall(PetscFinalize());
  return 0;
}

/*TEST

  test:
    suffix: 1
    requires: triangle

  # 2D P_1 on a triangle
  test:
    suffix: p1_2d_0
    requires: triangle
    args: -petscspace_degree 1 -qorder 1 -convergence
  test:
    suffix: p1_2d_1
    requires: triangle
    args: -petscspace_degree 1 -qorder 1 -porder 1
  test:
    suffix: p1_2d_2
    requires: triangle
    args: -petscspace_degree 1 -qorder 1 -porder 2
  test:
    suffix: p1_2d_3
    requires: triangle mmg
    args: -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -convergence -conv_refine 0
  test:
    suffix: p1_2d_4
    requires: triangle mmg
    args: -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -porder 1 -conv_refine 0
  test:
    suffix: p1_2d_5
    requires: triangle mmg
    args: -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -porder 2 -conv_refine 0

  # 3D P_1 on a tetrahedron
  test:
    suffix: p1_3d_0
    requires: ctetgen
    args: -dm_plex_dim 3 -petscspace_degree 1 -qorder 1 -convergence
  test:
    suffix: p1_3d_1
    requires: ctetgen
    args: -dm_plex_dim 3 -petscspace_degree 1 -qorder 1 -porder 1
  test:
    suffix: p1_3d_2
    requires: ctetgen
    args: -dm_plex_dim 3 -petscspace_degree 1 -qorder 1 -porder 2
  test:
    suffix: p1_3d_3
    requires: ctetgen mmg
    args: -dm_plex_dim 3 -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -convergence -conv_refine 0
  test:
    suffix: p1_3d_4
    requires: ctetgen mmg
    args: -dm_plex_dim 3 -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -porder 1 -conv_refine 0
  test:
    suffix: p1_3d_5
    requires: ctetgen mmg
    args: -dm_plex_dim 3 -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -porder 2 -conv_refine 0

  # 2D P_2 on a triangle
  test:
    suffix: p2_2d_0
    requires: triangle
    args: -petscspace_degree 2 -qorder 2 -convergence
  test:
    suffix: p2_2d_1
    requires: triangle
    args: -petscspace_degree 2 -qorder 2 -porder 1
  test:
    suffix: p2_2d_2
    requires: triangle
    args: -petscspace_degree 2 -qorder 2 -porder 2
  test:
    suffix: p2_2d_3
    requires: triangle mmg
    args: -petscspace_degree 2 -qorder 2 -dm_plex_hash_location -convergence -conv_refine 0
  test:
    suffix: p2_2d_4
    requires: triangle mmg
    args: -petscspace_degree 2 -qorder 2 -dm_plex_hash_location -porder 1 -conv_refine 0
  test:
    suffix: p2_2d_5
    requires: triangle mmg
    args: -petscspace_degree 2 -qorder 2 -dm_plex_hash_location -porder 2 -conv_refine 0

  # 3D P_2 on a tetrahedron
  test:
    suffix: p2_3d_0
    requires: ctetgen
    args: -dm_plex_dim 3 -petscspace_degree 2 -qorder 2 -convergence
  test:
    suffix: p2_3d_1
    requires: ctetgen
    args: -dm_plex_dim 3 -petscspace_degree 2 -qorder 2 -porder 1
  test:
    suffix: p2_3d_2
    requires: ctetgen
    args: -dm_plex_dim 3 -petscspace_degree 2 -qorder 2 -porder 2
  test:
    suffix: p2_3d_3
    requires: ctetgen mmg
    args: -dm_plex_dim 3 -petscspace_degree 2 -qorder 2 -dm_plex_hash_location -convergence -conv_refine 0
  test:
    suffix: p2_3d_4
    requires: ctetgen mmg
    args: -dm_plex_dim 3 -petscspace_degree 2 -qorder 2 -dm_plex_hash_location -porder 1 -conv_refine 0
  test:
    suffix: p2_3d_5
    requires: ctetgen mmg
    args: -dm_plex_dim 3 -petscspace_degree 2 -qorder 2 -dm_plex_hash_location -porder 2 -conv_refine 0

  # 2D Q_1 on a quadrilaterial DA
  test:
    suffix: q1_2d_da_0
    requires: broken
    args: -use_da 1 -petscspace_degree 1 -qorder 1 -convergence
  test:
    suffix: q1_2d_da_1
    requires: broken
    args: -use_da 1 -petscspace_degree 1 -qorder 1 -porder 1
  test:
    suffix: q1_2d_da_2
    requires: broken
    args: -use_da 1 -petscspace_degree 1 -qorder 1 -porder 2

  # 2D Q_1 on a quadrilaterial Plex
  test:
    suffix: q1_2d_plex_0
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 1 -convergence
  test:
    suffix: q1_2d_plex_1
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 1 -porder 1
  test:
    suffix: q1_2d_plex_2
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 1 -porder 2
  test:
    suffix: q1_2d_plex_3
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 1 -porder 1 -shear_coords
  test:
    suffix: q1_2d_plex_4
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 1 -porder 2 -shear_coords
  test:
    suffix: q1_2d_plex_5
    args: -dm_plex_simplex 0 -petscspace_degree 1 -petscspace_type tensor -qorder 1 -porder 0 -non_affine_coords -convergence
  test:
    suffix: q1_2d_plex_6
    args: -dm_plex_simplex 0 -petscspace_degree 1 -petscspace_type tensor -qorder 1 -porder 1 -non_affine_coords -convergence
  test:
    suffix: q1_2d_plex_7
    args: -dm_plex_simplex 0 -petscspace_degree 1 -petscspace_type tensor -qorder 1 -porder 2 -non_affine_coords -convergence

  # 2D Q_2 on a quadrilaterial
  test:
    suffix: q2_2d_plex_0
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -convergence
  test:
    suffix: q2_2d_plex_1
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 1
  test:
    suffix: q2_2d_plex_2
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 2
  test:
    suffix: q2_2d_plex_3
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 1 -shear_coords
  test:
    suffix: q2_2d_plex_4
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 2 -shear_coords
  test:
    suffix: q2_2d_plex_5
    args: -dm_plex_simplex 0 -petscspace_degree 2 -petscspace_type tensor -qorder 2 -porder 0 -non_affine_coords -convergence
  test:
    suffix: q2_2d_plex_6
    args: -dm_plex_simplex 0 -petscspace_degree 2 -petscspace_type tensor -qorder 2 -porder 1 -non_affine_coords -convergence
  test:
    suffix: q2_2d_plex_7
    args: -dm_plex_simplex 0 -petscspace_degree 2 -petscspace_type tensor -qorder 2 -porder 2 -non_affine_coords -convergence

  # 2D P_3 on a triangle
  test:
    suffix: p3_2d_0
    requires: triangle !single
    args: -petscspace_degree 3 -qorder 3 -convergence
  test:
    suffix: p3_2d_1
    requires: triangle !single
    args: -petscspace_degree 3 -qorder 3 -porder 1
  test:
    suffix: p3_2d_2
    requires: triangle !single
    args: -petscspace_degree 3 -qorder 3 -porder 2
  test:
    suffix: p3_2d_3
    requires: triangle !single
    args: -petscspace_degree 3 -qorder 3 -porder 3
  test:
    suffix: p3_2d_4
    requires: triangle mmg
    args: -petscspace_degree 3 -qorder 3 -dm_plex_hash_location -convergence -conv_refine 0
  test:
    suffix: p3_2d_5
    requires: triangle mmg
    args: -petscspace_degree 3 -qorder 3 -dm_plex_hash_location -porder 1 -conv_refine 0
  test:
    suffix: p3_2d_6
    requires: triangle mmg
    args: -petscspace_degree 3 -qorder 3 -dm_plex_hash_location -porder 3 -conv_refine 0

  # 2D Q_3 on a quadrilaterial
  test:
    suffix: q3_2d_0
    requires: !single
    args: -dm_plex_simplex 0 -petscspace_degree 3 -qorder 3 -convergence
  test:
    suffix: q3_2d_1
    requires: !single
    args: -dm_plex_simplex 0 -petscspace_degree 3 -qorder 3 -porder 1
  test:
    suffix: q3_2d_2
    requires: !single
    args: -dm_plex_simplex 0 -petscspace_degree 3 -qorder 3 -porder 2
  test:
    suffix: q3_2d_3
    requires: !single
    args: -dm_plex_simplex 0 -petscspace_degree 3 -qorder 3 -porder 3

  # 2D P_1disc on a triangle/quadrilateral
  test:
    suffix: p1d_2d_0
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_lagrange_continuity 0 -qorder 1 -convergence
  test:
    suffix: p1d_2d_1
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_lagrange_continuity 0 -qorder 1 -porder 1
  test:
    suffix: p1d_2d_2
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_lagrange_continuity 0 -qorder 1 -porder 2
  test:
    suffix: p1d_2d_3
    requires: triangle
    args: -dm_plex_simplex 0 -petscspace_degree 1 -petscdualspace_lagrange_continuity 0 -qorder 1 -convergence
    filter: sed  -e "s/convergence rate at refinement 0: 2/convergence rate at refinement 0: 1.9/g"
  test:
    suffix: p1d_2d_4
    requires: triangle
    args: -dm_plex_simplex 0 -petscspace_degree 1 -petscdualspace_lagrange_continuity 0 -qorder 1 -porder 1
  test:
    suffix: p1d_2d_5
    requires: triangle
    args: -dm_plex_simplex 0 -petscspace_degree 1 -petscdualspace_lagrange_continuity 0 -qorder 1 -porder 2

  # 2D BDM_1 on a triangle
  test:
    suffix: bdm1_2d_0
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_type bdm \
          -num_comp 2 -qorder 1 -convergence
  test:
    suffix: bdm1_2d_1
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_type bdm \
          -num_comp 2 -qorder 1 -porder 1
  test:
    suffix: bdm1_2d_2
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_type bdm \
          -num_comp 2 -qorder 1 -porder 2

  # 2D BDM_1 on a quadrilateral
  test:
    suffix: bdm1q_2d_0
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_type bdm \
          -petscdualspace_lagrange_tensor 1 \
          -dm_plex_simplex 0 -num_comp 2 -qorder 1 -convergence
  test:
    suffix: bdm1q_2d_1
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_type bdm \
          -petscdualspace_lagrange_tensor 1 \
          -dm_plex_simplex 0 -num_comp 2 -qorder 1 -porder 1
  test:
    suffix: bdm1q_2d_2
    requires: triangle
    args: -petscspace_degree 1 -petscdualspace_type bdm \
          -petscdualspace_lagrange_tensor 1 \
          -dm_plex_simplex 0 -num_comp 2 -qorder 1 -porder 2

  # Test high order quadrature
  test:
    suffix: p1_quad_2
    requires: triangle
    args: -petscspace_degree 1 -qorder 2 -porder 1
  test:
    suffix: p1_quad_5
    requires: triangle
    args: -petscspace_degree 1 -qorder 5 -porder 1
  test:
    suffix: p2_quad_3
    requires: triangle
    args: -petscspace_degree 2 -qorder 3 -porder 2
  test:
    suffix: p2_quad_5
    requires: triangle
    args: -petscspace_degree 2 -qorder 5 -porder 2
  test:
    suffix: q1_quad_2
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 2 -porder 1
  test:
    suffix: q1_quad_5
    args: -dm_plex_simplex 0 -petscspace_degree 1 -qorder 5 -porder 1
  test:
    suffix: q2_quad_3
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 3 -porder 1
  test:
    suffix: q2_quad_5
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 5 -porder 1

  # Nonconforming tests
  test:
    suffix: constraints
    args: -dm_coord_space 0 -dm_plex_simplex 0 -petscspace_type tensor -petscspace_degree 1 -qorder 0 -constraints
  test:
    suffix: nonconforming_tensor_2
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -test_injector -petscpartitioner_type simple -tree -dm_plex_simplex 0 -dm_plex_max_projection_height 1 -petscspace_type tensor -petscspace_degree 2 -qorder 2 -dm_view ascii::ASCII_INFO_DETAIL
  test:
    suffix: nonconforming_tensor_3
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -petscpartitioner_type simple -tree -dm_plex_simplex 0 -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -dm_plex_max_projection_height 2 -petscspace_type tensor -petscspace_degree 1 -qorder 1 -dm_view ascii::ASCII_INFO_DETAIL
  test:
    suffix: nonconforming_tensor_2_fv
    nsize: 4
    args: -dist_dm_distribute -test_fv_grad -test_injector -petsclimiter_type none -petscpartitioner_type simple -tree -dm_plex_simplex 0 -num_comp 2
  test:
    suffix: nonconforming_tensor_3_fv
    nsize: 4
    args: -dist_dm_distribute -test_fv_grad -test_injector -petsclimiter_type none -petscpartitioner_type simple -tree -dm_plex_simplex 0 -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -num_comp 3
  test:
    suffix: nonconforming_tensor_2_hi
    requires: !single
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -petscpartitioner_type simple -tree -dm_plex_simplex 0 -dm_plex_max_projection_height 1 -petscspace_type tensor -petscspace_degree 4 -qorder 4
  test:
    suffix: nonconforming_tensor_3_hi
    requires: !single skip
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -petscpartitioner_type simple -tree -dm_plex_simplex 0 -dm_plex_dim 3 -dm_plex_box_faces 2,2,2 -dm_plex_max_projection_height 2 -petscspace_type tensor -petscspace_degree 4 -qorder 4
  test:
    suffix: nonconforming_simplex_2
    requires: triangle
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -test_injector -petscpartitioner_type simple -tree -dm_plex_max_projection_height 1 -petscspace_degree 2 -qorder 2 -dm_view ascii::ASCII_INFO_DETAIL
  test:
    suffix: nonconforming_simplex_2_hi
    requires: triangle !single
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -petscpartitioner_type simple -tree -dm_plex_max_projection_height 1 -petscspace_degree 4 -qorder 4
  test:
    suffix: nonconforming_simplex_2_fv
    requires: triangle
    nsize: 4
    args: -dist_dm_distribute -test_fv_grad -test_injector -petsclimiter_type none -petscpartitioner_type simple -tree -num_comp 2
  test:
    suffix: nonconforming_simplex_3
    requires: ctetgen
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -test_injector -petscpartitioner_type simple -tree -dm_plex_dim 3 -dm_plex_max_projection_height 2 -petscspace_degree 2 -qorder 2 -dm_view ascii::ASCII_INFO_DETAIL
  test:
    suffix: nonconforming_simplex_3_hi
    requires: ctetgen skip
    nsize: 4
    args: -dist_dm_distribute -test_fe_jacobian -petscpartitioner_type simple -tree -dm_plex_dim 3 -dm_plex_max_projection_height 2 -petscspace_degree 4 -qorder 4
  test:
    suffix: nonconforming_simplex_3_fv
    requires: ctetgen
    nsize: 4
    args: -dist_dm_distribute -test_fv_grad -test_injector -petsclimiter_type none -petscpartitioner_type simple -tree -dm_plex_dim 3 -num_comp 3

  # 3D WXY on a triangular prism
  test:
    suffix: wxy_0
    args: -dm_plex_reference_cell_domain -dm_plex_cell triangular_prism -qorder 2 -porder 0 \
          -petscspace_type sum \
          -petscspace_variables 3 \
          -petscspace_components 3 \
          -petscspace_sum_spaces 2 \
          -petscspace_sum_concatenate false \
          -sumcomp_0_petscspace_variables 3 \
          -sumcomp_0_petscspace_components 3 \
          -sumcomp_0_petscspace_degree 1 \
          -sumcomp_1_petscspace_variables 3 \
          -sumcomp_1_petscspace_components 3 \
          -sumcomp_1_petscspace_type wxy \
          -petscdualspace_refcell triangular_prism \
          -petscdualspace_form_degree 0 \
          -petscdualspace_order 1 \
          -petscdualspace_components 3

TEST*/

/*
   # 2D Q_2 on a quadrilaterial Plex
  test:
    suffix: q2_2d_plex_0
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -convergence
  test:
    suffix: q2_2d_plex_1
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 1
  test:
    suffix: q2_2d_plex_2
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 2
  test:
    suffix: q2_2d_plex_3
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 1 -shear_coords
  test:
    suffix: q2_2d_plex_4
    args: -dm_plex_simplex 0 -petscspace_degree 2 -qorder 2 -porder 2 -shear_coords
  test:
    suffix: q2_2d_plex_5
    args: -dm_plex_simplex 0 -petscspace_degree 2 -petscspace_poly_tensor 1 -qorder 2 -porder 0 -non_affine_coords
  test:
    suffix: q2_2d_plex_6
    args: -dm_plex_simplex 0 -petscspace_degree 2 -petscspace_poly_tensor 1 -qorder 2 -porder 1 -non_affine_coords
  test:
    suffix: q2_2d_plex_7
    args: -dm_plex_simplex 0 -petscspace_degree 2 -petscspace_poly_tensor 1 -qorder 2 -porder 2 -non_affine_coords

  test:
    suffix: p1d_2d_6
    requires: mmg
    args: -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -convergence -conv_refine 0
  test:
    suffix: p1d_2d_7
    requires: mmg
    args: -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -porder 1 -conv_refine 0
  test:
    suffix: p1d_2d_8
    requires: mmg
    args: -petscspace_degree 1 -qorder 1 -dm_plex_hash_location -porder 2 -conv_refine 0
*/