Jules attempt at having a reflective condition on the top wall. SNES fails to converge under significant rotations (alpha). Also py3 petsc_gen_xdmf.py attached

ex71.c

static char help[] = "Poiseuille Flow in 2d and 3d channels with finite elements.\n\
We solve the Poiseuille flow problem in a rectangular\n\
domain, using a parallel unstructured mesh (DMPLEX) to discretize it.\n\n\n";

/*F
A Poiseuille flow is a steady-state isoviscous Stokes flow in a pipe of constant cross-section. We discretize using the
finite element method on an unstructured mesh. The weak form equations are
\begin{align*}
  < \nabla v, \nu (\nabla u + {\nabla u}^T) > - < \nabla\cdot v, p > + < v, \Delta \hat n >_{\Gamma_o} = 0
  < q, \nabla\cdot u >                                                                                 = 0
\end{align*}
where $\nu$ is the kinematic viscosity, $\Delta$ is the pressure drop per unit length, assuming that pressure is 0 on
the left edge, and $\Gamma_o$ is the outlet boundary at the right edge of the pipe. The normal velocity will be zero at
the wall, but we will allow a fixed tangential velocity $u_0$.

In order to test our global to local basis transformation, we will allow the pipe to be at an angle $\alpha$ to the
coordinate axes.

For visualization, use

  -dm_view hdf5:$PWD/sol.h5 -sol_vec_view hdf5:$PWD/sol.h5::append -exact_vec_view hdf5:$PWD/sol.h5::append
F*/

#include <petscdmplex.h>
#include <petscsnes.h>
#include <petscds.h>
#include <petscbag.h>

typedef struct {
  PetscReal Delta; /* Pressure drop per unit length */
  PetscReal nu;    /* Kinematic viscosity */
  PetscReal u_0;   /* Tangential velocity at the wall */
  PetscReal alpha; /* Angle of pipe wall to x-axis */
} Parameter;

typedef struct {
  /* Domain and mesh definition */
  PetscInt  dim;               /* The topological mesh dimension */
  PetscBool simplex;           /* Use simplices or tensor product cells */
  PetscInt  cells[3];          /* The initial domain division */
  /* Problem definition */
  PetscBag  bag;               /* Holds problem parameters */
  PetscErrorCode (**exactFuncs)(PetscInt dim, PetscReal time, const PetscReal x[], PetscInt Nf, PetscScalar *u, void *ctx);
} AppCtx;

/*
  In 2D, plane Poiseuille flow has exact solution:

    u = \Delta/(2 \nu) y (1 - y) + u_0
    v = 0
    p = -\Delta x
    f = 0

  so that

    -\nu \Delta u + \nabla p + f = <\Delta, 0> + <-\Delta, 0> + <0, 0> = 0
    \nabla \cdot u               = 0 + 0                               = 0

  In 3D we use exact solution:

    u = \Delta/(4 \nu) (y (1 - y) + z (1 - z)) + u_0
    v = 0
    w = 0
    p = -\Delta x
    f = 0

  so that

    -\nu \Delta u + \nabla p + f = <Delta, 0, 0> + <-Delta, 0, 0> + <0, 0, 0> = 0
    \nabla \cdot u               = 0 + 0 + 0                                  = 0

  Note that these functions use coordinates X in the global (rotated) frame
*/
PetscErrorCode quadratic_u(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  Parameter *param = (Parameter *) ctx;
  PetscReal  Delta = param->Delta;
  PetscReal  nu    = param->nu;
  PetscReal  u_0   = param->u_0;
  PetscReal  fac   = (PetscReal) (dim - 1);
  PetscInt   d;

  u[0] = u_0;
  for (d = 1; d < dim; ++d) u[0] += Delta/(fac * 2.0*nu) * X[d] * (1.0 - X[d]);
  for (d = 1; d < dim; ++d) u[d]  = 0.0;
  return 0;
}

PetscErrorCode linear_p(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *p, void *ctx)
{
  Parameter *param = (Parameter *) ctx;
  PetscReal  Delta = param->Delta;

  p[0] = -Delta * X[0];
  return 0;
}

PetscErrorCode static_wall(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  Parameter *param = (Parameter *) ctx;
  PetscInt   d;

  for (d = 0; d < dim; ++d) u[d] = 0.0;
  return 0;
}

PetscErrorCode top_wall_velocity(PetscInt dim, PetscReal time, const PetscReal X[], PetscInt Nf, PetscScalar *u, void *ctx)
{
  Parameter *param = (Parameter *) ctx;
  PetscReal  u_0   = param->u_0;
  PetscInt   d;

  //u[0] = u_0;
  for (d = 1; d < dim; ++d) u[d] = 0.0;
  return 0;
}

/* gradU[comp*dim+d] = {u_x, u_y, v_x, v_y} or {u_x, u_y, u_z, v_x, v_y, v_z, w_x, w_y, w_z}
   u[Ncomp]          = {p} */
void f1_u(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, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f1[])
{
  const PetscReal nu = PetscRealPart(constants[1]);
  const PetscInt  Nc = dim;
  PetscInt        c, d;

  for (c = 0; c < Nc; ++c) {
    for (d = 0; d < dim; ++d) {
      /* f1[c*dim+d] = 0.5*nu*(u_x[c*dim+d] + u_x[d*dim+c]); */
      f1[c*dim+d] = nu*u_x[c*dim+d];
    }
    f1[c*dim+c] -= u[uOff[1]];
  }
}

/* gradU[comp*dim+d] = {u_x, u_y, v_x, v_y} or {u_x, u_y, u_z, v_x, v_y, v_z, w_x, w_y, w_z} */
void f0_p(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, const PetscReal x[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
{
  PetscInt d;
  for (d = 0, f0[0] = 0.0; d < dim; ++d) f0[0] += u_x[d*dim+d];
}

/* Residual functions are in reference coordinates */
static void f0_bd_u(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, const PetscReal x[], const PetscReal n[], PetscInt numConstants, const PetscScalar constants[], PetscScalar f0[])
{
  const PetscReal Delta = PetscRealPart(constants[0]);
  PetscReal       alpha = PetscRealPart(constants[3]);
  PetscReal       X     = PetscCosReal(alpha)*x[0] + PetscSinReal(alpha)*x[1];
  PetscInt        d;

  for (d = 0; d < dim; ++d) {
    f0[d] = -Delta * X * n[d];
  }
}

/* < q, \nabla\cdot u >
   NcompI = 1, NcompJ = dim */
void g1_pu(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 g1[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) g1[d*dim+d] = 1.0; /* \frac{\partial\phi^{u_d}}{\partial x_d} */
}

/* -< \nabla\cdot v, p >
    NcompI = dim, NcompJ = 1 */
void g2_up(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 g2[])
{
  PetscInt d;
  for (d = 0; d < dim; ++d) g2[d*dim+d] = -1.0; /* \frac{\partial\psi^{u_d}}{\partial x_d} */
}

/* < \nabla v, \nabla u + {\nabla u}^T >
   This just gives \nabla u, give the perdiagonal for the transpose */
void g3_uu(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 g3[])
{
  const PetscReal nu = PetscRealPart(constants[1]);
  const PetscInt  Nc = dim;
  PetscInt        c, d;

  for (c = 0; c < Nc; ++c) {
    for (d = 0; d < dim; ++d) {
      g3[((c*Nc+c)*dim+d)*dim+d] = nu;
    }
  }
}

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

  PetscFunctionBeginUser;
  options->dim      = 2;
  options->simplex  = PETSC_TRUE;
  options->cells[0] = 3;
  options->cells[1] = 3;
  options->cells[2] = 3;

  ierr = PetscOptionsBegin(comm, "", "Poiseuille Flow Options", "DMPLEX");CHKERRQ(ierr);
  ierr = PetscOptionsInt("-dim", "The topological mesh dimension", "ex62.c", options->dim, &options->dim, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-simplex", "Use simplices or tensor product cells", "ex62.c", options->simplex, &options->simplex, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsIntArray("-cells", "The initial mesh division", "ex62.c", options->cells, &n, NULL);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();
  PetscFunctionReturn(0);
}

static PetscErrorCode SetupParameters(AppCtx *user)
{
  PetscBag       bag;
  Parameter     *p;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  /* setup PETSc parameter bag */
  ierr = PetscBagGetData(user->bag, (void **) &p);CHKERRQ(ierr);
  ierr = PetscBagSetName(user->bag, "par", "Poiseuille flow parameters");CHKERRQ(ierr);
  bag  = user->bag;
  ierr = PetscBagRegisterReal(bag, &p->Delta, 1.0, "Delta", "Pressure drop per unit length");CHKERRQ(ierr);
  ierr = PetscBagRegisterReal(bag, &p->nu,    1.0, "nu",    "Kinematic viscosity");CHKERRQ(ierr);
  ierr = PetscBagRegisterReal(bag, &p->u_0,   0.0, "u_0",   "Tangential velocity at the wall");CHKERRQ(ierr);
  ierr = PetscBagRegisterReal(bag, &p->alpha, 0.0, "alpha", "Angle of pipe wall to x-axis");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode CreateMesh(MPI_Comm comm, AppCtx *user, DM *dm)
{
  PetscInt       dim = user->dim;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = DMPlexCreateBoxMesh(comm, dim, user->simplex, user->cells, NULL, NULL, NULL, PETSC_TRUE, dm);CHKERRQ(ierr);
  {
    Parameter   *param;
    Vec          coordinates;
    PetscScalar *coords;
    PetscReal    alpha;
    PetscInt     cdim, N, bs, i;

    ierr = DMGetCoordinateDim(*dm, &cdim);CHKERRQ(ierr);
    ierr = DMGetCoordinates(*dm, &coordinates);CHKERRQ(ierr);
    ierr = VecGetLocalSize(coordinates, &N);CHKERRQ(ierr);
    ierr = VecGetBlockSize(coordinates, &bs);CHKERRQ(ierr);
    if (bs != cdim) SETERRQ2(comm, PETSC_ERR_ARG_WRONG, "Invalid coordinate blocksize %D != embedding dimension %D", bs, cdim);
    ierr = VecGetArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = PetscBagGetData(user->bag, (void **) &param);CHKERRQ(ierr);
    alpha = param->alpha;
    for (i = 0; i < N; i += cdim) {
      PetscScalar x = coords[i+0];
      PetscScalar y = coords[i+1];

      coords[i+0] = PetscCosReal(alpha)*x - PetscSinReal(alpha)*y;
      coords[i+1] = PetscSinReal(alpha)*x + PetscCosReal(alpha)*y;
#if 0
      if ((PetscAbsReal(x - 0.333333333) < 1.0e-7) && (PetscAbsReal(y - 0.333333333) < 1.0e-7)) {
        coords[i+0] += PetscCosReal(alpha)*0.05;
        coords[i+1] += PetscSinReal(alpha)*0.05;
      }
#endif
    }
    ierr = VecRestoreArray(coordinates, &coords);CHKERRQ(ierr);
    ierr = DMSetCoordinates(*dm, coordinates);CHKERRQ(ierr);
  }
  {
    DM               pdm = NULL;
    PetscPartitioner part;

    ierr = DMPlexGetPartitioner(*dm, &part);CHKERRQ(ierr);
    ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);
    ierr = DMPlexDistribute(*dm, 0, NULL, &pdm);CHKERRQ(ierr);
    if (pdm) {
      ierr = DMDestroy(dm);CHKERRQ(ierr);
      *dm  = pdm;
    }
  }
  ierr = DMSetFromOptions(*dm);CHKERRQ(ierr);
  ierr = DMViewFromOptions(*dm, NULL, "-dm_view");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode SetupProblem(DM dm, AppCtx *user)
{
  PetscDS        prob;
  Parameter     *ctx;
  PetscInt       id;
  PetscErrorCode ierr;

  PetscFunctionBeginUser;
  ierr = DMGetDS(dm, &prob);CHKERRQ(ierr);
  ierr = PetscDSSetResidual(prob, 0, NULL, f1_u);CHKERRQ(ierr);
  ierr = PetscDSSetResidual(prob, 1, f0_p, NULL);CHKERRQ(ierr);
  ierr = PetscDSSetBdResidual(prob, 0, f0_bd_u, NULL);CHKERRQ(ierr);
  ierr = PetscDSSetJacobian(prob, 0, 0, NULL, NULL,  NULL,  g3_uu);CHKERRQ(ierr);
  ierr = PetscDSSetJacobian(prob, 0, 1, NULL, NULL,  g2_up, NULL);CHKERRQ(ierr);
  ierr = PetscDSSetJacobian(prob, 1, 0, NULL, g1_pu, NULL,  NULL);CHKERRQ(ierr);
  /* Setup constants */
  {
    Parameter  *param;
    PetscScalar constants[4];

    ierr = PetscBagGetData(user->bag, (void **) &param);CHKERRQ(ierr);

    constants[0] = param->Delta;
    constants[1] = param->nu;
    constants[2] = param->u_0;
    constants[3] = param->alpha;
    ierr = PetscDSSetConstants(prob, 4, constants);CHKERRQ(ierr);
  }
  /* Setup Boundary Conditions */
  ierr = PetscBagGetData(user->bag, (void **) &ctx);CHKERRQ(ierr);
  PetscInt dofs[2] = {0,1};
  /* Top wall conditions */
  id   = 3;
  ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "top wall_vy",  "marker", 0, 1, &dofs[1], (void (*)(void)) top_wall_velocity, 1, &id, ctx);CHKERRQ(ierr);
  //ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL,   "top wall_vx",  "marker", 0, 1, &dofs[0], (void (*)(void)) top_wall_vx,    1, &id, ctx);CHKERRQ(ierr);
  id   = 1;
  ierr = PetscDSAddBoundary(prob, DM_BC_ESSENTIAL, "bottom wall", "marker", 0, 0, NULL, (void (*)(void)) static_wall, 1, &id, ctx);CHKERRQ(ierr);
  id   = 2;
  ierr = PetscDSAddBoundary(prob, DM_BC_NATURAL,   "right wall",  "marker", 0, 0, NULL, (void (*)(void)) NULL,          1, &id, ctx);CHKERRQ(ierr);
  /* Setup exact solution */
  user->exactFuncs[0] = quadratic_u;
  user->exactFuncs[1] = linear_p;
  ierr = PetscDSSetExactSolution(prob, 0, user->exactFuncs[0], ctx);CHKERRQ(ierr);
  ierr = PetscDSSetExactSolution(prob, 1, user->exactFuncs[1], ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode SetupDiscretization(DM dm, AppCtx *user)
{
  DM              cdm   = dm;
  const PetscInt  dim   = user->dim;
  PetscFE         fe[2];
  PetscQuadrature q;
  Parameter      *param;
  MPI_Comm        comm;
  PetscErrorCode  ierr;

  PetscFunctionBeginUser;
  /* Create finite element */
  ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
  ierr = PetscFECreateDefault(comm, dim, dim, user->simplex, "vel_", PETSC_DEFAULT, &fe[0]);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) fe[0], "velocity");CHKERRQ(ierr);
  ierr = PetscFEGetQuadrature(fe[0], &q);CHKERRQ(ierr);
  ierr = PetscFECreateDefault(comm, dim, 1, user->simplex, "pres_", PETSC_DEFAULT, &fe[1]);CHKERRQ(ierr);
  ierr = PetscFESetQuadrature(fe[1], q);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) fe[1], "pressure");CHKERRQ(ierr);
  /* Set discretization and boundary conditions for each mesh */
  ierr = DMSetField(dm, 0, NULL, (PetscObject) fe[0]);CHKERRQ(ierr);
  ierr = DMSetField(dm, 1, NULL, (PetscObject) fe[1]);CHKERRQ(ierr);
  ierr = DMCreateDS(dm);CHKERRQ(ierr);
  ierr = SetupProblem(dm, user);CHKERRQ(ierr);
  ierr = PetscBagGetData(user->bag, (void **) &param);CHKERRQ(ierr);
  while (cdm) {
    ierr = DMCopyDisc(dm, cdm);CHKERRQ(ierr);
    ierr = DMPlexCreateBasisRotation(cdm, param->alpha, 0.0, 0.0);CHKERRQ(ierr);
    ierr = DMGetCoarseDM(cdm, &cdm);CHKERRQ(ierr);
  }
  ierr = PetscFEDestroy(&fe[0]);CHKERRQ(ierr);
  ierr = PetscFEDestroy(&fe[1]);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

int main(int argc, char **argv)
{
  SNES           snes; /* nonlinear solver */
  DM             dm;   /* problem definition */
  Vec            u, r; /* solution and residual */
  AppCtx         user; /* user-defined work context */
  PetscErrorCode ierr;

  ierr = PetscInitialize(&argc, &argv, NULL,help);if (ierr) return ierr;
  ierr = ProcessOptions(PETSC_COMM_WORLD, &user);CHKERRQ(ierr);
  ierr = PetscBagCreate(PETSC_COMM_WORLD, sizeof(Parameter), &user.bag);CHKERRQ(ierr);
  ierr = SetupParameters(&user);CHKERRQ(ierr);
  ierr = SNESCreate(PETSC_COMM_WORLD, &snes);CHKERRQ(ierr);
  ierr = CreateMesh(PETSC_COMM_WORLD, &user, &dm);CHKERRQ(ierr);
  ierr = SNESSetDM(snes, dm);CHKERRQ(ierr);
  ierr = DMSetApplicationContext(dm, &user);CHKERRQ(ierr);
  /* Setup problem */
  ierr = PetscMalloc(2 * sizeof(void (*)(const PetscReal[], PetscScalar *, void *)), &user.exactFuncs);CHKERRQ(ierr);
  ierr = SetupDiscretization(dm, &user);CHKERRQ(ierr);
  ierr = DMPlexCreateClosureIndex(dm, NULL);CHKERRQ(ierr);

  ierr = DMCreateGlobalVector(dm, &u);CHKERRQ(ierr);
  ierr = VecDuplicate(u, &r);CHKERRQ(ierr);

  ierr = DMPlexSetSNESLocalFEM(dm,&user,&user,&user);CHKERRQ(ierr);

  ierr = SNESSetFromOptions(snes);CHKERRQ(ierr);

  {
    Parameter *param;
    void      *ctxs[2];

    ierr = PetscBagGetData(user.bag, (void **) &param);CHKERRQ(ierr);
    ctxs[0] = ctxs[1] = param;
    ierr = DMProjectFunction(dm, 0.0, user.exactFuncs, ctxs, INSERT_ALL_VALUES, u);CHKERRQ(ierr);
    ierr = PetscObjectSetName((PetscObject) u, "Exact Solution");CHKERRQ(ierr);
    ierr = VecViewFromOptions(u, NULL, "-exact_vec_view");CHKERRQ(ierr);
  }
  ierr = DMSNESCheckFromOptions(snes, u, NULL, NULL);CHKERRQ(ierr);
  ierr = VecSet(u, 0.0);CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject) u, "Solution");CHKERRQ(ierr);
  ierr = SNESSolve(snes, NULL, u);CHKERRQ(ierr);
  ierr = VecViewFromOptions(u, NULL, "-sol_vec_view");CHKERRQ(ierr);

  ierr = VecDestroy(&u);CHKERRQ(ierr);
  ierr = VecDestroy(&r);CHKERRQ(ierr);
  ierr = PetscFree(user.exactFuncs);CHKERRQ(ierr);
  ierr = DMDestroy(&dm);CHKERRQ(ierr);
  ierr = SNESDestroy(&snes);CHKERRQ(ierr);
  ierr = PetscBagDestroy(&user.bag);CHKERRQ(ierr);
  ierr = PetscFinalize();
  return ierr;
}

/*TEST

  # Convergence
  test:
    suffix: 2d_quad_q1_p0_conv
    requires: !single
    args: -simplex 0 -dm_plex_separate_marker -dm_refine 1 \
      -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
      -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type lu \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
  test:
    suffix: 2d_quad_q1_p0_conv_u0
    requires: !single
    args: -simplex 0 -dm_plex_separate_marker -dm_refine 1 -u_0 0.125 \
      -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
      -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type lu \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
  test:
    suffix: 2d_quad_q1_p0_conv_u0_alpha
    requires: !single
    args: -simplex 0 -dm_plex_separate_marker -dm_refine 1 -u_0 0.125 -alpha 0.3927 \
      -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
      -snes_convergence_estimate -convest_num_refine 2 -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type lu \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
  test:
    suffix: 2d_quad_q1_p0_conv_gmg_vanka
    requires: !single
    args: -simplex 0 -dm_plex_separate_marker -cells 2,2 -dm_refine_hierarchy 1 \
      -vel_petscspace_degree 1 -pres_petscspace_degree 0 \
      -snes_convergence_estimate -convest_num_refine 1 -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type mg \
          -fieldsplit_velocity_mg_levels_pc_type patch -fieldsplit_velocity_mg_levels_pc_patch_partition_of_unity 0 \
          -fieldsplit_velocity_mg_levels_pc_patch_construct_codim 0 -fieldsplit_velocity_mg_levels_pc_patch_construct_type vanka \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
  test:
    suffix: 2d_tri_p2_p1_conv
    requires: triangle !single
    args: -dm_plex_separate_marker -dm_refine 1 \
      -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
      -dmsnes_check -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type lu \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
  test:
    suffix: 2d_tri_p2_p1_conv_u0_alpha
    requires: triangle !single
    args: -dm_plex_separate_marker -dm_refine 0 -u_0 0.125 -alpha 0.3927 \
      -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
      -dmsnes_check -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type lu \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
  test:
    suffix: 2d_tri_p2_p1_conv_gmg_vcycle
    requires: triangle !single
    args: -dm_plex_separate_marker -cells 2,2 -dm_refine_hierarchy 1 \
      -vel_petscspace_degree 2 -pres_petscspace_degree 1 \
      -dmsnes_check -snes_error_if_not_converged \
      -ksp_type fgmres -ksp_gmres_restart 10 -ksp_rtol 1.0e-9 -ksp_error_if_not_converged \
      -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_factorization_type full \
        -fieldsplit_velocity_pc_type mg \
        -fieldsplit_pressure_ksp_rtol 1e-10 -fieldsplit_pressure_pc_type jacobi
TEST*/

petsc_gen_xdmf.py

#!/usr/bin/env python
import h5py
import numpy as np
import os, sys


class Xdmf:
  def __init__(self, filename):
    self.filename = filename
    self.cellMap  = {1 : {1 : 'Polyvertex', 2 : 'Polyline'}, 2 : {3 : 'Triangle', 4 : 'Quadrilateral'}, 3 : {4 : 'Tetrahedron', 6: 'Wedge', 8 : 'Hexahedron'}}
    self.typeMap  = {b'scalar' : 'Scalar', b'vector' : 'Vector', b'tensor' :
            'Tensor6', b'matrix' : 'Matrix'}
    self.typeExt  = {2 : {b'vector' : ['x', 'y'], b'tensor' : ['xx', 'yy',
        'xy']}, 3 : {b'vector' : ['x', 'y', 'z'], b'tensor' : ['xx', 'yy', 'zz', 'xy', 'yz', 'xz']}}
    return

  def writeHeader(self, fp, hdfFilename):
    fp.write('''\
<?xml version="1.0" ?>
<!DOCTYPE Xdmf SYSTEM "Xdmf.dtd" [
<!ENTITY HeavyData "%s">
]>
''' % os.path.basename(hdfFilename))
    fp.write('\n<Xdmf>\n  <Domain Name="domain">\n')
    return

  def writeCells(self, fp, topologyPath, numCells, numCorners):
    fp.write('''\
    <DataItem Name="cells"
              ItemType="Uniform"
              Format="HDF"
              NumberType="Float" Precision="8"
              Dimensions="%d %d">
      &HeavyData;:/%s/cells
    </DataItem>
''' % (numCells, numCorners, topologyPath))
    return

  def writeVertices(self, fp, geometryPath, numVertices, spaceDim):
    fp.write('''\
    <DataItem Name="vertices"
              Format="HDF"
              Dimensions="%d %d">
      &HeavyData;:/%s/vertices
    </DataItem>
    <!-- ============================================================ -->
''' % (numVertices, spaceDim, geometryPath))
    return

  def writeLocations(self, fp, numParticles, spaceDim):
    fp.write('''\
    <DataItem Name="xcoord"
              Format="HDF"
              Dimensions="%d">
      &HeavyData;:/particles/xcoord
    </DataItem>
''' % (numParticles))
    if spaceDim == 1: return
    fp.write('''\
    <DataItem Name="ycoord"
              Format="HDF"
              Dimensions="%d">
      &HeavyData;:/particles/ycoord
    </DataItem>
''' % (numParticles))
    if spaceDim == 2: return
    fp.write('''\
    <DataItem Name="zcoord"
              Format="HDF"
              Dimensions="%d">
      &HeavyData;:/particles/zcoord
    </DataItem>
''' % (numParticles))
    return

  def writeTimeGridHeader(self, fp, time):
    fp.write('''\
    <Grid Name="TimeSeries" GridType="Collection" CollectionType="Temporal">
      <Time TimeType="List">
        <DataItem Format="XML" NumberType="Float" Dimensions="%d">
          ''' % (len(time)))
    fp.write(' '.join([str(float(t)) for t in time]))
    fp.write('''
        </DataItem>
      </Time>
''')
    return

  def writeSpaceGridHeader(self, fp, numCells, numCorners, cellDim, spaceDim):
    fp.write('''\
      <Grid Name="domain" GridType="Uniform">
        <Topology
           TopologyType="%s"
           NumberOfElements="%d">
          <DataItem Reference="XML">
            /Xdmf/Domain/DataItem[@Name="cells"]
          </DataItem>
        </Topology>
        <Geometry GeometryType="%s">
          <DataItem Reference="XML">
            /Xdmf/Domain/DataItem[@Name="vertices"]
          </DataItem>
        </Geometry>
''' % (self.cellMap[cellDim][numCorners], numCells, "XYZ" if spaceDim > 2 else "XY"))
    return

  def writeFieldSingle(self, fp, numSteps, timestep, spaceDim, name, f, domain):
    if len(f[1].shape) > 2:
      dof = f[1].shape[1]
      bs  = f[1].shape[2]
    elif len(f[1].shape) > 1:
      if numSteps > 1:
        dof = f[1].shape[1]
        bs  = 1
      else:
        dof = f[1].shape[0]
        bs  = f[1].shape[1]
    else:
      dof = f[1].shape[0]
      bs  = 1
    fp.write('''\
        <Attribute
           Name="%s"
           Type="%s"
           Center="%s">
          <DataItem ItemType="HyperSlab"
        	    Dimensions="1 %d %d"
        	    Type="HyperSlab">
            <DataItem
               Dimensions="3 3"
               Format="XML">
              %d 0 0
              1 1 1
              1 %d %d
            </DataItem>
            <DataItem
               DataType="Float" Precision="8"
               Dimensions="%d %d %d"
               Format="HDF">
              &HeavyData;:%s
            </DataItem>
          </DataItem>
        </Attribute>
''' % (f[0], self.typeMap[f[1].attrs['vector_field_type']], domain, dof, bs, timestep, dof, bs, numSteps, dof, bs, name))
    return

  def writeFieldComponents(self, fp, numSteps, timestep, spaceDim, name, f, domain):
    vtype = f[1].attrs['vector_field_type']
    if len(f[1].shape) > 2:
      dof    = f[1].shape[1]
      bs     = f[1].shape[2]
      cdims  = '1 %d 1' % dof
      dims   = '%d %d %d' % (numSteps, dof, bs)
      stride = '1 1 1'
      size   = '1 %d 1' % dof
    else:
      dof    = f[1].shape[0]
      bs     = f[1].shape[1]
      cdims  = '%d 1' % dof
      dims   = '%d %d' % (dof, bs)
      stride = '1 1'
      size   = '%d 1' % dof
    for c in range(bs):
      ext = self.typeExt[spaceDim][vtype][c]
      if len(f[1].shape) > 2: start  = '%d 0 %d' % (timestep, c)
      else:                   start  = '0 %d' % c
      fp.write('''\
        <Attribute
           Name="%s"
           Type="Scalar"
           Center="%s">
          <DataItem ItemType="HyperSlab"
        	    Dimensions="%s"
        	    Type="HyperSlab">
            <DataItem
               Dimensions="3 %d"
               Format="XML">
              %s
              %s
              %s
            </DataItem>
            <DataItem
               DataType="Float" Precision="8"
               Dimensions="%s"
               Format="HDF">
              &HeavyData;:%s
            </DataItem>
          </DataItem>
        </Attribute>
''' % (f[0]+'_'+ext, domain, cdims, len(f[1].shape), start, stride, size, dims, name))
    return

  def writeField(self, fp, numSteps, timestep, cellDim, spaceDim, name, f, domain):
    ctypes = [b'tensor', b'matrix']
    if spaceDim == 2 or cellDim != spaceDim: ctypes.append(b'vector')
    if f[1].attrs['vector_field_type'] in ctypes:
      self.writeFieldComponents(fp, numSteps, timestep, spaceDim, name, f, domain)
    else:
      self.writeFieldSingle(fp, numSteps, timestep, spaceDim, name, f, domain)
    return

  def writeSpaceGridFooter(self, fp):
    fp.write('      </Grid>\n')
    return

  def writeParticleGridHeader(self, fp, numParticles, spaceDim):
    fp.write('''\
      <Grid Name="particle_domain" GridType="Uniform">
        <Topology TopologyType="Polyvertex" NodesPerElement="%d" />
        <Geometry GeometryType="%s">
          <DataItem Reference="XML">/Xdmf/Domain/DataItem[@Name="xcoord"]</DataItem>
          <DataItem Reference="XML">/Xdmf/Domain/DataItem[@Name="ycoord"]</DataItem>
          %s
        </Geometry>
''' % (numParticles, "X_Y_Z" if spaceDim > 2 else "X_Y", "<DataItem Reference=\"XML\">/Xdmf/Domain/DataItem[@Name=\"zcoord\"]</DataItem>" if spaceDim > 2 else ""))
    return

  def writeParticleField(self, fp, numParticles, spaceDim):
    fp.write('''\
    <Attribute Name="particles/icoord">
      <DataItem Name="icoord"
                Format="HDF"
                Dimensions="%d">
                &HeavyData;:/particles/icoord
      </DataItem>
    </Attribute>''' % (numParticles))
    return

  def writeTimeGridFooter(self, fp):
    fp.write('    </Grid>\n')
    return

  def writeFooter(self, fp):
    fp.write('  </Domain>\n</Xdmf>\n')
    return

  def write(self, hdfFilename, topologyPath, numCells, numCorners, cellDim, geometryPath, numVertices, spaceDim, time, vfields, cfields, numParticles):
    useTime = not (len(time) < 2 and time[0] == -1)
    with open(self.filename, 'w') as fp:
      self.writeHeader(fp, hdfFilename)
      # Field information
      self.writeCells(fp, topologyPath, numCells, numCorners)
      self.writeVertices(fp, geometryPath, numVertices, spaceDim)
      if useTime: self.writeTimeGridHeader(fp, time)
      for t in range(len(time)):
        self.writeSpaceGridHeader(fp, numCells, numCorners, cellDim, spaceDim)
        for vf in vfields: self.writeField(fp, len(time), t, cellDim, spaceDim, '/vertex_fields/'+vf[0], vf, 'Node')
        for cf in cfields: self.writeField(fp, len(time), t, cellDim, spaceDim, '/cell_fields/'+cf[0], cf, 'Cell')
        self.writeSpaceGridFooter(fp)
      if useTime: self.writeTimeGridFooter(fp)
      if numParticles:
        self.writeLocations(fp, numParticles, spaceDim)
        if useTime: self.writeTimeGridHeader(fp, time)
        for t in range(len(time)):
          self.writeParticleGridHeader(fp, numParticles, spaceDim)
          self.writeSpaceGridFooter(fp)
        if useTime: self.writeTimeGridFooter(fp)
      self.writeFooter(fp)
    return

def generateXdmf(hdfFilename, xdmfFilename = None):
  if xdmfFilename is None:
    xdmfFilename = os.path.splitext(hdfFilename)[0] + '.xmf'
  # Read mesh
  h5          = h5py.File(hdfFilename, 'r')
  if 'viz' in h5 and 'geometry' in h5['viz']:
    geomPath  = 'viz/geometry'
    geom      = h5['viz']['geometry']
  else:
    geomPath  = 'geometry'
    geom      = h5['geometry']
  if 'viz' in h5 and 'topology' in h5['viz']:
    topoPath  = 'viz/topology'
    topo      = h5['viz']['topology']
  else:
    topoPath  = 'topology'
    topo      = h5['topology']
  vertices    = geom['vertices']
  numVertices = vertices.shape[0]
  spaceDim    = vertices.shape[1]
  cells       = topo['cells']
  numCells    = cells.shape[0]
  numCorners  = cells.shape[1]
  cellDim     = topo['cells'].attrs['cell_dim']
  if 'time' in h5:
    time      = np.array(h5['time']).flatten()
  else:
    time      = [-1]
  vfields     = []
  cfields     = []
  if 'vertex_fields' in h5: vfields = h5['vertex_fields'].items()
  if 'cell_fields' in h5: cfields = h5['cell_fields'].items()
  numParticles = 0
  if 'particles' in h5: numParticles = h5['particles']['xcoord'].shape[0]
  '''
  if 'vertex_fields' in h5: vfields = list(h5['vertex_fields'].items())
  if 'cell_fields' in h5: cfields = list(h5['cell_fields'].items())
  numParticles = 0
  if 'particles' in h5: numParticles = list(h5['particles']['xcoord'].shape[0])
  '''

  # Write Xdmf
  Xdmf(xdmfFilename).write(hdfFilename, topoPath, numCells, numCorners, cellDim, geomPath, numVertices, spaceDim, time, vfields, cfields, numParticles)
  h5.close()
  return

if __name__ == '__main__':
  for f in sys.argv[1:]:
    generateXdmf(f)