xref: /petsc/src/dm/impls/plex/tests/ex26f90.F90 (revision 749c190bad46ba447444c173d8c7a4080c70750e)

#include "petsc/finclude/petscdmplex.h"
program ex62f90
  use petscdmplex
  implicit none
#include "exodusII.inc"

  ! Get the Fortran kind associated with PetscInt and PetscReal so that we can use literal constants.
  PetscInt                           :: dummyPetscInt
  PetscReal                          :: dummyPetscreal
  integer, parameter                  :: kPI = kind(dummyPetscInt)
  integer, parameter                  :: kPR = kind(dummyPetscReal)

  type(tDM)                          :: dm, dmU, dmA, dmS, dmUA, dmUA2, pDM
  type(tDM), dimension(:), pointer     :: dmList
  type(tVec)                         :: X, U, A, S, UA, UA2
  type(tIS)                          :: isU, isA, isS, isUA
  type(tPetscSection)                :: section
  PetscInt                           :: fieldU = 0
  PetscInt                           :: fieldA = 2
  PetscInt                           :: fieldS = 1
  PetscInt, dimension(2)              :: fieldUA = [0, 2]
  character(len=PETSC_MAX_PATH_LEN)  :: ifilename, ofilename, IOBuffer
  integer                            :: exoid = -1
  type(tIS)                          :: csIS
  PetscInt, dimension(:), pointer      :: csID
  PetscInt, dimension(:), pointer      :: pStartDepth, pEndDepth
  PetscInt                           :: order = 1
  integer                            :: i
  PetscInt                           :: sdim, d, pStart, pEnd, p, numCS, set, j
  PetscMPIInt                        :: rank, numProc
  PetscBool                          :: flg
  PetscErrorCode                     :: ierr
  MPIU_Comm                          :: comm
  type(tPetscViewer)                 :: viewer

  character(len=MXSTLN)              :: sJunk
  PetscInt                           :: numstep = 3, step
  integer                            :: numNodalVar, numZonalVar
  character(len=MXNAME), dimension(4) :: nodalVarName2D = ["U_x  ", &
                                                           "U_y  ", &
                                                           "Alpha", &
                                                           "Beta "]
  character(len=MXNAME), dimension(3) :: zonalVarName2D = ["Sigma_11", &
                                                           "Sigma_12", &
                                                           "Sigma_22"]
  character(len=MXNAME), dimension(5) :: nodalVarName3D = ["U_x  ", &
                                                           "U_y  ", &
                                                           "U_z  ", &
                                                           "Alpha", &
                                                           "Beta "]
  character(len=MXNAME), dimension(6) :: zonalVarName3D = ["Sigma_11", &
                                                           "Sigma_22", &
                                                           "Sigma_33", &
                                                           "Sigma_23", &
                                                           "Sigma_13", &
                                                           "Sigma_12"]
  logical, dimension(:, :), pointer     :: truthtable

  type(tIS)                          :: cellIS
  PetscInt, dimension(:), pointer      :: cellID
  PetscInt                           :: numCells, cell, closureSize
  PetscInt, dimension(:), pointer      :: closureA, closure

  type(tPetscSection)                :: sectionUA, coordSection
  type(tVec)                         :: UALoc, coord
  PetscScalar, dimension(:), pointer   :: cval, xyz
  PetscInt                           :: dofUA, offUA, c

  ! dof layout ordered by increasing height in the DAG: cell, face, edge, vertex
  PetscInt, dimension(3), target        :: dofS2D = [0, 0, 3]
  PetscInt, dimension(3), target        :: dofUP1Tri = [2, 0, 0]
  PetscInt, dimension(3), target        :: dofAP1Tri = [1, 0, 0]
  PetscInt, dimension(3), target        :: dofUP2Tri = [2, 2, 0]
  PetscInt, dimension(3), target        :: dofAP2Tri = [1, 1, 0]
  PetscInt, dimension(3), target        :: dofUP1Quad = [2, 0, 0]
  PetscInt, dimension(3), target        :: dofAP1Quad = [1, 0, 0]
  PetscInt, dimension(3), target        :: dofUP2Quad = [2, 2, 2]
  PetscInt, dimension(3), target        :: dofAP2Quad = [1, 1, 1]
  PetscInt, dimension(4), target        :: dofS3D = [0, 0, 0, 6]
  PetscInt, dimension(4), target        :: dofUP1Tet = [3, 0, 0, 0]
  PetscInt, dimension(4), target        :: dofAP1Tet = [1, 0, 0, 0]
  PetscInt, dimension(4), target        :: dofUP2Tet = [3, 3, 0, 0]
  PetscInt, dimension(4), target        :: dofAP2Tet = [1, 1, 0, 0]
  PetscInt, dimension(4), target        :: dofUP1Hex = [3, 0, 0, 0]
  PetscInt, dimension(4), target        :: dofAP1Hex = [1, 0, 0, 0]
  PetscInt, dimension(4), target        :: dofUP2Hex = [3, 3, 3, 3]
  PetscInt, dimension(4), target        :: dofAP2Hex = [1, 1, 1, 1]
  PetscInt, dimension(:), pointer       :: dofU, dofA, dofS

  type(tPetscSF)                      :: migrationSF
  PetscPartitioner                    :: part
  PetscLayout                         :: layout

  type(tVec)                          :: tmpVec
  PetscReal                           :: norm
  PetscReal                           :: time = 1.234_kPR

  PetscCallA(PetscInitialize(PETSC_NULL_CHARACTER, ierr))
  if (ierr /= 0) then
    print *, 'Unable to initialize PETSc'
    stop
  end if

  PetscCallMPIA(MPI_Comm_rank(PETSC_COMM_WORLD, rank, ierr))
  PetscCallMPIA(MPI_Comm_size(PETSC_COMM_WORLD, numProc, ierr))
  PetscCallA(PetscOptionsGetString(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-i', ifilename, flg, ierr))
  PetscCheckA(flg, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, 'missing input file name -i <input file name>')
  PetscCallA(PetscOptionsGetString(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-o', ofilename, flg, ierr))
  PetscCheckA(flg, PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, 'missing output file name -o <output file name>')
  PetscCallA(PetscOptionsGetInt(PETSC_NULL_OPTIONS, PETSC_NULL_CHARACTER, '-order', order, flg, ierr))
  if ((order > 2) .or. (order < 1)) then
    write (IOBuffer, '("Unsupported polynomial order ", I2, " not in [1,2]")') order
    SETERRA(PETSC_COMM_WORLD, PETSC_ERR_ARG_OUTOFRANGE, IOBuffer)
  end if

  ! Read the mesh in any supported format
  PetscCallA(DMPlexCreateFromFile(PETSC_COMM_WORLD, ifilename, PETSC_NULL_CHARACTER, PETSC_TRUE, dm, ierr))
  PetscCallA(DMPlexDistributeSetDefault(dm, PETSC_FALSE, ierr))
  PetscCallA(DMSetFromOptions(dm, ierr))
  PetscCallA(DMGetDimension(dm, sdim, ierr))
  PetscCallA(DMViewFromOptions(dm, PETSC_NULL_OBJECT, '-dm_view', ierr))

  ! Create the exodus result file

  ! enable exodus debugging information
  PetscCallA(exopts(EXVRBS + EXDEBG, ierr))
  ! Create the exodus file
  PetscCallA(PetscViewerExodusIIOpen(PETSC_COMM_WORLD, ofilename, FILE_MODE_WRITE, viewer, ierr))
  ! The long way would be
  !
  ! PetscCallA(PetscViewerCreate(PETSC_COMM_WORLD,viewer,ierr))
  ! PetscCallA(PetscViewerSetType(viewer,PETSCVIEWEREXODUSII,ierr))
  ! PetscCallA(PetscViewerFileSetMode(viewer,FILE_MODE_WRITE,ierr))
  ! PetscCallA(PetscViewerFileSetName(viewer,ofilename,ierr))

  ! set the mesh order
  PetscCallA(PetscViewerExodusIISetOrder(viewer, order, ierr))
  PetscCallA(PetscViewerView(viewer, PETSC_VIEWER_STDOUT_WORLD, ierr))
  !
  !    Notice how the exodus file is actually NOT open at this point (exoid is -1)
  !    Since we are overwriting the file (mode is FILE_MODE_WRITE), we are going to have to
  !    write the geometry (the DM), which can only be done on a brand new file.
  !

  ! Save the geometry to the file, erasing all previous content
  PetscCallA(DMView(dm, viewer, ierr))
  PetscCallA(PetscViewerView(viewer, PETSC_VIEWER_STDOUT_WORLD, ierr))
  !
  !    Note how the exodus file is now open
  !
  ! 'Format' the exodus result file, i.e. allocate space for nodal and zonal variables
  select case (sdim)
  case (2)
    numNodalVar = 4
    numZonalVar = 3
    PetscCallA(PetscViewerExodusIISetZonalVariable(viewer, numZonalVar, ierr))
    PetscCallA(PetscViewerExodusIISetNodalVariable(viewer, numNodalVar, ierr))
    do i = 1, numZonalVar
      PetscCallA(PetscViewerExodusIISetZonalVariableName(viewer, i - 1, zonalVarName2D(i), ierr))
    end do
    do i = 1, numNodalVar
      PetscCallA(PetscViewerExodusIISetNodalVariableName(viewer, i - 1, nodalVarName2D(i), ierr))
    end do
  case (3)
    numNodalVar = 5
    numZonalVar = 6
    PetscCallA(PetscViewerExodusIISetZonalVariable(viewer, numZonalVar, ierr))
    PetscCallA(PetscViewerExodusIISetNodalVariable(viewer, numNodalVar, ierr))
    do i = 1, numZonalVar
      PetscCallA(PetscViewerExodusIISetZonalVariableName(viewer, i - 1, zonalVarName3D(i), ierr))
    end do
    do i = 1, numNodalVar
      PetscCallA(PetscViewerExodusIISetNodalVariableName(viewer, i - 1, nodalVarName3D(i), ierr))
    end do
  case default
    write (IOBuffer, '("No layout for dimension ",I2)') sdim
  end select
  PetscCallA(PetscViewerView(viewer, PETSC_VIEWER_STDOUT_WORLD, ierr))

  !    An ExodusII truth table specifies which fields are saved at which time step
  !    It speeds up I/O but reserving space for fields in the file ahead of time.
  PetscCallA(PetscViewerExodusIIGetId(viewer, exoid, ierr))
  PetscCallA(exinq(exoid, EX_INQ_ELEM_BLK, numCS, PETSC_NULL_REAL, sjunk, ierr))
  allocate (truthtable(numCS, numZonalVar))
  truthtable = .true.
  PetscCallA(expvtt(exoid, numCS, numZonalVar, truthtable, ierr))
  deallocate (truthtable)

  !   Writing time step information in the file. Note that this is currently broken in the exodus library for netcdf4 (HDF5-based) files */
  do step = 1, numstep
    PetscCallA(exptim(exoid, step, real(step, kind=kPR), ierr))
  end do

  PetscCallA(PetscObjectGetComm(dm, comm, ierr))
  PetscCallA(PetscSectionCreate(comm, section, ierr))
  PetscCallA(PetscSectionSetNumFields(section, 3_kPI, ierr))
  PetscCallA(PetscSectionSetFieldName(section, fieldU, 'U', ierr))
  PetscCallA(PetscSectionSetFieldName(section, fieldA, 'Alpha', ierr))
  PetscCallA(PetscSectionSetFieldName(section, fieldS, 'Sigma', ierr))
  PetscCallA(DMPlexGetChart(dm, pStart, pEnd, ierr))
  PetscCallA(PetscSectionSetChart(section, pStart, pEnd, ierr))

  allocate (pStartDepth(sdim + 1))
  allocate (pEndDepth(sdim + 1))
  do d = 1, sdim + 1
    PetscCallA(DMPlexGetDepthStratum(dm, d - 1, pStartDepth(d), pEndDepth(d), ierr))
  end do

  ! Vector field U, Scalar field Alpha, Tensor field Sigma
  PetscCallA(PetscSectionSetFieldComponents(section, fieldU, sdim, ierr))
  PetscCallA(PetscSectionSetFieldComponents(section, fieldA, 1_kPI, ierr))
  PetscCallA(PetscSectionSetFieldComponents(section, fieldS, sdim*(sdim + 1)/2, ierr))

  ! Going through cell sets then cells, and setting up storage for the sections
  PetscCallA(DMGetLabelSize(dm, 'Cell Sets', numCS, ierr))
  PetscCallA(DMGetLabelIdIS(dm, 'Cell Sets', csIS, ierr))
  PetscCallA(ISGetIndices(csIS, csID, ierr))
  do set = 1, numCS
        !!! This is pointless but will avoid a warning with gfortran and -Werror=maybe-uninitialized
    nullify (dofA)
    nullify (dofU)
    nullify (dofS)
    PetscCallA(DMGetStratumSize(dm, 'Cell Sets', csID(set), numCells, ierr))
    PetscCallA(DMGetStratumIS(dm, 'Cell Sets', csID(set), cellIS, ierr))
    if (numCells > 0) then
      select case (sdim)
      case (2)
        dofs => dofS2D
      case (3)
        dofs => dofS3D
      case default
        write (IOBuffer, '("No layout for dimension ",I2)') sdim
        SETERRA(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, IOBuffer)
      end select ! sdim

      ! Identify cell type based on closure size only. This works for Tri/Tet/Quad/Hex meshes
      ! It will not be enough to identify more exotic elements like pyramid or prisms...  */
      PetscCallA(ISGetIndices(cellIS, cellID, ierr))
      nullify (closureA)
      PetscCallA(DMPlexGetTransitiveClosure(dm, cellID(1), PETSC_TRUE, PETSC_NULL_INTEGER, closureA, ierr))
      select case (size(closureA)/2)
      case (7) ! Tri
        if (order == 1) then
          dofU => dofUP1Tri
          dofA => dofAP1Tri
        else
          dofU => dofUP2Tri
          dofA => dofAP2Tri
        end if
      case (9) ! Quad
        if (order == 1) then
          dofU => dofUP1Quad
          dofA => dofAP1Quad
        else
          dofU => dofUP2Quad
          dofA => dofAP2Quad
        end if
      case (15) ! Tet
        if (order == 1) then
          dofU => dofUP1Tet
          dofA => dofAP1Tet
        else
          dofU => dofUP2Tet
          dofA => dofAP2Tet
        end if
      case (27) ! Hex
        if (order == 1) then
          dofU => dofUP1Hex
          dofA => dofAP1Hex
        else
          dofU => dofUP2Hex
          dofA => dofAP2Hex
        end if
      case default
        write (IOBuffer, '("Unknown element with closure size ",I2)') size(closureA)/2
        SETERRA(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, IOBuffer)
      end select
      PetscCallA(DMPlexRestoreTransitiveClosure(dm, cellID(1), PETSC_TRUE, PETSC_NULL_INTEGER, closureA, ierr))
      do cell = 1, numCells!
        nullify (closure)
        PetscCallA(DMPlexGetTransitiveClosure(dm, cellID(cell), PETSC_TRUE, PETSC_NULL_INTEGER, closure, ierr))
        do p = 1, size(closure), 2
          ! find the depth of p
          do d = 1, sdim + 1
            if ((closure(p) >= pStartDepth(d)) .and. (closure(p) < pEndDepth(d))) then
              PetscCallA(PetscSectionSetDof(section, closure(p), dofU(d) + dofA(d) + dofS(d), ierr))
              PetscCallA(PetscSectionSetFieldDof(section, closure(p), fieldU, dofU(d), ierr))
              PetscCallA(PetscSectionSetFieldDof(section, closure(p), fieldA, dofA(d), ierr))
              PetscCallA(PetscSectionSetFieldDof(section, closure(p), fieldS, dofS(d), ierr))
            end if ! closure(p)
          end do ! d
        end do ! p
        PetscCallA(DMPlexRestoreTransitiveClosure(dm, cellID(cell), PETSC_TRUE, PETSC_NULL_INTEGER, closure, ierr))
      end do ! cell
      PetscCallA(ISRestoreIndices(cellIS, cellID, ierr))
      PetscCallA(ISDestroy(cellIS, ierr))
    end if ! numCells
  end do ! set
  PetscCallA(ISRestoreIndices(csIS, csID, ierr))
  PetscCallA(ISDestroy(csIS, ierr))
  PetscCallA(PetscSectionSetUp(section, ierr))
  PetscCallA(DMSetLocalSection(dm, section, ierr))
  PetscCallA(PetscObjectViewFromOptions(section, PETSC_NULL_OBJECT, '-dm_section_view', ierr))
  PetscCallA(PetscSectionGetValueLayout(PETSC_COMM_WORLD, section, layout, ierr))
  PetscCallA(PetscLayoutDestroy(layout, ierr))
  PetscCallA(PetscSectionDestroy(section, ierr))

  PetscCallA(DMSetUseNatural(dm, PETSC_TRUE, ierr))
  PetscCallA(DMPlexGetPartitioner(dm, part, ierr))
  PetscCallA(PetscPartitionerSetFromOptions(part, ierr))
  PetscCallA(DMPlexDistribute(dm, 0_kPI, migrationSF, pdm, ierr))

  if (numProc > 1) then
    PetscCallA(DMPlexSetMigrationSF(pdm, migrationSF, ierr))
    PetscCallA(PetscSFDestroy(migrationSF, ierr))
  else
    pdm = dm
  end if
  PetscCallA(DMViewFromOptions(pdm, PETSC_NULL_OBJECT, '-dm_view', ierr))

  ! Get DM and IS for each field of dm
  PetscCallA(DMCreateSubDM(pdm, 1_kPI, [fieldU], isU, dmU, ierr))
  PetscCallA(DMCreateSubDM(pdm, 1_kPI, [fieldA], isA, dmA, ierr))
  PetscCallA(DMCreateSubDM(pdm, 1_kPI, [fieldS], isS, dmS, ierr))
  PetscCallA(DMCreateSubDM(pdm, 2_kPI, fieldUA, isUA, dmUA, ierr))

  !Create the exodus result file
  allocate (dmList(2))
  dmList(1) = dmU
  dmList(2) = dmA
  PetscCallA(DMCreateSuperDM(dmList, 2_kPI, PETSC_NULL_IS_POINTER, dmUA2, ierr))
  deallocate (dmList)

  PetscCallA(DMGetGlobalVector(pdm, X, ierr))
  PetscCallA(DMGetGlobalVector(dmU, U, ierr))
  PetscCallA(DMGetGlobalVector(dmA, A, ierr))
  PetscCallA(DMGetGlobalVector(dmS, S, ierr))
  PetscCallA(DMGetGlobalVector(dmUA, UA, ierr))
  PetscCallA(DMGetGlobalVector(dmUA2, UA2, ierr))

  PetscCallA(PetscObjectSetName(U, 'U', ierr))
  PetscCallA(PetscObjectSetName(A, 'Alpha', ierr))
  PetscCallA(PetscObjectSetName(S, 'Sigma', ierr))
  PetscCallA(PetscObjectSetName(UA, 'UAlpha', ierr))
  PetscCallA(PetscObjectSetName(UA2, 'UAlpha2', ierr))
  PetscCallA(VecSet(X, -111.0_kPR, ierr))

  ! Setting u to [x,y,z]  and alpha to x^2+y^2+z^2 by writing in UAlpha then restricting to U and Alpha */
  PetscCallA(DMGetLocalSection(dmUA, sectionUA, ierr))
  PetscCallA(DMGetLocalVector(dmUA, UALoc, ierr))
  PetscCallA(VecGetArray(UALoc, cval, ierr))
  PetscCallA(DMGetCoordinateSection(dmUA, coordSection, ierr))
  PetscCallA(DMGetCoordinatesLocal(dmUA, coord, ierr))
  PetscCallA(DMPlexGetChart(dmUA, pStart, pEnd, ierr))

  do p = pStart, pEnd - 1
    PetscCallA(PetscSectionGetDof(sectionUA, p, dofUA, ierr))
    if (dofUA > 0) then
      PetscCallA(PetscSectionGetOffset(sectionUA, p, offUA, ierr))
      PetscCallA(DMPlexVecGetClosure(dmUA, coordSection, coord, p, PETSC_NULL_INTEGER, xyz, ierr))
      closureSize = size(xyz)
      do i = 1, sdim
        do j = 0, closureSize - 1, sdim
          cval(offUA + i) = cval(offUA + i) + xyz(j/sdim + i)
        end do
        cval(offUA + i) = cval(offUA + i)*sdim/closureSize
        cval(offUA + sdim + 1) = cval(offUA + sdim + 1) + cval(offUA + i)**2
      end do
      PetscCallA(DMPlexVecRestoreClosure(dmUA, coordSection, coord, p, PETSC_NULL_INTEGER, xyz, ierr))
    end if
  end do

  PetscCallA(VecRestoreArray(UALoc, cval, ierr))
  PetscCallA(DMLocalToGlobalBegin(dmUA, UALoc, INSERT_VALUES, UA, ierr))
  PetscCallA(DMLocalToGlobalEnd(dmUA, UALoc, INSERT_VALUES, UA, ierr))
  PetscCallA(DMRestoreLocalVector(dmUA, UALoc, ierr))

  !Update X
  PetscCallA(VecISCopy(X, isUA, SCATTER_FORWARD, UA, ierr))
  ! Restrict to U and Alpha
  PetscCallA(VecISCopy(X, isU, SCATTER_REVERSE, U, ierr))
  PetscCallA(VecISCopy(X, isA, SCATTER_REVERSE, A, ierr))
  PetscCallA(VecViewFromOptions(UA, PETSC_NULL_OBJECT, '-ua_vec_view', ierr))
  PetscCallA(VecViewFromOptions(U, PETSC_NULL_OBJECT, '-u_vec_view', ierr))
  PetscCallA(VecViewFromOptions(A, PETSC_NULL_OBJECT, '-a_vec_view', ierr))
  ! restrict to UA2
  PetscCallA(VecISCopy(X, isUA, SCATTER_REVERSE, UA2, ierr))
  PetscCallA(VecViewFromOptions(UA2, PETSC_NULL_OBJECT, '-ua2_vec_view', ierr))

  ! Getting Natural Vec
  PetscCallA(DMSetOutputSequenceNumber(dmU, 0_kPI, time, ierr))
  PetscCallA(DMSetOutputSequenceNumber(dmA, 0_kPI, time, ierr))

  PetscCallA(VecView(U, viewer, ierr))
  PetscCallA(VecView(A, viewer, ierr))

  !Saving U and Alpha in one shot.
  !For this, we need to cheat and change the Vec's name
  !Note that in the end we write variables one component at a time,
  !so that there is no real value in doing this
  PetscCallA(DMSetOutputSequenceNumber(dmUA, 1_kPI, time, ierr))
  PetscCallA(DMGetGlobalVector(dmUA, tmpVec, ierr))
  PetscCallA(VecCopy(UA, tmpVec, ierr))
  PetscCallA(PetscObjectSetName(tmpVec, 'U', ierr))
  PetscCallA(VecView(tmpVec, viewer, ierr))

  ! Reading nodal variables in Exodus file
  PetscCallA(VecSet(tmpVec, -1000.0_kPR, ierr))
  PetscCallA(VecLoad(tmpVec, viewer, ierr))
  PetscCallA(VecAXPY(UA, -1.0_kPR, tmpVec, ierr))
  PetscCallA(VecNorm(UA, NORM_INFINITY, norm, ierr))
  if (norm > PETSC_SQRT_MACHINE_EPSILON) then
    write (IOBuffer, '("UAlpha ||Vin - Vout|| = ",ES12.5)') norm
  end if
  PetscCallA(DMRestoreGlobalVector(dmUA, tmpVec, ierr))

  ! same thing with the UA2 Vec obtained from the superDM
  PetscCallA(DMGetGlobalVector(dmUA2, tmpVec, ierr))
  PetscCallA(VecCopy(UA2, tmpVec, ierr))
  PetscCallA(PetscObjectSetName(tmpVec, 'U', ierr))
  PetscCallA(DMSetOutputSequenceNumber(dmUA2, 2_kPI, time, ierr))
  PetscCallA(VecView(tmpVec, viewer, ierr))

  ! Reading nodal variables in Exodus file
  PetscCallA(VecSet(tmpVec, -1000.0_kPR, ierr))
  PetscCallA(VecLoad(tmpVec, viewer, ierr))
  PetscCallA(VecAXPY(UA2, -1.0_kPR, tmpVec, ierr))
  PetscCallA(VecNorm(UA2, NORM_INFINITY, norm, ierr))
  if (norm > PETSC_SQRT_MACHINE_EPSILON) then
    write (IOBuffer, '("UAlpha2 ||Vin - Vout|| = ",ES12.5)') norm
  end if
  PetscCallA(DMRestoreGlobalVector(dmUA2, tmpVec, ierr))

  ! Building and saving Sigma
  !   We set sigma_0 = rank (to see partitioning)
  !          sigma_1 = cell set ID
  !          sigma_2 = x_coordinate of the cell center of mass
  PetscCallA(DMGetCoordinateSection(dmS, coordSection, ierr))
  PetscCallA(DMGetCoordinatesLocal(dmS, coord, ierr))
  PetscCallA(DMGetLabelIdIS(dmS, 'Cell Sets', csIS, ierr))
  PetscCallA(DMGetLabelSize(dmS, 'Cell Sets', numCS, ierr))
  PetscCallA(ISGetIndices(csIS, csID, ierr))

  do set = 1, numCS
    PetscCallA(DMGetStratumIS(dmS, 'Cell Sets', csID(set), cellIS, ierr))
    PetscCallA(ISGetIndices(cellIS, cellID, ierr))
    PetscCallA(ISGetSize(cellIS, numCells, ierr))
    do cell = 1, numCells
      PetscCallA(DMPlexVecGetClosure(dmS, PETSC_NULL_SECTION, S, cellID(cell), PETSC_NULL_INTEGER, cval, ierr))
      PetscCallA(DMPlexVecGetClosure(dmS, coordSection, coord, cellID(cell), PETSC_NULL_INTEGER, xyz, ierr))
      cval(1) = rank
      cval(2) = csID(set)
      cval(3) = 0.0_kPR
      do c = 1, size(xyz), sdim
        cval(3) = cval(3) + xyz(c)
      end do
      cval(3) = cval(3)*sdim/size(xyz)
      PetscCallA(DMPlexVecSetClosure(dmS, PETSC_NULL_SECTION, S, cellID(cell), cval, INSERT_ALL_VALUES, ierr))
      PetscCallA(DMPlexVecRestoreClosure(dmS, PETSC_NULL_SECTION, S, cellID(cell), PETSC_NULL_INTEGER, cval, ierr))
      PetscCallA(DMPlexVecRestoreClosure(dmS, coordSection, coord, cellID(cell), PETSC_NULL_INTEGER, xyz, ierr))
    end do
    PetscCallA(ISRestoreIndices(cellIS, cellID, ierr))
    PetscCallA(ISDestroy(cellIS, ierr))
  end do
  PetscCallA(ISRestoreIndices(csIS, csID, ierr))
  PetscCallA(ISDestroy(csIS, ierr))
  PetscCallA(VecViewFromOptions(S, PETSC_NULL_OBJECT, '-s_vec_view', ierr))

  ! Writing zonal variables in Exodus file
  PetscCallA(DMSetOutputSequenceNumber(dmS, 0_kPI, time, ierr))
  PetscCallA(VecView(S, viewer, ierr))

  ! Reading zonal variables in Exodus file */
  PetscCallA(DMGetGlobalVector(dmS, tmpVec, ierr))
  PetscCallA(VecSet(tmpVec, -1000.0_kPR, ierr))
  PetscCallA(PetscObjectSetName(tmpVec, 'Sigma', ierr))
  PetscCallA(VecLoad(tmpVec, viewer, ierr))
  PetscCallA(VecAXPY(S, -1.0_kPR, tmpVec, ierr))
  PetscCallA(VecNorm(S, NORM_INFINITY, norm, ierr))
  if (norm > PETSC_SQRT_MACHINE_EPSILON) then
    write (IOBuffer, '("Sigma ||Vin - Vout|| = ",ES12.5)') norm
  end if
  PetscCallA(DMRestoreGlobalVector(dmS, tmpVec, ierr))

  PetscCallA(DMRestoreGlobalVector(dmUA2, UA2, ierr))
  PetscCallA(DMRestoreGlobalVector(dmUA, UA, ierr))
  PetscCallA(DMRestoreGlobalVector(dmS, S, ierr))
  PetscCallA(DMRestoreGlobalVector(dmA, A, ierr))
  PetscCallA(DMRestoreGlobalVector(dmU, U, ierr))
  PetscCallA(DMRestoreGlobalVector(pdm, X, ierr))
  PetscCallA(DMDestroy(dmU, ierr))
  PetscCallA(ISDestroy(isU, ierr))
  PetscCallA(DMDestroy(dmA, ierr))
  PetscCallA(ISDestroy(isA, ierr))
  PetscCallA(DMDestroy(dmS, ierr))
  PetscCallA(ISDestroy(isS, ierr))
  PetscCallA(DMDestroy(dmUA, ierr))
  PetscCallA(ISDestroy(isUA, ierr))
  PetscCallA(DMDestroy(dmUA2, ierr))
  PetscCallA(DMDestroy(pdm, ierr))
  if (numProc > 1) then
    PetscCallA(DMDestroy(dm, ierr))
  end if

  deallocate (pStartDepth)
  deallocate (pEndDepth)

  PetscCallA(PetscViewerDestroy(viewer, ierr))
  PetscCallA(PetscFinalize(ierr))
end program ex62f90

! /*TEST
!
! build:
!   requires: exodusii pnetcdf !complex
!   # 2D seq
! test:
!   suffix: 0
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareT-large.exo -o FourSquareT-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints
! test:
!   suffix: 1
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareQ-large.exo -o FourSquareQ-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!
! test:
!   suffix: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareH-large.exo -o FourSquareH-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints
! test:
!   suffix: 3
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareT-large.exo -o FourSquareT-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
! test:
!   suffix: 4
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareQ-large.exo -o FourSquareQ-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
! test:
!   suffix: 5
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareH-large.exo -o FourSquareH-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
!   # 2D par
! test:
!   suffix: 6
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareT-large.exo -o FourSquareT-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints
! test:
!   suffix: 7
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareQ-large.exo -o FourSquareQ-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
! test:
!   suffix: 8
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareH-large.exo -o FourSquareH-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: invalid dimension ID or name
! test:
!   suffix: 9
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareT-large.exo -o FourSquareT-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
! test:
!   suffix: 10
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareQ-large.exo -o FourSquareQ-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
! test:
!   # Something is now broken with parallel read/write for whatever shape H is
!   TODO: broken
!   suffix: 11
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourSquareH-large.exo -o FourSquareH-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2

!   #3d seq
! test:
!   suffix: 12
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickHex-large.exo -o FourBrickHex-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
! test:
!   suffix: 13
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickTet-large.exo -o FourBrickTet-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints
! test:
!   suffix: 14
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickHex-large.exo -o FourBrickHex-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
! test:
!   suffix: 15
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickTet-large.exo -o FourBrickTet-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints
!   #3d par
! test:
!   suffix: 16
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickHex-large.exo -o FourBrickHex-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
! test:
!   suffix: 17
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickTet-large.exo -o FourBrickTet-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 1
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints
! test:
!   suffix: 18
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickHex-large.exo -o FourBrickHex-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
! test:
!   suffix: 19
!   nsize: 2
!   args: -i ${wPETSC_DIR}/share/petsc/datafiles/meshes/FourBrickTet-large.exo -o FourBrickTet-large_out.exo -dm_view -dm_section_view -petscpartitioner_type simple -order 2
!   #TODO: bug in PetscCallA(to NetCDF failed to complete invalid type definition in file id 65536 NetCDF: One or more variable sizes violate format constraints

! TEST*/