xref: /petsc/src/dm/impls/plex/tests/ex62f90.F90 (revision dcb3e68992f1c4897946af7e8406e2b4165e50f2)

program ex62f90
#include "petsc/finclude/petsc.h"
    use petsc
    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, rootSection, leafSection
    PetscInt,dimension(1)              :: fieldU = [0]
    PetscInt,dimension(1)              :: fieldA = [2]
    PetscInt,dimension(1)              :: 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
    PetscInt                           :: sdim,d,pStart,pEnd,p,numCS,set,i,j
    PetscMPIInt                        :: rank,numProc
    PetscBool                          :: flg
    PetscErrorCode                     :: ierr
    MPI_Comm                           :: comm
    type(tPetscViewer)                 :: viewer

    Character(len=MXSTLN)              :: sJunk
    PetscInt                           :: numstep = 3, step
    PetscInt                           :: numNodalVar,numZonalVar
    character(len=MXSTLN)              :: nodalVarName(4)
    character(len=MXSTLN)              :: zonalVarName(6)
    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, natSF, natPointSF, natPointSFInv
    PetscPartitioner                    :: part

    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
    endif

    PetscCallA(MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr))
    PetscCallA(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
        SETERRQ(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_OPTIONS,'-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 = 3
        nodalVarName(1:numNodalVar) = ['U_x  ','U_y  ','Alpha']
        numZonalVar = 3
        zonalVarName(1:numZonalVar) = ['Sigma_11','Sigma_22','Sigma_12']
    case(3)
        numNodalVar = 4
        nodalVarName(1:numNodalVar) = ['U_x  ','U_y  ','U_z  ','Alpha']
        numZonalVar = 6
        zonalVarName(1:numZonalVar) = ['Sigma_11','Sigma_22','Sigma_33','Sigma_23','Sigma_13','Sigma_12']
    case default
        write(IOBuffer,'("No layout for dimension ",I2)') sdim
    end select
    PetscCallA(PetscViewerExodusIIGetId(viewer,exoid,ierr))
    PetscCallA(expvp(exoid, 'E', numZonalVar,ierr))
    PetscCallA(expvan(exoid, 'E', numZonalVar, zonalVarName,ierr))
    PetscCallA(expvp(exoid, 'N', numNodalVar,ierr))
    PetscCallA(expvan(exoid, 'N', numNodalVar, nodalVarName,ierr))
    PetscCallA(exinq(exoid, EX_INQ_ELEM_BLK,numCS,PETSC_NULL_REAL,sjunk,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.
    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(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_OPTIONS,'-dm_view',ierr))

    PetscCallA(PetscObjectGetComm(pdm,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(pdm, pStart, pEnd,ierr))
    PetscCallA(PetscSectionSetChart(section, pStart, pEnd,ierr))

    allocate(pStartDepth(sdim+1))
    allocate(pEndDepth(sdim+1))
    do d = 1, sdim+1
        PetscCallA(DMPlexGetDepthStratum(pdm, 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(pdm, 'Cell Sets', numCS, ierr))
    PetscCallA(DMGetLabelIdIS(pdm, 'Cell Sets', csIS, ierr))
    PetscCallA(ISGetIndicesF90(csIS, csID, ierr))
    do set = 1,numCS
        PetscCallA(DMGetStratumSize(pdm, 'Cell Sets', csID(set), numCells,ierr))
        PetscCallA(DMGetStratumIS(pdm, '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
                SETERRQ(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(ISGetIndicesF90(cellIS, cellID,ierr))
            nullify(closureA)
            PetscCallA(DMPlexGetTransitiveClosure(pdm,cellID(1), PETSC_TRUE, 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
                SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP,IOBuffer)
            end select
            PetscCallA(DMPlexRestoreTransitiveClosure(pdm, cellID(1), PETSC_TRUE,closureA,ierr))
            do cell = 1,numCells!
                nullify(closure)
                PetscCallA(DMPlexGetTransitiveClosure(pdm, cellID(cell), PETSC_TRUE, 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(pdm, cellID(cell), PETSC_TRUE, closure,ierr))
            end do ! cell
            PetscCallA(ISRestoreIndicesF90(cellIS, cellID,ierr))
            PetscCallA(ISDestroy(cellIS,ierr))
        end if ! numCells
    end do ! set
    PetscCallA(ISRestoreIndicesF90(csIS, csID,ierr))
    PetscCallA(ISDestroy(csIS,ierr))
    PetscCallA(PetscSectionSetUp(section,ierr))
    PetscCallA(DMSetLocalSection(pdm, section,ierr))
    PetscCallA(PetscObjectViewFromOptions(section, PETSC_NULL_SECTION, '-dm_section_view',ierr))
    PetscCallA(PetscSectionDestroy(section,ierr))

    ! Creating section on the sequential DM + creating the GlobalToNatural SF
    if (numProc > 1) then
        PetscCallA(DMPlexGetMigrationSF(pdm, natPointSF, ierr))
        PetscCallA(DMGetLocalSection(pdm, rootSection, ierr))
        PetscCallA(PetscSFCreateInverseSF(natPointSF, natPointSFInv, ierr))
        PetscCallA(PetscSectionCreate(PETSC_COMM_WORLD, leafSection, ierr))
        PetscCallA(PetscSFDistributeSection(natPointSFInv, rootSection, PETSC_NULL_INTEGER, leafSection, ierr))
        PetscCallA(DMSetLocalSection(dm, leafSection, ierr))
        PetscCallA(DMPlexCreateGlobalToNaturalSF(pdm, leafSection, natPointSF, natSF, ierr))
        PetscCallA(PetscSFDestroy(natPointSFInv, ierr))
        PetscCallA(PetscSectionDestroy(leafSection,ierr))
        PetscCallA(DMSetNaturalSF(pdm, natSF, ierr))
        PetscCallA(PetscObjectDereference(natSF, ierr))
    end if

    ! 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,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(VecGetArrayF90(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, 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, xyz,ierr))
        end if
    end do

    PetscCallA(VecRestoreArrayF90(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_OPTIONS, '-ua_vec_view',ierr))
    PetscCallA(VecViewFromOptions(U, PETSC_NULL_OPTIONS, '-u_vec_view',ierr))
    PetscCallA(VecViewFromOptions(A, PETSC_NULL_OPTIONS, '-a_vec_view',ierr))
    ! restrict to UA2
    PetscCallA(VecISCopy(X, isUA, SCATTER_REVERSE, UA2,ierr))
    PetscCallA(VecViewFromOptions(UA2, PETSC_NULL_OPTIONS, '-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(ISGetIndicesF90(csIS, csID,ierr))

    do set = 1, numCS
        PetscCallA(DMGetStratumIS(dmS, 'Cell Sets', csID(set), cellIS,ierr))
        PetscCallA(ISGetIndicesF90(cellIS, cellID,ierr))
        PetscCallA(ISGetSize(cellIS, numCells,ierr))
        do cell = 1,numCells
            PetscCallA(DMPlexVecGetClosure(dmS, PETSC_NULL_SECTION, S, cellID(cell), cval,ierr))
            PetscCallA(DMPlexVecGetClosure(dmS, coordSection, coord, cellID(cell), 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), cval,ierr))
            PetscCallA(DMPlexVecRestoreClosure(dmS, coordSection, coord, cellID(cell), xyz,ierr))
        end do
        PetscCallA(ISRestoreIndicesF90(cellIS, cellID,ierr))
        PetscCallA(ISDestroy(cellIS,ierr))
    end do
    PetscCallA(ISRestoreIndicesF90(csIS, csID,ierr))
    PetscCallA(ISDestroy(csIS,ierr))
    PetscCallA(VecViewFromOptions(S, PETSC_NULL_OPTIONS, '-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 -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 -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 -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 -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 -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 -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 -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 -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 -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 -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 -petscpartitioner_type simple -order 2
! test:
!   # Something is now broken with parallel read/write for wahtever 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 -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 -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 -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 -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 -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 -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 -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 -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 -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*/