SELF_MappedScalar_3D_t.f90 Source File


This file depends on

sourcefile~~self_mappedscalar_3d_t.f90~~EfferentGraph sourcefile~self_mappedscalar_3d_t.f90 SELF_MappedScalar_3D_t.f90 sourcefile~self_constants.f90 SELF_Constants.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_constants.f90 sourcefile~self_scalar_3d.f90 SELF_Scalar_3D.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_scalar_3d.f90 sourcefile~self_lagrange.f90 SELF_Lagrange.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_lagrange.f90 sourcefile~self_tensor_3d.f90 SELF_Tensor_3D.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_tensor_3d.f90 sourcefile~self_mesh_3d.f90 SELF_Mesh_3D.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_mesh_3d.f90 sourcefile~self_geometry_3d.f90 SELF_Geometry_3D.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_geometry_3d.f90 sourcefile~self_domaindecomposition.f90 SELF_DomainDecomposition.f90 sourcefile~self_mappedscalar_3d_t.f90->sourcefile~self_domaindecomposition.f90 sourcefile~self_scalar_3d.f90->sourcefile~self_constants.f90 sourcefile~self_scalar_3d_t.f90 SELF_Scalar_3D_t.f90 sourcefile~self_scalar_3d.f90->sourcefile~self_scalar_3d_t.f90 sourcefile~self_lagrange.f90->sourcefile~self_constants.f90 sourcefile~self_lagrange_t.f90 SELF_Lagrange_t.f90 sourcefile~self_lagrange.f90->sourcefile~self_lagrange_t.f90 sourcefile~self_tensor_3d_t.f90 SELF_Tensor_3D_t.f90 sourcefile~self_tensor_3d.f90->sourcefile~self_tensor_3d_t.f90 sourcefile~self_mesh_3d_t.f90 SELF_Mesh_3D_t.f90 sourcefile~self_mesh_3d.f90->sourcefile~self_mesh_3d_t.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_constants.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_scalar_3d.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_lagrange.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_tensor_3d.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_mesh_3d.f90 sourcefile~self_vector_3d.f90 SELF_Vector_3D.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_vector_3d.f90 sourcefile~self_data.f90 SELF_Data.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_data.f90 sourcefile~self_supportroutines.f90 SELF_SupportRoutines.f90 sourcefile~self_geometry_3d.f90->sourcefile~self_supportroutines.f90 sourcefile~self_domaindecomposition_t.f90 SELF_DomainDecomposition_t.f90 sourcefile~self_domaindecomposition.f90->sourcefile~self_domaindecomposition_t.f90 sourcefile~self_scalar_3d_t.f90->sourcefile~self_constants.f90 sourcefile~self_scalar_3d_t.f90->sourcefile~self_lagrange.f90 sourcefile~self_scalar_3d_t.f90->sourcefile~self_data.f90 sourcefile~self_hdf5.f90 SELF_HDF5.f90 sourcefile~self_scalar_3d_t.f90->sourcefile~self_hdf5.f90 sourcefile~self_datapool.f90 SELF_DataPool.f90 sourcefile~self_scalar_3d_t.f90->sourcefile~self_datapool.f90 sourcefile~self_metadata.f90 SELF_Metadata.f90 sourcefile~self_scalar_3d_t.f90->sourcefile~self_metadata.f90 sourcefile~self_tensor_3d_t.f90->sourcefile~self_constants.f90 sourcefile~self_tensor_3d_t.f90->sourcefile~self_lagrange.f90 sourcefile~self_tensor_3d_t.f90->sourcefile~self_data.f90 sourcefile~self_tensor_3d_t.f90->sourcefile~self_hdf5.f90 sourcefile~self_tensor_3d_t.f90->sourcefile~self_datapool.f90 sourcefile~self_tensor_3d_t.f90->sourcefile~self_metadata.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_constants.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_lagrange.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_domaindecomposition.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_supportroutines.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_hdf5.f90 sourcefile~self_quadrature.f90 SELF_Quadrature.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_quadrature.f90 sourcefile~self_mesh.f90 SELF_Mesh.f90 sourcefile~self_mesh_3d_t.f90->sourcefile~self_mesh.f90 sourcefile~self_vector_3d_t.f90 SELF_Vector_3D_t.f90 sourcefile~self_vector_3d.f90->sourcefile~self_vector_3d_t.f90 sourcefile~self_lagrange_t.f90->sourcefile~self_constants.f90 sourcefile~self_lagrange_t.f90->sourcefile~self_supportroutines.f90 sourcefile~self_lagrange_t.f90->sourcefile~self_hdf5.f90 sourcefile~self_lagrange_t.f90->sourcefile~self_quadrature.f90 sourcefile~self_data.f90->sourcefile~self_constants.f90 sourcefile~self_data.f90->sourcefile~self_lagrange.f90 sourcefile~self_data.f90->sourcefile~self_hdf5.f90 sourcefile~self_data.f90->sourcefile~self_metadata.f90 sourcefile~self_supportroutines.f90->sourcefile~self_constants.f90 sourcefile~self_domaindecomposition_t.f90->sourcefile~self_constants.f90 sourcefile~self_domaindecomposition_t.f90->sourcefile~self_lagrange.f90 sourcefile~self_domaindecomposition_t.f90->sourcefile~self_supportroutines.f90 sourcefile~self_hdf5.f90->sourcefile~self_constants.f90 sourcefile~self_datapool.f90->sourcefile~self_constants.f90 sourcefile~self_quadrature.f90->sourcefile~self_constants.f90 sourcefile~self_mesh.f90->sourcefile~self_constants.f90 sourcefile~self_mesh.f90->sourcefile~self_domaindecomposition.f90 sourcefile~self_metadata.f90->sourcefile~self_hdf5.f90 sourcefile~self_vector_3d_t.f90->sourcefile~self_constants.f90 sourcefile~self_vector_3d_t.f90->sourcefile~self_lagrange.f90 sourcefile~self_vector_3d_t.f90->sourcefile~self_data.f90 sourcefile~self_vector_3d_t.f90->sourcefile~self_hdf5.f90 sourcefile~self_vector_3d_t.f90->sourcefile~self_datapool.f90 sourcefile~self_vector_3d_t.f90->sourcefile~self_metadata.f90

Files dependent on this one

sourcefile~~self_mappedscalar_3d_t.f90~~AfferentGraph sourcefile~self_mappedscalar_3d_t.f90 SELF_MappedScalar_3D_t.f90 sourcefile~self_mappedscalar_3d.f90 SELF_MappedScalar_3D.f90 sourcefile~self_mappedscalar_3d.f90->sourcefile~self_mappedscalar_3d_t.f90 sourcefile~self_mappedscalar_3d.f90~2 SELF_MappedScalar_3D.f90 sourcefile~self_mappedscalar_3d.f90~2->sourcefile~self_mappedscalar_3d_t.f90 sourcefile~self_dgmodel3d_t.f90 SELF_DGModel3D_t.f90 sourcefile~self_dgmodel3d_t.f90->sourcefile~self_mappedscalar_3d.f90 sourcefile~self_points_t.f90 SELF_Points_t.f90 sourcefile~self_points_t.f90->sourcefile~self_mappedscalar_3d.f90 sourcefile~self_points.f90~2 SELF_Points.f90 sourcefile~self_points.f90~2->sourcefile~self_mappedscalar_3d.f90 sourcefile~self_points.f90~2->sourcefile~self_points_t.f90 sourcefile~self_esatmo3d_t.f90 SELF_ESAtmo3D_t.f90 sourcefile~self_esatmo3d_t.f90->sourcefile~self_mappedscalar_3d.f90 sourcefile~self_ecdgmodel3d.f90 SELF_ECDGModel3D.f90 sourcefile~self_esatmo3d_t.f90->sourcefile~self_ecdgmodel3d.f90 sourcefile~self_dgmodel3d.f90 SELF_DGModel3D.f90 sourcefile~self_dgmodel3d.f90->sourcefile~self_dgmodel3d_t.f90 sourcefile~self_esatmo3d.f90 SELF_ESAtmo3D.f90 sourcefile~self_esatmo3d.f90->sourcefile~self_esatmo3d_t.f90 sourcefile~self_points.f90 SELF_Points.f90 sourcefile~self_points.f90->sourcefile~self_points_t.f90 sourcefile~self_dgmodel3d.f90~2 SELF_DGModel3D.f90 sourcefile~self_dgmodel3d.f90~2->sourcefile~self_dgmodel3d_t.f90 sourcefile~self_amrcontroller_3d.f90 SELF_AMRController_3D.f90 sourcefile~self_amrcontroller_3d.f90->sourcefile~self_dgmodel3d_t.f90 sourcefile~self_esatmo3d.f90~2 SELF_ESAtmo3D.f90 sourcefile~self_esatmo3d.f90~2->sourcefile~self_esatmo3d_t.f90 sourcefile~self_ecdgmodel3d_t.f90 SELF_ECDGModel3D_t.f90 sourcefile~self_esatmo3d.f90~2->sourcefile~self_ecdgmodel3d_t.f90 sourcefile~self_ecdgmodel3d_t.f90->sourcefile~self_dgmodel3d.f90 sourcefile~self_advection_diffusion_3d_t.f90 SELF_advection_diffusion_3d_t.f90 sourcefile~self_advection_diffusion_3d_t.f90->sourcefile~self_dgmodel3d.f90 sourcefile~self_lineareuler3d_t.f90 SELF_LinearEuler3D_t.f90 sourcefile~self_lineareuler3d_t.f90->sourcefile~self_dgmodel3d.f90 sourcefile~self_nulldgmodel3d_t.f90 SELF_NullDGModel3D_t.f90 sourcefile~self_nulldgmodel3d_t.f90->sourcefile~self_dgmodel3d.f90 sourcefile~self_ecdgmodel3d.f90->sourcefile~self_ecdgmodel3d_t.f90 sourcefile~self_advection_diffusion_3d.f90 SELF_advection_diffusion_3d.f90 sourcefile~self_advection_diffusion_3d.f90->sourcefile~self_advection_diffusion_3d_t.f90 sourcefile~self_advection_diffusion_3d.f90~2 SELF_advection_diffusion_3d.f90 sourcefile~self_advection_diffusion_3d.f90~2->sourcefile~self_advection_diffusion_3d_t.f90 sourcefile~self_ecadvection3d.f90~2 SELF_ECAdvection3D.f90 sourcefile~self_ecadvection3d.f90~2->sourcefile~self_ecdgmodel3d_t.f90 sourcefile~self_ecadvection3d_t.f90 SELF_ECAdvection3D_t.f90 sourcefile~self_ecadvection3d.f90~2->sourcefile~self_ecadvection3d_t.f90 sourcefile~self_ecdgmodel3d.f90~2 SELF_ECDGModel3D.f90 sourcefile~self_ecdgmodel3d.f90~2->sourcefile~self_ecdgmodel3d_t.f90 sourcefile~self_lineareuler3d.f90 SELF_LinearEuler3D.f90 sourcefile~self_lineareuler3d.f90->sourcefile~self_lineareuler3d_t.f90 sourcefile~self_lineareuler3d.f90~2 SELF_LinearEuler3D.f90 sourcefile~self_lineareuler3d.f90~2->sourcefile~self_lineareuler3d_t.f90 sourcefile~self_nulldgmodel3d.f90 SELF_NullDGModel3D.f90 sourcefile~self_nulldgmodel3d.f90->sourcefile~self_nulldgmodel3d_t.f90 sourcefile~self_nulldgmodel3d.f90~2 SELF_NullDGModel3D.f90 sourcefile~self_nulldgmodel3d.f90~2->sourcefile~self_nulldgmodel3d_t.f90 sourcefile~self_ecadvection3d_t.f90->sourcefile~self_ecdgmodel3d.f90 sourcefile~self_ecadvection3d.f90 SELF_ECAdvection3D.f90 sourcefile~self_ecadvection3d.f90->sourcefile~self_ecadvection3d_t.f90

Contents


Source Code

! //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// !
!
! Maintainers : support@fluidnumerics.com
! Official Repository : https://github.com/FluidNumerics/self/
!
! Copyright © 2024 Fluid Numerics LLC
!
! Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
!
! 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
!
! 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in
!    the documentation and/or other materials provided with the distribution.
!
! 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from
!    this software without specific prior written permission.
!
! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
! LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
! HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
! LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
! THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
! THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
!
! //////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// !

module SELF_MappedScalar_3D_t

  use SELF_Constants
  use SELF_Lagrange
  use SELF_Scalar_3D
  use SELF_Tensor_3D
  use SELF_Mesh_3D
  use SELF_Geometry_3D
  use SELF_DomainDecomposition
  use FEQParse
  use iso_c_binding

  implicit none

  type,extends(Scalar3D),public :: MappedScalar3D_t
    logical :: geometry_associated = .false.
    type(SEMHex),pointer :: geometry => null()

    ! Mortar exchange work array, allocated on first use for meshes with 2:1
    ! nonconforming interfaces. mortarBuff(i,j,slot,m,ivar) holds face traces in the
    ! big face's coordinates for mortar m :
    !   slots 1..4 - big-face trace, used to compute sub-face q's external state
    !   slots 5..8 - small-face traces on sub-faces 1..4
    ! Slots 1..4 carry the same data when the big element is rank-local; they are
    ! distinct so that MPI receives of the big-face trace on the small faces' ranks
    ! never alias.
    real(prec),allocatable,dimension(:,:,:,:,:) :: mortarBuff

  contains

    procedure,public :: AssociateGeometry => AssociateGeometry_MappedScalar3D_t
    procedure,public :: DissociateGeometry => DissociateGeometry_MappedScalar3D_t

    procedure,public :: SideExchange => SideExchange_MappedScalar3D_t
    procedure,public :: MortarExchange => MortarExchange_MappedScalar3D_t
    procedure,private :: MPIMortarExchangeAsync => MPIMortarExchangeAsync_MappedScalar3D_t

    generic,public :: MappedGradient => MappedGradient_MappedScalar3D_t
    procedure,private :: MappedGradient_MappedScalar3D_t

    generic,public :: MappedDGGradient => MappedDGGradient_MappedScalar3D_t
    procedure,private :: MappedDGGradient_MappedScalar3D_t

    procedure,private :: MPIExchangeAsync => MPIExchangeAsync_MappedScalar3D_t
    procedure,private :: ApplyFlip => ApplyFlip_MappedScalar3D_t

    procedure,public :: Resize => Resize_MappedScalar3D_t

    procedure,public :: SetInteriorFromEquation => SetInteriorFromEquation_MappedScalar3D_t

    ! procedure,public :: WriteTecplot => WriteTecplot_MappedScalar3D_t

  endtype MappedScalar3D_t

contains

  subroutine Resize_MappedScalar3D_t(this,interp,nVar,nElem)
    !! Rebind to a new element count, reusing storage where it fits (AMR Stage 6b). The mortar
    !! staging buffer is sized by mesh%nMortars rather than nElem, and nMortars changes with the
    !! mesh independently of the element count, so it is invalidated here and lazily re-created
    !! at the correct size by the next mortar exchange.
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(Lagrange),intent(in),target :: interp
    integer,intent(in) :: nVar
    integer,intent(in) :: nElem

    call Resize_Scalar3D_t(this,interp,nVar,nElem)
    if(allocated(this%mortarBuff)) deallocate(this%mortarBuff)

    ! The geometry binding refers to the PREVIOUS mesh's geometry, which the caller is
    ! about to destroy. It must be dropped here so the AssociateGeometry that follows a
    ! regrid actually rebinds: AssociateGeometry is a no-op when a geometry is already
    ! associated, so leaving the stale one in place silently kept every mapped operation
    ! reading freed metric terms - observed as NaN entropy on the first step after an
    ! adaptation. Free + Init used to hide this by nulling the pointer.
    call this%DissociateGeometry()

  endsubroutine Resize_MappedScalar3D_t

  subroutine AssociateGeometry_MappedScalar3D_t(this,geometry)
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(SEMHex),target,intent(in) :: geometry

    if(.not. associated(this%geometry)) then
      this%geometry => geometry
      this%geometry_associated = .true.
    endif

  endsubroutine AssociateGeometry_MappedScalar3D_t

  subroutine DissociateGeometry_MappedScalar3D_t(this)
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this

    if(associated(this%geometry)) then
      this%geometry => null()
      this%geometry_associated = .false.
    endif

  endsubroutine DissociateGeometry_MappedScalar3D_t

  subroutine SetInteriorFromEquation_MappedScalar3D_t(this,geometry,time)
  !!  Sets the this % interior attribute using the eqn attribute,
  !!  geometry (for physical positions), and provided simulation time.
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(SEMHex),intent(in) :: geometry
    real(prec),intent(in) :: time
    ! Local
    integer :: i,j,k,iEl,iVar
    real(prec) :: x
    real(prec) :: y
    real(prec) :: z

    do iVar = 1,this%nVar
      do iEl = 1,this%nElem
        do k = 1,this%interp%N+1
          do j = 1,this%interp%N+1
            do i = 1,this%interp%N+1

              ! Get the mesh positions
              x = geometry%x%interior(i,j,k,iEl,1,1)
              y = geometry%x%interior(i,j,k,iEl,1,2)
              z = geometry%x%interior(i,j,k,iEl,1,3)

              this%interior(i,j,k,iEl,iVar) = &
                this%eqn(iVar)%Evaluate((/x,y,z,time/))

            enddo
          enddo
        enddo
      enddo
    enddo

  endsubroutine SetInteriorFromEquation_MappedScalar3D_t

  subroutine MPIExchangeAsync_MappedScalar3D_t(this,mesh)
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(Mesh3D),intent(inout) :: mesh
    ! Local
    integer :: e1,s1,e2,s2,ivar
    integer :: globalSideId,r2,tag
    integer :: iError
    integer :: msgCount

    msgCount = 0

    do ivar = 1,this%nvar
      do e1 = 1,this%nElem
        do s1 = 1,6

          e2 = mesh%sideInfo(3,s1,e1) ! Neighbor Element
          if(e2 > 0) then
            r2 = mesh%decomp%elemToRank(e2) ! Neighbor Rank

            if(r2 /= mesh%decomp%rankId) then

              s2 = mesh%sideInfo(4,s1,e1)/10
              globalSideId = abs(mesh%sideInfo(2,s1,e1))
              tag = globalsideid+mesh%nUniqueSides*(ivar-1)

              msgCount = msgCount+1
              call MPI_IRECV(this%extBoundary(:,:,s1,e1,ivar), &
                             (this%interp%N+1)*(this%interp%N+1), &
                             mesh%decomp%mpiPrec, &
                             r2,globalSideId, &
                             mesh%decomp%mpiComm, &
                             mesh%decomp%requests(msgCount),iError)

              msgCount = msgCount+1
              call MPI_ISEND(this%boundary(:,:,s1,e1,ivar), &
                             (this%interp%N+1)*(this%interp%N+1), &
                             mesh%decomp%mpiPrec, &
                             r2,globalSideId, &
                             mesh%decomp%mpiComm, &
                             mesh%decomp%requests(msgCount),iError)
            endif
          endif

        enddo
      enddo
    enddo

    mesh%decomp%msgCount = msgCount

  endsubroutine MPIExchangeAsync_MappedScalar3D_t

  subroutine ApplyFlip_MappedScalar3D_t(this,mesh)
    ! Apply side flips to sides where MPI exchanges took place.
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(Mesh3D),intent(inout) :: mesh
    ! Local
    integer :: e1,s1,e2,s2
    integer :: i,i2,j,j2
    integer :: r2,flip,ivar
    integer :: bcid
    real(prec) :: extBuff(1:this%interp%N+1,1:this%interp%N+1)

    do ivar = 1,this%nvar
      do e1 = 1,this%nElem
        do s1 = 1,6

          e2 = mesh%sideInfo(3,s1,e1) ! Neighbor Element
          s2 = mesh%sideInfo(4,s1,e1)/10
          bcid = mesh%sideInfo(5,s1,e1)
          if(e2 > 0) then ! Interior Element
            r2 = mesh%decomp%elemToRank(e2) ! Neighbor Rank

            if(r2 /= mesh%decomp%rankId) then

              flip = mesh%sideInfo(4,s1,e1)-s2*10

              ! Need to update extBoundary with flip applied
              if(flip == 0) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    extBuff(i,j) = this%extBoundary(i,j,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 1) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    i2 = this%interp%N+2-i
                    j2 = j
                    extBuff(i,j) = this%extBoundary(i2,j2,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 2) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    i2 = this%interp%N+2-i
                    j2 = this%interp%N+2-j
                    extBuff(i,j) = this%extBoundary(i2,j2,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 3) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    i2 = i
                    j2 = this%interp%N+2-j
                    extBuff(i,j) = this%extBoundary(i2,j2,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 4) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    extBuff(i,j) = this%extBoundary(j,i,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 5) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    i2 = this%interp%N+2-j
                    j2 = i
                    extBuff(i,j) = this%extBoundary(i2,j2,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 6) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    i2 = this%interp%N+2-j
                    j2 = this%interp%N+2-i
                    extBuff(i,j) = this%extBoundary(i2,j2,s1,e1,ivar)
                  enddo
                enddo

              else if(flip == 7) then

                do j = 1,this%interp%N+1
                  do i = 1,this%interp%N+1
                    i2 = j
                    j2 = this%interp%N+2-i
                    extBuff(i,j) = this%extBoundary(i2,j2,s1,e1,ivar)
                  enddo
                enddo

              endif

              do j = 1,this%interp%N+1
                do i = 1,this%interp%N+1
                  this%extBoundary(i,j,s1,e1,ivar) = extBuff(i,j)
                enddo
              enddo

            endif

          endif

        enddo
      enddo
    enddo

  endsubroutine ApplyFlip_MappedScalar3D_t

  subroutine SideExchange_MappedScalar3D_t(this,mesh)
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(Mesh3D),intent(inout) :: mesh
    ! Local
    integer :: e1,e2,s1,s2,e2Global
    integer :: flip
    integer :: i,i2,j,j2,ivar
    integer :: r2
    integer :: rankId,offset
    integer,pointer :: elemtorank(:)

    elemtorank => mesh%decomp%elemToRank(:)
    rankId = mesh%decomp%rankId
    offset = mesh%decomp%offsetElem(rankId+1)

    if(mesh%decomp%mpiEnabled) then
      call this%MPIExchangeAsync(mesh)
    endif

    do concurrent(s1=1:6,e1=1:mesh%nElem,ivar=1:this%nvar)

      e2Global = mesh%sideInfo(3,s1,e1)
      s2 = mesh%sideInfo(4,s1,e1)/10
      flip = mesh%sideInfo(4,s1,e1)-s2*10

      if(e2Global > 0) then

        r2 = elemToRank(e2Global)

        if(r2 == rankId) then

          e2 = e2Global-offset

          if(flip == 0) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i,j,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 1) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                i2 = this%interp%N+2-i
                j2 = j
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i2,j2,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 2) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                i2 = this%interp%N+2-i
                j2 = this%interp%N+2-j
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i2,j2,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 3) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                i2 = i
                j2 = this%interp%N+2-j
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i2,j2,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 4) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(j,i,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 5) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                i2 = this%interp%N+2-j
                j2 = i
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i2,j2,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 6) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                i2 = this%interp%N+2-j
                j2 = this%interp%N+2-i
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i2,j2,s2,e2,ivar)
              enddo
            enddo

          else if(flip == 7) then

            do j = 1,this%interp%N+1
              do i = 1,this%interp%N+1
                i2 = j
                j2 = this%interp%N+2-i
                this%extBoundary(i,j,s1,e1,ivar) = this%boundary(i2,j2,s2,e2,ivar)
              enddo
            enddo

          endif

        endif
      endif

    enddo

    if(mesh%decomp%mpiEnabled) then
      call mesh%decomp%FinalizeMPIExchangeAsync()
      ! Apply side flips for data exchanged with MPI
      call this%ApplyFlip(mesh)
    endif

  endsubroutine SideExchange_MappedScalar3D_t

  subroutine MPIMortarExchangeAsync_MappedScalar3D_t(this,mesh)
    !! Posts the point-to-point messages required for mortar interfaces whose big and
    !! small elements reside on different ranks. The big-face rank sends its face trace
    !! to each remote small-face rank and receives each remote small-face trace; tags
    !! are built from the sub-face global side ids, following the conforming
    !! SideExchange tag convention.
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(Mesh3D),intent(inout) :: mesh
    ! Local
    integer :: m,q,ivar
    integer :: eB,sB,rB,eS,sS,rS
    integer :: globalSideId,tag
    integer :: offset
    integer :: iError
    integer :: msgCount

    msgCount = 0
    offset = mesh%decomp%offsetElem(mesh%decomp%rankId+1)

    do ivar = 1,this%nvar
      do m = 1,mesh%nMortars

        eB = mesh%mortarInfo(1,m)
        sB = mesh%mortarInfo(2,m)
        rB = mesh%decomp%elemToRank(eB)

        do q = 1,4

          eS = mesh%mortarInfo(2*q+1,m)
          sS = mesh%mortarInfo(2*q+2,m)/10
          rS = mesh%decomp%elemToRank(eS)
          globalSideId = mesh%mortarInfo(10+q,m)
          tag = globalSideId+mesh%nUniqueSides*(ivar-1)

          if(rB == mesh%decomp%rankId .and. rS /= mesh%decomp%rankId) then

            msgCount = msgCount+1
            call MPI_IRECV(this%mortarBuff(:,:,4+q,m,ivar), &
                           (this%interp%N+1)*(this%interp%N+1), &
                           mesh%decomp%mpiPrec, &
                           rS,tag, &
                           mesh%decomp%mpiComm, &
                           mesh%decomp%requests(msgCount),iError)

            msgCount = msgCount+1
            call MPI_ISEND(this%boundary(:,:,sB,eB-offset,ivar), &
                           (this%interp%N+1)*(this%interp%N+1), &
                           mesh%decomp%mpiPrec, &
                           rS,tag, &
                           mesh%decomp%mpiComm, &
                           mesh%decomp%requests(msgCount),iError)

          elseif(rS == mesh%decomp%rankId .and. rB /= mesh%decomp%rankId) then

            msgCount = msgCount+1
            call MPI_IRECV(this%mortarBuff(:,:,q,m,ivar), &
                           (this%interp%N+1)*(this%interp%N+1), &
                           mesh%decomp%mpiPrec, &
                           rB,tag, &
                           mesh%decomp%mpiComm, &
                           mesh%decomp%requests(msgCount),iError)

            msgCount = msgCount+1
            call MPI_ISEND(this%boundary(:,:,sS,eS-offset,ivar), &
                           (this%interp%N+1)*(this%interp%N+1), &
                           mesh%decomp%mpiPrec, &
                           rB,tag, &
                           mesh%decomp%mpiComm, &
                           mesh%decomp%requests(msgCount),iError)

          endif

        enddo
      enddo
    enddo

    mesh%decomp%msgCount = msgCount

  endsubroutine MPIMortarExchangeAsync_MappedScalar3D_t

  subroutine MortarExchange_MappedScalar3D_t(this,mesh)
    !! Fills the extBoundary attribute on all faces that participate in a 2:1
    !! nonconforming (mortar) interface.
    !!
    !! Each small face receives the big face's trace restricted (exactly) to its
    !! sub-face with the tensor product of the interp's 1-D mortarR matrices. The big
    !! face receives the L2 projection of the four small-face traces onto its trace
    !! space with the tensor product of the interp's mortarP matrices (each 1-D
    !! projection carries the 1/2 sub-interval Jacobian, so the tensor product carries
    !! the 1/4 sub-face Jacobian required for the solution-trace projection). Traces
    !! are staged in mortarBuff in the big face's coordinates; the flip recorded in
    !! mesh%mortarInfo translates between the small faces' coordinates and the big
    !! face's coordinates (see MortarFaceMap). Must be called after BoundaryInterp and
    !! may be called before, after, or without SideExchange (the face sets touched are
    !! disjoint from conforming faces).
    implicit none
    class(MappedScalar3D_t),intent(inout) :: this
    type(Mesh3D),intent(inout) :: mesh
    ! Local
    integer :: m,q,ivar,i,j,i2,j2
    integer :: eB,eS,sS,flip
    integer :: rankId,offset,N
    integer,pointer :: elemtorank(:)
    real(prec) :: extBuff(1:this%interp%N+1,1:this%interp%N+1)

    ! See https://github.com/FluidNumerics/SELF/issues/54 for the reason behind
    ! this pointer alias
    elemtorank => mesh%decomp%elemToRank(:)
    rankId = mesh%decomp%rankId
    offset = mesh%decomp%offsetElem(rankId+1)
    N = this%interp%N

    if(.not. allocated(this%mortarBuff)) then
      allocate(this%mortarBuff(1:N+1,1:N+1,1:8,1:mesh%nMortars,1:this%nvar))
      this%mortarBuff = 0.0_prec
    endif

    if(mesh%decomp%mpiEnabled) then
      call this%MPIMortarExchangeAsync(mesh)
    endif

    ! Stage rank-local traces in the big face's coordinates
    do concurrent(m=1:mesh%nMortars,ivar=1:this%nvar)
      block
        integer :: i,j,i2,j2,q
        integer :: eB,sB,eS,sS,flip

        eB = mesh%mortarInfo(1,m)
        if(elemtorank(eB) == rankId) then
          sB = mesh%mortarInfo(2,m)
          do q = 1,4
            do j = 1,N+1
              do i = 1,N+1
                this%mortarBuff(i,j,q,m,ivar) = this%boundary(i,j,sB,eB-offset,ivar)
              enddo
            enddo
          enddo
        endif

        do q = 1,4
          eS = mesh%mortarInfo(2*q+1,m)
          if(elemtorank(eS) == rankId) then
            sS = mesh%mortarInfo(2*q+2,m)/10
            flip = mesh%mortarInfo(2*q+2,m)-10*sS
            do j = 1,N+1
              do i = 1,N+1
                call MortarFaceMap(i,j,N,flip,i2,j2)
                this%mortarBuff(i,j,4+q,m,ivar) = this%boundary(i2,j2,sS,eS-offset,ivar)
              enddo
            enddo
          endif
        enddo
      endblock
    enddo

    if(mesh%decomp%mpiEnabled) then
      call mesh%decomp%FinalizeMPIExchangeAsync()

      ! Reorient small-face traces received over MPI into the big face's coordinates
      do ivar = 1,this%nvar
        do m = 1,mesh%nMortars
          eB = mesh%mortarInfo(1,m)
          if(elemtorank(eB) == rankId) then
            do q = 1,4
              eS = mesh%mortarInfo(2*q+1,m)
              sS = mesh%mortarInfo(2*q+2,m)/10
              flip = mesh%mortarInfo(2*q+2,m)-10*sS
              if(elemtorank(eS) /= rankId .and. flip /= 0) then
                do j = 1,N+1
                  do i = 1,N+1
                    call MortarFaceMap(i,j,N,flip,i2,j2)
                    extBuff(i,j) = this%mortarBuff(i2,j2,4+q,m,ivar)
                  enddo
                enddo
                do j = 1,N+1
                  do i = 1,N+1
                    this%mortarBuff(i,j,4+q,m,ivar) = extBuff(i,j)
                  enddo
                enddo
              endif
            enddo
          endif
        enddo
      enddo
    endif

    ! Compute external states :
    !  small faces get the restricted big-face trace (exact),
    !  the big face gets the L2 projection of the small-face traces
    do concurrent(m=1:mesh%nMortars,ivar=1:this%nvar)
      block
        integer :: i,j,ii,jj,i2,j2,kx,ky,q
        integer :: eB,sB,eS,sS,flip
        real(prec) :: fm
        real(prec) :: tmp(1:N+1,1:N+1)
        real(prec) :: acc(1:N+1,1:N+1)

        do q = 1,4
          eS = mesh%mortarInfo(2*q+1,m)
          if(elemtorank(eS) == rankId) then
            sS = mesh%mortarInfo(2*q+2,m)/10
            flip = mesh%mortarInfo(2*q+2,m)-10*sS
            kx = mortarQuadKx(q)
            ky = mortarQuadKy(q)
            do jj = 1,N+1
              do i = 1,N+1
                fm = 0.0_prec
                do ii = 1,N+1
                  fm = fm+this%interp%mortarR(ii,i,kx)*this%mortarBuff(ii,jj,q,m,ivar)
                enddo
                tmp(i,jj) = fm
              enddo
            enddo
            do j = 1,N+1
              do i = 1,N+1
                fm = 0.0_prec
                do jj = 1,N+1
                  fm = fm+this%interp%mortarR(jj,j,ky)*tmp(i,jj)
                enddo
                call MortarFaceMap(i,j,N,flip,i2,j2)
                this%extBoundary(i2,j2,sS,eS-offset,ivar) = fm
              enddo
            enddo
          endif
        enddo

        eB = mesh%mortarInfo(1,m)
        if(elemtorank(eB) == rankId) then
          sB = mesh%mortarInfo(2,m)
          acc = 0.0_prec
          do q = 1,4
            kx = mortarQuadKx(q)
            ky = mortarQuadKy(q)
            do jj = 1,N+1
              do i = 1,N+1
                fm = 0.0_prec
                do ii = 1,N+1
                  fm = fm+this%interp%mortarP(ii,i,kx)*this%mortarBuff(ii,jj,4+q,m,ivar)
                enddo
                tmp(i,jj) = fm
              enddo
            enddo
            do j = 1,N+1
              do i = 1,N+1
                fm = 0.0_prec
                do jj = 1,N+1
                  fm = fm+this%interp%mortarP(jj,j,ky)*tmp(i,jj)
                enddo
                acc(i,j) = acc(i,j)+fm
              enddo
            enddo
          enddo
          do j = 1,N+1
            do i = 1,N+1
              this%extBoundary(i,j,sB,eB-offset,ivar) = acc(i,j)
            enddo
          enddo
        endif
      endblock
    enddo

  endsubroutine MortarExchange_MappedScalar3D_t

  subroutine MappedGradient_MappedScalar3D_t(this,df)
  !! Calculates the gradient of a function using the strong form of the gradient
  !! in mapped coordinates.
    implicit none
    class(MappedScalar3D_t),intent(in) :: this
    real(prec),intent(out) :: df(1:this%N+1,1:this%N+1,1:this%N+1,1:this%nelem,1:this%nvar,1:3)
    ! Local
    integer :: iEl,iVar,i,j,k,ii,idir
    real(prec) :: dfdx,ja

    do concurrent(i=1:this%N+1,j=1:this%N+1, &
                  k=1:this%N+1,iel=1:this%nelem,ivar=1:this%nvar,idir=1:3)

      dfdx = 0.0_prec
      do ii = 1,this%N+1
        ! dsdx(j,i) is contravariant vector i, component j
        ja = this%geometry%dsdx%interior(ii,j,k,iel,1,idir,1)
        dfdx = dfdx+this%interp%dMatrix(ii,i)* &
               this%interior(ii,j,k,iel,ivar)*ja

      enddo
      df(i,j,k,iel,ivar,idir) = dfdx

    enddo

    do concurrent(i=1:this%N+1,j=1:this%N+1, &
                  k=1:this%N+1,iel=1:this%nelem,ivar=1:this%nvar,idir=1:3)

      dfdx = 0.0_prec
      do ii = 1,this%N+1
        ja = this%geometry%dsdx%interior(i,ii,k,iel,1,idir,2)
        dfdx = dfdx+this%interp%dMatrix(ii,j)* &
               this%interior(i,ii,k,iel,ivar)*ja
      enddo
      df(i,j,k,iel,ivar,idir) = (df(i,j,k,iel,ivar,idir)+dfdx)

    enddo

    do concurrent(i=1:this%N+1,j=1:this%N+1, &
                  k=1:this%N+1,iel=1:this%nelem,ivar=1:this%nvar,idir=1:3)

      dfdx = 0.0_prec
      do ii = 1,this%N+1
        ja = this%geometry%dsdx%interior(i,j,ii,iel,1,idir,3)
        dfdx = dfdx+this%interp%dMatrix(ii,k)* &
               this%interior(i,j,ii,iel,ivar)*ja
      enddo
      df(i,j,k,iel,ivar,idir) = (df(i,j,k,iel,ivar,idir)+dfdx)/ &
                                this%geometry%J%interior(i,j,k,iEl,1)

    enddo

  endsubroutine MappedGradient_MappedScalar3D_t

  subroutine MappedDGGradient_MappedScalar3D_t(this,df)
    !! Calculates the gradient of a function using the weak form of the gradient
    !! and the average boundary state.
    !! This method will compute the average boundary state from the
    !! and  attributes of
    implicit none
    class(MappedScalar3D_t),intent(in) :: this
    real(prec),intent(out) :: df(1:this%N+1,1:this%N+1,1:this%N+1,1:this%nelem,1:this%nvar,1:3)
    ! Local
    integer :: iEl,iVar,i,j,k,ii,idir
    real(prec) :: dfdx,jaf,bfl,bfr

    do concurrent(i=1:this%N+1,j=1:this%N+1, &
                  k=1:this%N+1,iel=1:this%nelem,ivar=1:this%nvar,idir=1:3)

      dfdx = 0.0_prec
      do ii = 1,this%N+1
        ! dsdx(j,i) is contravariant vector i, component j
        jaf = this%geometry%dsdx%interior(ii,j,k,iel,1,idir,1)* &
              this%interior(ii,j,k,iel,ivar)

        dfdx = dfdx+this%interp%dgMatrix(ii,i)*jaf
      enddo
      bfl = this%avgboundary(j,k,5,iel,ivar)* &
            this%geometry%dsdx%boundary(j,k,5,iel,1,idir,1) ! west
      bfr = this%avgboundary(j,k,3,iel,ivar)* &
            this%geometry%dsdx%boundary(j,k,3,iel,1,idir,1) ! east
      df(i,j,k,iel,ivar,idir) = dfdx+ &
                                (this%interp%bMatrix(i,1)*bfl+ &
                                 this%interp%bMatrix(i,2)*bfr)/this%interp%qweights(i)

    enddo

    do concurrent(i=1:this%N+1,j=1:this%N+1, &
                  k=1:this%N+1,iel=1:this%nelem,ivar=1:this%nvar,idir=1:3)

      dfdx = 0.0_prec
      do ii = 1,this%N+1
        jaf = this%geometry%dsdx%interior(i,ii,k,iel,1,idir,2)* &
              this%interior(i,ii,k,iel,ivar)

        dfdx = dfdx+this%interp%dgMatrix(ii,j)*jaf
      enddo
      bfl = this%avgboundary(i,k,2,iel,ivar)* &
            this%geometry%dsdx%boundary(i,k,2,iel,1,idir,2) ! south
      bfr = this%avgboundary(i,k,4,iel,ivar)* &
            this%geometry%dsdx%boundary(i,k,4,iel,1,idir,2) ! north
      dfdx = dfdx+(this%interp%bMatrix(j,1)*bfl+ &
                   this%interp%bMatrix(j,2)*bfr)/this%interp%qweights(j)

      df(i,j,k,iel,ivar,idir) = (df(i,j,k,iel,ivar,idir)+dfdx)

    enddo

    do concurrent(i=1:this%N+1,j=1:this%N+1, &
                  k=1:this%N+1,iel=1:this%nelem,ivar=1:this%nvar,idir=1:3)

      dfdx = 0.0_prec
      do ii = 1,this%N+1
        jaf = this%geometry%dsdx%interior(i,j,ii,iel,1,idir,3)* &
              this%interior(i,j,ii,iel,ivar)
        dfdx = dfdx+this%interp%dgMatrix(ii,k)*jaf
      enddo
      bfl = this%avgboundary(i,j,1,iel,ivar)* &
            this%geometry%dsdx%boundary(i,j,1,iel,1,idir,3) ! bottom
      bfr = this%avgboundary(i,j,6,iel,ivar)* &
            this%geometry%dsdx%boundary(i,j,6,iel,1,idir,3) ! top
      dfdx = dfdx+(this%interp%bMatrix(k,1)*bfl+ &
                   this%interp%bMatrix(k,2)*bfr)/this%interp%qweights(k)

      df(i,j,k,iel,ivar,idir) = (df(i,j,k,iel,ivar,idir)+dfdx)/ &
                                this%geometry%J%interior(i,j,k,iEl,1)

    enddo

  endsubroutine MappedDGGradient_MappedScalar3D_t

  ! subroutine WriteTecplot_MappedScalar3D_t(this,geometry,filename)
  !   implicit none
  !   class(MappedScalar3D_t),intent(inout) :: this
  !   type(SEMHex),intent(in) :: geometry
  !   character(*),intent(in),optional :: filename
  !   ! Local
  !   character(8) :: zoneID
  !   integer :: fUnit
  !   integer :: iEl,i,j,k,iVar
  !   character(LEN=self_FileNameLength) :: tecFile
  !   character(LEN=self_TecplotHeaderLength) :: tecHeader
  !   character(LEN=self_FormatLength) :: fmat
  !   character(13) :: timeStampString
  !   character(5) :: rankString
  !   real(prec) :: f(1:this%M+1,1:this%M+1,1:this%M+1,1:this%nelem,1:this%nvar)
  !   real(prec) :: x(1:this%M+1,1:this%M+1,1:this%M+1,1:this%nelem,1:this%nvar,1:3)

  !   if(present(filename)) then
  !     tecFile = filename
  !   else
  !     tecFile = "mappedscalar.tec"
  !   endif

  !   ! Map the mesh positions to the target grid
  !   x = geometry%x%GridInterp()

  !   ! Map the solution to the target grid
  !   f = this%GridInterp()

  !   open(UNIT=NEWUNIT(fUnit), &
  !        FILE=trim(tecFile), &
  !        FORM='formatted', &
  !        STATUS='replace')

  !   tecHeader = 'VARIABLES = "X", "Y", "Z"'
  !   do iVar = 1,this%nVar
  !     tecHeader = trim(tecHeader)//', "'//trim(this%meta(iVar)%name)//'"'
  !   enddo

  !   write(fUnit,*) trim(tecHeader)

  !   ! Create format statement
  !   write(fmat,*) this%nvar+3
  !   fmat = '('//trim(fmat)//'(ES16.7E3,1x))'

  !   do iEl = 1,this%nElem

  !     write(zoneID,'(I8.8)') iEl
  !     write(fUnit,*) 'ZONE T="el'//trim(zoneID)//'", I=',this%interp%M+1, &
  !       ', J=',this%interp%M+1,', K=',this%interp%M+1

  !     do k = 1,this%interp%M+1
  !       do j = 1,this%interp%M+1
  !         do i = 1,this%interp%M+1

  !           write(fUnit,fmat) x(i,j,k,iEl,1,1), &
  !             x(i,j,k,iEl,1,2), &
  !             x(i,j,k,iEl,1,3), &
  !             f(i,j,k,iEl,1:this%nvar)

  !         enddo
  !       enddo
  !     enddo

  !   enddo

  !   close(UNIT=fUnit)

  ! endsubroutine WriteTecplot_MappedScalar3D_t

endmodule SELF_MappedScalar_3D_t