ValidateSetPartition Function

  function ValidateSetPartition(globalMesh,setOfElem,nSets) result(ok)
    !! Check that a global set map can be split into sub-meshes.
    !!
    !! The partition is valid when
    !!   1. 1 <= s(e) <= nSets for every global element e;
    !!   2. every set k = 1..nSets holds at least one element;
    !!   3. every 2:1 mortar (big element and its four small elements) and every
    !!      anisotropic mortar (big element and its two small elements) lies in a single
    !!      set, because the interface exchange between sets handles conforming faces
    !!      only.
    !! The mortar tables hold global element ids and are replicated, and setOfElem is
    !! global, so every rank returns the same answer without communication. The first
    !! violation found is printed on rank 0.
    !!
    !!  Input
    !!    - globalMesh : the decomposed global mesh
    !!    - setOfElem(1:nGlobalElem) : set id of each global element (GatherSetOfElem)
    !!    - nSets : number of sets, >= 1
    !!  Output
    !!    - ok : .true. when all three conditions hold
    implicit none
    type(Mesh3D),intent(in) :: globalMesh
    integer,intent(in) :: setOfElem(1:)
    integer,intent(in) :: nSets
    logical :: ok
    ! Local
    integer :: e,k,m,q,s0
    integer,allocatable :: nInSet(:)
    logical :: report

    ok = .true.
    report = (globalMesh%decomp%rankId == 0)

    if(nSets < 1) then
      ok = .false.
      if(report) print*,__FILE__," : Error : nSets must be at least 1, got ",nSets
      return
    endif

    allocate(nInSet(1:nSets))
    nInSet = 0
    do e = 1,size(setOfElem)
      if(setOfElem(e) < 1 .or. setOfElem(e) > nSets) then
        ok = .false.
        if(report) print*,__FILE__," : Error : element ",e," has set id ",setOfElem(e), &
          " outside 1..",nSets
        deallocate(nInSet)
        return
      endif
      nInSet(setOfElem(e)) = nInSet(setOfElem(e))+1
    enddo
    do k = 1,nSets
      if(nInSet(k) == 0) then
        ok = .false.
        if(report) print*,__FILE__," : Error : element set ",k," is empty"
        deallocate(nInSet)
        return
      endif
    enddo
    deallocate(nInSet)

    ! Mortar element rows: 1 (big) and 3,5,7,9 (small) in mortarInfo; 1 (big) and 3,5
    ! (small) in anisoMortarInfo.
    do m = 1,globalMesh%nMortars
      s0 = setOfElem(globalMesh%mortarInfo(1,m))
      do q = 1,4
        if(setOfElem(globalMesh%mortarInfo(1+2*q,m)) /= s0) then
          ok = .false.
          if(report) print*,__FILE__," : Error : mortar ",m," crosses element sets"
          return
        endif
      enddo
    enddo
    do m = 1,globalMesh%nAnisoMortars
      s0 = setOfElem(globalMesh%anisoMortarInfo(1,m))
      do q = 1,2
        if(setOfElem(globalMesh%anisoMortarInfo(1+2*q,m)) /= s0) then
          ok = .false.
          if(report) print*,__FILE__," : Error : anisotropic mortar ",m, &
            " crosses element sets"
          return
        endif
      enddo
    enddo

  endfunction ValidateSetPartition