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GetVertexDOF

The GetVertexDOF method retrieves the degree of freedom (DOF) number associated with a specified vertex (node) in the mesh. In finite element analysis, each vertex in the mesh is typically assigned one or more degrees of freedom, which represent the unknown values to be solved for.

Interface​

INTERFACE
  MODULE SUBROUTINE GetVertexDOF(obj, globalNode, ans, tsize, islocal)
    CLASS(FEDOF_), INTENT(IN) :: obj
    INTEGER(I4B), INTENT(IN) :: globalNode
    INTEGER(I4B), INTENT(INOUT) :: ans(:)
    INTEGER(I4B), INTENT(OUT) :: tsize
    LOGICAL(LGT), INTENT(IN), OPTIONAL :: islocal
  END SUBROUTINE GetVertexDOF
END INTERFACE

Parameters​

  • obj - The FEDOF_ object containing degree of freedom information
  • globalNode - The global or local node number, depending on the value of islocal
  • ans - An array that will store the degree of freedom number(s) associated with the specified node
  • tsize - The number of degrees of freedom written to the ans array
  • islocal - Optional logical flag. If present and .TRUE., globalNode is interpreted as a local node number; otherwise, it's a global node number

Implementation Details​

The implementation is straightforward for vertex DOFs:

tsize = 1
ans(1) = obj%mesh%GetLocalNodeNumber(globalNode, islocal=islocal)

For vertex DOFs in most finite element formulations:

  1. The method sets tsize to 1, indicating that one degree of freedom is associated with each vertex
  2. It obtains the local node number using the mesh's GetLocalNodeNumber method, which converts global node numbers to local ones if necessary
  3. The local node number itself is used as the degree of freedom number

Notes​

  • This method assumes a simple one-to-one mapping between mesh vertices and degrees of freedom, which is typical for scalar problems (e.g., heat conduction, potential flow)
  • For vector problems (e.g., elasticity) or higher-order problems, a more complex mapping might be needed, potentially requiring multiple DOFs per vertex
  • The implementation reflects that in typical finite element numbering schemes, vertex DOFs are numbered first, followed by edge, face, and cell DOFs
  • In the current implementation, the DOF number for a vertex is identical to its local node number in the mesh

Example Usage​

This method is typically used when assembling the global system of equations or when mapping local element matrices to the global system:

INTEGER(I4B) :: nodeDOF(1), tsize, nodeNum

! Get the DOF number for node 5
nodeNum = 5
CALL fedof%GetVertexDOF(globalNode=nodeNum, ans=nodeDOF, tsize=tsize)

! nodeDOF(1) now contains the DOF number for node 5
! tsize will be 1

This method is often called internally by other methods in the FEDOF_ class, particularly when constructing element connectivity arrays that map local element degrees of freedom to global system degrees of freedom.

Example 1​

!> author: Vikas Sharma, Ph. D.
! date: 2025-06-07
! summary:  Testing GetVertexDOF method of FEDOF class
! H1 Heirarchical Second Order Triangular Mesh

PROGRAM main
USE FEDOF_Class
USE FEDomain_Class
USE AbstractMesh_Class
USE HDF5File_Class
USE Display_Method
USE GlobalData
USE Test_Method
USE ExceptionHandler_Class, ONLY: e, EXCEPTION_INFORMATION
USE AppendUtility
USE ArangeUtility
use ReallocateUtility

IMPLICIT NONE

CHARACTER(*), PARAMETER :: &
  filename = "../../FEMesh/examples/meshdata/small_tri3_mesh.h5", &
  baseContinuity = "H1", &
  baseInterpolation = "Heirarchical", &
  testname = baseContinuity//" "//baseInterpolation

TYPE(FEDOF_) :: fedof
TYPE(FEDomain_) :: dom
CLASS(AbstractMesh_), POINTER :: meshptr => NULL()
TYPE(HDF5File_) :: meshfile
INTEGER(I4B), ALLOCATABLE :: found(:), want(:)
INTEGER(I4B) :: order, totalVertexNodes, totalFaces
LOGICAL(LGT) :: isok

CALL e%SetQuietMode(EXCEPTION_INFORMATION, .TRUE.)

CALL meshfile%Initiate(filename, mode="READ")
CALL meshfile%OPEN()
CALL dom%Initiate(meshfile, '')
meshptr => dom%GetMeshPointer()
totalVertexNodes = meshptr%GetTotalVertexNodes()
totalFaces = meshptr%GetTotalFaces()

CALL test1
CALL test2
CALL test3

CALL dom%DEALLOCATE()
CALL meshfile%DEALLOCATE()

CONTAINS

!----------------------------------------------------------------------------
!                                                                      test1
!----------------------------------------------------------------------------

SUBROUTINE test1

  INTEGER(I4B) :: tsize

  order = 1
  CALL fedof%Initiate(baseContinuity=baseContinuity, &
                      baseInterpolation=baseInterpolation, &
                      order=order, mesh=meshptr)

  CALL Reallocate(found, 2, want, 2)
  CALL fedof%GetVertexDOF(globalNode=1, islocal=.TRUE., &
                            ans=found, tsize=tsize)

  want(1) = 1

  isok = ALL(found == want)
  CALL OK(isok, testname//" GetVertexDOF (order= "//ToString(order)//"): ")

END SUBROUTINE test1

!----------------------------------------------------------------------------
!                                                                      test2
!----------------------------------------------------------------------------

SUBROUTINE test2

  INTEGER(I4B) :: tsize

  order = 2
  CALL fedof%Initiate(baseContinuity=baseContinuity, &
                      baseInterpolation=baseInterpolation, &
                      order=order, mesh=meshptr)

  CALL Reallocate(found, 2, want, 2)
  CALL fedof%GetVertexDOF(globalNode=1, islocal=.TRUE., &
                            ans=found, tsize=tsize)

  want(1) = 1

  isok = ALL(found == want)
  CALL OK(isok, testname//" GetVertexDOF (order= "//ToString(order)//"): ")

END SUBROUTINE test2

!----------------------------------------------------------------------------
!                                                                     test3
!----------------------------------------------------------------------------

SUBROUTINE test3

  INTEGER(I4B) :: tsize

  order = 3
  CALL fedof%Initiate(baseContinuity=baseContinuity, &
                      baseInterpolation=baseInterpolation, &
                      order=order, mesh=meshptr)

  CALL Reallocate(found, 2, want, 2)
  CALL fedof%GetVertexDOF(globalNode=1, islocal=.TRUE., &
                            ans=found, tsize=tsize)

  want(1) = 1

  isok = ALL(found == want)
  CALL OK(isok, testname//" GetVertexDOF (order= "//ToString(order)//"): ")

END SUBROUTINE test3

!----------------------------------------------------------------------------
!                                                                 
!----------------------------------------------------------------------------

END PROGRAM main

Example 2​

!> author: Vikas Sharma, Ph. D.
! date: 2025-06-07
! summary:  Testing GetVertexDOF method of FEDOF class
! H1 Heirarchical Second Order Triangular Mesh

PROGRAM main
USE FEDOF_Class
USE FEDomain_Class
USE AbstractMesh_Class
USE HDF5File_Class
USE Display_Method
USE GlobalData
USE Test_Method
USE ExceptionHandler_Class, ONLY: e, EXCEPTION_INFORMATION
USE AppendUtility
USE ArangeUtility
USE ReallocateUtility

IMPLICIT NONE

CHARACTER(*), PARAMETER :: &
  filename = "../../FEMesh/examples/meshdata/small_tri6_mesh.h5", &
  baseContinuity = "H1", &
  baseInterpolation = "Heirarchical", &
  testname = baseContinuity//" "//baseInterpolation

TYPE(FEDOF_) :: fedof
TYPE(FEDomain_) :: dom
CLASS(AbstractMesh_), POINTER :: meshptr => NULL()
TYPE(HDF5File_) :: meshfile
INTEGER(I4B), ALLOCATABLE :: found(:), want(:)
INTEGER(I4B) :: order, totalVertexNodes, totalFaces
LOGICAL(LGT) :: isok

CALL e%SetQuietMode(EXCEPTION_INFORMATION, .TRUE.)

CALL meshfile%Initiate(filename, mode="READ")
CALL meshfile%OPEN()
CALL dom%Initiate(meshfile, '')
meshptr => dom%GetMeshPointer()
totalVertexNodes = meshptr%GetTotalVertexNodes()
totalFaces = meshptr%GetTotalFaces()

CALL test1
CALL test2
CALL test3

CALL dom%DEALLOCATE()
CALL meshfile%DEALLOCATE()

CONTAINS

!----------------------------------------------------------------------------
!                                                                      test1
!----------------------------------------------------------------------------

SUBROUTINE test1

  INTEGER(I4B) :: tsize

  order = 1
  CALL fedof%Initiate(baseContinuity=baseContinuity, &
                      baseInterpolation=baseInterpolation, &
                      order=order, mesh=meshptr)

  CALL Reallocate(found, 2, want, 2)
  CALL fedof%GetVertexDOF(globalNode=1, islocal=.TRUE., &
                          ans=found, tsize=tsize)

  want(1) = 1

  isok = ALL(found == want)
  CALL OK(isok, testname//" GetVertexDOF "//ToString(order)//"): ")

END SUBROUTINE test1

!----------------------------------------------------------------------------
!                                                                      test2
!----------------------------------------------------------------------------

SUBROUTINE test2

  INTEGER(I4B) :: tsize

  order = 2
  CALL fedof%Initiate(baseContinuity=baseContinuity, &
                      baseInterpolation=baseInterpolation, &
                      order=order, mesh=meshptr)

  CALL Reallocate(found, 2, want, 2)
  CALL fedof%GetVertexDOF(globalNode=1, islocal=.TRUE., &
                          ans=found, tsize=tsize)

  want(1) = 1

  isok = ALL(found == want)
  CALL OK(isok, testname//" GetVertexDOF (order= "//ToString(order)//"): ")

END SUBROUTINE test2

!----------------------------------------------------------------------------
!                                                                     test3
!----------------------------------------------------------------------------

SUBROUTINE test3

  INTEGER(I4B) :: tsize

  order = 3
  CALL fedof%Initiate(baseContinuity=baseContinuity, &
                      baseInterpolation=baseInterpolation, &
                      order=order, mesh=meshptr)

  CALL Reallocate(found, 2, want, 2)
  CALL fedof%GetVertexDOF(globalNode=1, islocal=.TRUE., &
                          ans=found, tsize=tsize)

  want(1) = 1

  isok = ALL(found == want)
  CALL OK(isok, testname//" GetVertexDOF (order= "//ToString(order)//"): ")

END SUBROUTINE test3

!----------------------------------------------------------------------------
!
!----------------------------------------------------------------------------

END PROGRAM main
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