GetLocalElemShapeData

The GetLocalElemShapeData method retrieves local element shape function data for a specific element in a finite element mesh. This method acts as a dispatcher that calls the appropriate shape function evaluation method based on the continuity and interpolation type of the finite element space.

Syntax

CALL obj%GetLocalElemShapeData(globalElement, elemsd, quad, islocal)

Arguments

Argument	Intent	Description
`obj`	`INOUT`	An instance of the `FEDOF_` class
`globalElement`	`IN`	Global element number (or local element number if `islocal=.TRUE.`)
`elemsd`	`INOUT`	`ElemShapedata_` object to store the shape function data
`quad`	`IN`	`QuadraturePoint_` object containing quadrature points
`islocal`	`IN`, `OPTIONAL`	Logical flag - if true, `globalElement` is treated as a local element number

Description

This method determines the appropriate shape function evaluation strategy based on the case name derived from the basis continuity and interpolation type. Currently, it supports:

H1LAGR: H1-conforming Lagrange interpolation
H1HIER: H1-conforming Hierarchical interpolation

The method dispatches to the appropriate specialized method:

GetLocalElemShapeDataH1Lagrange for Lagrange interpolation
GetLocalElemShapeDataH1Hierarchical for Hierarchical interpolation

Implementation Details

The method performs the following steps:

Obtains the case name by calling obj%GetCaseName()
Uses a SELECT CASE statement to call the appropriate specialized method
Raises an error if no matching case is found

Example Usage

TYPE(FEDOF_) :: fedof
TYPE(ElemShapedata_) :: elemsd
TYPE(QuadraturePoint_) :: quad
INTEGER :: elemNumber

! Initialize fedof, elemsd, quad, and elemNumber

! Get local element shape data
CALL fedof%GetLocalElemShapeData(globalElement=elemNumber, elemsd=elemsd, quad=quad)

Notes

The method depends on the continuity and interpolation type settings in the FEDOF object
Error checking is performed in debug mode to ensure the element is valid
This method serves as a high-level interface to different shape function implementations

Would you like me to explain any specific part of this method in more detail?

Example 1

!> author: Vikas Sharma, Ph. D.
! date: 2025-06-09
! summary:  This program tests the GetLocalElemshapeData
! method of the FEDOF class.

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 BaseType, ONLY: QuadraturePoint_, TypeQuadratureOpt, ElemshapeData_
USE QuadraturePoint_Method
USE ElemshapeData_Method
USE ApproxUtility

IMPLICIT NONE

TYPE(FEDOF_) :: obj, geoobj
TYPE(FEDomain_) :: dom
CLASS(AbstractMesh_), POINTER :: meshptr => NULL()
CHARACTER(*), PARAMETER :: &
  filename = "../../FEMesh/examples/meshdata/small_tri3_mesh.h5", &
  baseContinuity = "H1", &
  baseInterpolation = "Heirarchical", &
  testname = baseContinuity//" "//baseInterpolation//" GetLocalElemshapeData "

TYPE(HDF5File_) :: meshfile

TYPE(QuadraturePoint_) :: quad

TYPE(ElemshapeData_) :: elemsd, geoelemsd

INTEGER(I4B) :: globalElement, telements, order, &
                nodecon(100), ii, jj, nsd

REAL(DFP) :: nodecoord(3, 100)

LOGICAL(LGT) :: islocal, isok

CALL e%setQuietMode(EXCEPTION_INFORMATION, .TRUE.)
CALL meshfile%Initiate(filename, mode="READ")
CALL meshfile%OPEN()
CALL dom%Initiate(meshfile, '')
meshptr => dom%GetMeshPointer()
nsd = meshptr%GetNSD()

CALL test1
CALL test2
CALL test3

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

CONTAINS

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

SUBROUTINE test1

  REAL(DFP) :: found(1), want(1)

  order = 1
  CALL obj%Initiate(baseContinuity=baseContinuity, &
                    baseInterpolation=baseInterpolation, &
                    order=order, mesh=meshptr, &
                    ipType=TypeQuadratureOpt%equidistance)

  globalElement = 1; islocal = .TRUE.
  CALL obj%GetQuadraturePoints(quad=quad, globalElement=globalElement, &
                             quadratureType=TypeQuadratureOpt%GaussLegendre, &
                               order=order, islocal=islocal)

  CALL obj%GetLocalElemshapeData(quad=quad, elemsd=elemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL meshptr%GetNodeCoord(nodecoord=nodecoord, nrow=ii, ncol=jj, &
                            globalElement=globalElement, islocal=islocal)

  CALL obj%GetGlobalElemshapeData(elemsd=elemsd, xij=nodecoord(1:nsd, 1:jj), &
                                 globalElement=globalElement, islocal=islocal)

  found = SUM(elemsd%N, dim=1)
  want = 1.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXi(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXi(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXt(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXt(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

END SUBROUTINE test1

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

SUBROUTINE test2

  REAL(DFP) :: found(1), want(1)

  order = 2
  CALL obj%Initiate(baseContinuity=baseContinuity, &
                    baseInterpolation=baseInterpolation, &
                    order=order, mesh=meshptr, &
                    ipType=TypeQuadratureOpt%equidistance)

  CALL geoobj%Initiate(baseContinuity="H1", &
                       baseInterpolation="Lagrange", &
                       order=1, mesh=meshptr, &
                       ipType=TypeQuadratureOpt%equidistance)

  globalElement = 1; islocal = .TRUE.
  CALL obj%GetQuadraturePoints(quad=quad, globalElement=globalElement, &
                             quadratureType=TypeQuadratureOpt%GaussLegendre, &
                               order=1, islocal=islocal)

  CALL obj%GetLocalElemshapeData(quad=quad, elemsd=elemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL geoobj%GetLocalElemshapeData(quad=quad, elemsd=geoelemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL meshptr%GetNodeCoord(nodecoord=nodecoord, nrow=ii, ncol=jj, &
                            globalElement=globalElement, islocal=islocal)

  CALL obj%GetGlobalElemshapeData(elemsd=elemsd, xij=nodecoord(1:nsd, 1:jj), &
                               globalElement=globalElement, islocal=islocal, &
                                  geoelemsd=geoelemsd)

  found = SUM(elemsd%N(1:3, :), dim=1)
  want = 1.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%N")

  found(1) = SUM(elemsd%dNdXi(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXi(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXt(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXt")

  found(1) = SUM(elemsd%dNdXt(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXt")

END SUBROUTINE test2

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

SUBROUTINE test3

  REAL(DFP) :: found(1), want(1)

  order = 3
  CALL obj%Initiate(baseContinuity=baseContinuity, &
                    baseInterpolation=baseInterpolation, &
                    order=order, mesh=meshptr, &
                    ipType=TypeQuadratureOpt%equidistance)

  CALL geoobj%Initiate(baseContinuity="H1", &
                       baseInterpolation="Lagrange", &
                       order=1, mesh=meshptr, &
                       ipType=TypeQuadratureOpt%equidistance)

  globalElement = 1; islocal = .TRUE.
  CALL obj%GetQuadraturePoints(quad=quad, globalElement=globalElement, &
                             quadratureType=TypeQuadratureOpt%GaussLegendre, &
                               order=1, islocal=islocal)

  CALL obj%GetLocalElemshapeData(quad=quad, elemsd=elemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL geoobj%GetLocalElemshapeData(quad=quad, elemsd=geoelemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL meshptr%GetNodeCoord(nodecoord=nodecoord, nrow=ii, ncol=jj, &
                            globalElement=globalElement, islocal=islocal)

  CALL obj%GetGlobalElemshapeData(elemsd=elemsd, xij=nodecoord(1:nsd, 1:jj), &
                               globalElement=globalElement, islocal=islocal, &
                                  geoelemsd=geoelemsd)

  found = SUM(elemsd%N(1:3, :), dim=1)
  want = 1.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%N")

  found(1) = SUM(elemsd%dNdXi(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXi(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXt(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXt")

  found(1) = SUM(elemsd%dNdXt(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXt")

END SUBROUTINE test3

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

END PROGRAM main

! total nodes = 25
! total elements = 16
! total faces = 40
! total edges = 0

Example 2

!> author: Vikas Sharma, Ph. D.
! date: 2025-06-09
! summary:  This program tests the GetLocalElemshapeData
! method of the FEDOF class.

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 BaseType, ONLY: QuadraturePoint_, TypeQuadratureOpt, ElemshapeData_
USE QuadraturePoint_Method
USE ElemshapeData_Method
USE ApproxUtility

IMPLICIT NONE

TYPE(FEDOF_) :: obj, geoobj
TYPE(FEDomain_) :: dom
CLASS(AbstractMesh_), POINTER :: meshptr => NULL()
CHARACTER(*), PARAMETER :: &
  filename = "../../FEMesh/examples/meshdata/small_tri6_mesh.h5", &
  baseContinuity = "H1", &
  baseInterpolation = "Heirarchical", &
  testname = baseContinuity//" "//baseInterpolation//" GetLocalElemshapeData "

TYPE(HDF5File_) :: meshfile

TYPE(QuadraturePoint_) :: quad

TYPE(ElemshapeData_) :: elemsd, geoelemsd

INTEGER(I4B) :: globalElement, telements, order, &
                nodecon(100), ii, jj, nsd

REAL(DFP) :: nodecoord(3, 100)

LOGICAL(LGT) :: islocal, isok

CALL e%setQuietMode(EXCEPTION_INFORMATION, .TRUE.)
CALL meshfile%Initiate(filename, mode="READ")
CALL meshfile%OPEN()
CALL dom%Initiate(meshfile, '')
meshptr => dom%GetMeshPointer()
nsd = meshptr%GetNSD()

CALL test1
CALL test2
CALL test3

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

CONTAINS

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

SUBROUTINE test1

  REAL(DFP) :: found(1), want(1)

  order = 1
  CALL obj%Initiate(baseContinuity=baseContinuity, &
                    baseInterpolation=baseInterpolation, &
                    order=order, mesh=meshptr, &
                    ipType=TypeQuadratureOpt%equidistance)

  globalElement = 1; islocal = .TRUE.
  CALL obj%GetQuadraturePoints(quad=quad, globalElement=globalElement, &
                             quadratureType=TypeQuadratureOpt%GaussLegendre, &
                               order=order, islocal=islocal)

  CALL obj%GetLocalElemshapeData(quad=quad, elemsd=elemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL meshptr%GetNodeCoord(nodecoord=nodecoord, nrow=ii, ncol=jj, &
                            globalElement=globalElement, islocal=islocal)

  CALL obj%GetGlobalElemshapeData(elemsd=elemsd, xij=nodecoord(1:nsd, 1:jj), &
                                 globalElement=globalElement, islocal=islocal)

  found = SUM(elemsd%N, dim=1)
  want = 1.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXi(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXi(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXt(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

  found(1) = SUM(elemsd%dNdXt(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname)

END SUBROUTINE test1

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

SUBROUTINE test2

  REAL(DFP) :: found(1), want(1)

  order = 2
  CALL obj%Initiate(baseContinuity=baseContinuity, &
                    baseInterpolation=baseInterpolation, &
                    order=order, mesh=meshptr, &
                    ipType=TypeQuadratureOpt%equidistance)

  CALL geoobj%Initiate(baseContinuity="H1", &
                       baseInterpolation="Lagrange", &
                       order=1, mesh=meshptr, &
                       ipType=TypeQuadratureOpt%equidistance)

  globalElement = 1; islocal = .TRUE.
  CALL obj%GetQuadraturePoints(quad=quad, globalElement=globalElement, &
                             quadratureType=TypeQuadratureOpt%GaussLegendre, &
                               order=1, islocal=islocal)

  CALL obj%GetLocalElemshapeData(quad=quad, elemsd=elemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL geoobj%GetLocalElemshapeData(quad=quad, elemsd=geoelemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL meshptr%GetNodeCoord(nodecoord=nodecoord, nrow=ii, ncol=jj, &
                            globalElement=globalElement, islocal=islocal)

  CALL obj%GetGlobalElemshapeData(elemsd=elemsd, xij=nodecoord(1:nsd, 1:jj), &
                               globalElement=globalElement, islocal=islocal, &
                                  geoelemsd=geoelemsd)

  found = SUM(elemsd%N(1:3, :), dim=1)
  want = 1.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%N")

  found(1) = SUM(elemsd%dNdXi(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXi(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXt(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXt")

  found(1) = SUM(elemsd%dNdXt(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test2 elemsd%dNdXt")

END SUBROUTINE test2

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

SUBROUTINE test3

  REAL(DFP) :: found(1), want(1)

  order = 3
  CALL obj%Initiate(baseContinuity=baseContinuity, &
                    baseInterpolation=baseInterpolation, &
                    order=order, mesh=meshptr, &
                    ipType=TypeQuadratureOpt%equidistance)

  CALL geoobj%Initiate(baseContinuity="H1", &
                       baseInterpolation="Lagrange", &
                       order=1, mesh=meshptr, &
                       ipType=TypeQuadratureOpt%equidistance)

  globalElement = 1; islocal = .TRUE.
  CALL obj%GetQuadraturePoints(quad=quad, globalElement=globalElement, &
                             quadratureType=TypeQuadratureOpt%GaussLegendre, &
                               order=1, islocal=islocal)

  CALL obj%GetLocalElemshapeData(quad=quad, elemsd=elemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL geoobj%GetLocalElemshapeData(quad=quad, elemsd=geoelemsd, &
                                 globalElement=globalElement, islocal=islocal)

  CALL meshptr%GetNodeCoord(nodecoord=nodecoord, nrow=ii, ncol=jj, &
                            globalElement=globalElement, islocal=islocal)

  CALL obj%GetGlobalElemshapeData(elemsd=elemsd, xij=nodecoord(1:nsd, 1:jj), &
                               globalElement=globalElement, islocal=islocal, &
                                  geoelemsd=geoelemsd)

  found = SUM(elemsd%N(1:3, :), dim=1)
  want = 1.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%N")

  found(1) = SUM(elemsd%dNdXi(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXi(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXi")

  found(1) = SUM(elemsd%dNdXt(:, 1, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXt")

  found(1) = SUM(elemsd%dNdXt(:, 2, 1), dim=1)
  want(1) = 0.0_DFP
  isok = found(1) .approxeq.want(1)
  CALL OK(isok, testname//" test3 elemsd%dNdXt")

END SUBROUTINE test3

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

END PROGRAM main

! total nodes = 25
! total elements = 16
! total faces = 40
! total edges = 0

Syntax​

Arguments​

Description​

Implementation Details​

Example Usage​

Notes​

Example 1​

Example 2​