Initiate

We can construct an instance of ElemshapeData by using a generic method called Initiate(). There are several ways to construct the instance. You can learn about this method from following examples.

Interface 1

MODULE SUBROUTINE Initiate(obj, quad, refElem, continuityType, &
                           interpolType)
  CLASS(ElemshapeData_), INTENT(INOUT) :: obj
  !! ElemshapeData to be formed
  CLASS(QuadraturePoint_), INTENT(IN) :: quad
  !! Quadrature points
  CLASS(ReferenceElement_), INTENT(IN) :: refelem
  !! reference element
  CHARACTER(LEN=*), INTENT(IN) :: continuityType
  !! continuity/ conformity of shape function
  CHARACTER(LEN=*), INTENT(IN) :: interpolType
  !! interpolation/polynomial family type
END SUBROUTINE Initiate

Interface 2

MODULE SUBROUTINE Initiate(obj1, obj2)
  TYPE(ElemshapeData_), INTENT(INOUT) :: obj1
  TYPE(ElemshapeData_), INTENT(IN) :: obj2
END SUBROUTINE Initiate

In interface-2, we copy an instance of ElemshapeData into another instance of same class. This method is used for extending the [[#Assignment(=)]] operator.

Interface 3

MODULE PURE SUBROUTINE Initiate(obj, elemsd)
  TYPE(STElemshapeData_), ALLOCATABLE, INTENT(INOUT) :: obj(:)
  TYPE(ElemshapeData_), INTENT(IN) :: elemsd
  !! It has information about location shape function for time element
END SUBROUTINE Initiate

• This subroutine initiates the shape-function data related to time domain in the instance of STElemshapeData_.
• User should provide an instance of Elemshapedata_ elemsd,
• The elemsd, actually contains the information of the shape-function in the time domain
• The shape-function data in the time domain is
  • $T$
  • $\frac{dT}{d\theta}$
• This routine uses elemsd to set obj%T, obj%dTdTheta, obj%Jt, obj%Wt, obj%Theta.

Assignment(=)

MODULE SUBROUTINE Initiate(obj1, obj2)
  TYPE(ElemshapeData_), INTENT(INOUT) :: obj1
  TYPE(ElemshapeData_), INTENT(IN) :: obj2
END SUBROUTINE Initiate

MODULE SUBROUTINE Initiate(obj1, obj2)
  TYPE(ElemshapeData_), INTENT(INOUT) :: obj1
  TYPE(STElemshapeData_), INTENT(IN) :: obj2
END SUBROUTINE Initiate

MODULE SUBROUTINE Initiate(obj1, obj2)
  TYPE(STElemshapeData_), INTENT(INOUT) :: obj1
  TYPE(ElemshapeData_), INTENT(IN) :: obj2
END SUBROUTINE Initiate

MODULE SUBROUTINE Initiate(obj1, obj2)
  TYPE(STElemshapeData_), INTENT(INOUT) :: obj1
  TYPE(STElemshapeData_), INTENT(IN) :: obj2
END SUBROUTINE Initiate

Examples: shape functions on line element

️Lagrange polynomial

This example tests the Initiate method for constructing ElemShapeData.

PROGRAM main
USE GlobalData, ONLY: I4B, DFP, LGT
USE BaseType, ONLY: ElemShapeData_, QuadraturePoint_, ReferenceLine_, &
                    TypePolynomialOpt, TypeQuadratureOpt, TypeH1, &
                    TypeLagrangeInterpolation
USE ReferenceElement_Method
USE ReferenceLine_Method
USE QuadraturePoint_Method
USE ElemShapeData_Method
USE Display_Method
USE String_Class

IMPLICIT NONE

TYPE(ElemShapeData_) :: elemsd
TYPE(QuadraturePoint_) :: quad
TYPE(ReferenceLine_) :: refelem
INTEGER(I4B) :: quadratureType, ipType, basisType, order

refelem = ReferenceLine(nsd=1_I4B)

order = 4_I4B
quadratureType = TypeQuadratureOpt%gaussLegendre

CALL Initiate(obj=quad, refElem=refElem, order=order, &
              quadratureType=quadratureType)

order = 1
ipType = TypeQuadratureOpt%equidistance
basisType = TypePolynomialOpt%monomial

CALL Initiate(obj=elemsd, quad=quad, refelem=refelem, &
              baseContinuity=TypeH1, &
              baseInterpolation=TypeLagrangeInterpolation, &
              ipType=ipType, basisType=basisType, order=order)

! CALL Display(elemsd%N, "elemsd: ")
! CALL Display(elemsd%dNdXi, "elemsd: ")

CALL Display(ElemShapeData_MdEncode(elemsd), "")

END PROGRAM main

See results

x1	-0.7746	1.59632E-16	0.7746
w	0.55556	0.88889	0.55556

N

	$ips_{1}$	$ips_{2}$	$ips_{3}$
$N_{1}$	0.8873	0.5	0.1127
$N_{2}$	0.1127	0.5	0.8873

dNdXi(:, :, 1 )

	$\frac{\partial N}{\partial \xi_{1}}$
$\frac{\partial N^{1}}{\partial \xi}$	-0.5
$\frac{\partial N^{2}}{\partial \xi}$	0.5

dNdXi(:, :, 2 )

	$\frac{\partial N}{\partial \xi_{1}}$
$\frac{\partial N^{1}}{\partial \xi}$	-0.5
$\frac{\partial N^{2}}{\partial \xi}$	0.5

dNdXi(:, :, 3 )

	$\frac{\partial N}{\partial \xi_{1}}$
$\frac{\partial N^{1}}{\partial \xi}$	-0.5
$\frac{\partial N^{2}}{\partial \xi}$	0.5

dNdXt(:, :, 1 )

	$\frac{\partial N}{\partial {x}_{1}}$
$\frac{\partial N^{1}}{\partial x}$	0
$\frac{\partial N^{2}}{\partial x}$	0

dNdXt(:, :, 2 )

	$\frac{\partial N}{\partial {x}_{1}}$
$\frac{\partial N^{1}}{\partial x}$	0
$\frac{\partial N^{2}}{\partial x}$	0

dNdXt(:, :, 3 )

	$\frac{\partial N}{\partial {x}_{1}}$
$\frac{\partial N^{1}}{\partial x}$	0
$\frac{\partial N^{2}}{\partial x}$	0

jacobian(:, :, 1 )

	col-1
row-1	0

jacobian(:, :, 2 )

	col-1
row-1	0

jacobian(:, :, 3 )

	col-1
row-1	0

Js

	$js_{1}$	$js_{2}$	$js_{3}$
js	0	0	0

thickness

	thickness${}_{1}$	thickness${}_{2}$	thickness${}_{3}$
thickness	1	1	1

normal

	$ips_{1}$	$ips_{2}$	$ips_{3}$
$n_{1}$	0	0	0
$n_{2}$	0	0	0
$n_{3}$	0	0	0

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