STElemshapeData example 1

Modules and classes

• [[STElemshapeData_]]

Usage

!!! note "" IMPORT modules and declare variables.

PROGRAM main
    USE easifemBase
    IMPLICIT NONE
    TYPE(STElemshapeData_), ALLOCATABLE :: obj(:)
    TYPE(ElemshapeData_) :: time_elemsd
    TYPE(Quadraturepoint_) :: quad
    CLASS(ReferenceElement_), POINTER :: refelem => NULL()
    CLASS(ReferenceElement_), POINTER :: highOrderElem => NULL()
    INTEGER(I4B) :: ii, NNT
    INTEGER(I4B), PARAMETER :: nsd=2, nns=3
    REAL(DFP) :: tiJ(1, 2)
    REAL(DFP), ALLOCATABLE :: xiJ(:, :)
    ! spatial nodal coordinates
    REAL(DFP), ALLOCATABLE :: xiJa(:, :, :)
    ! spatial-temporal nodal coordinates

!!! note "" First, we initiate a [[ReferenceLine_]] element for time domain. Note that nsd should be 1 when making reference element for time domain.

    ALLOCATE (ReferenceLine_ :: refelem)
    refelem = ReferenceLine(nsd=1)
    CALL Display(refelem, "ReferenceElement :: ")

??? example "Results"

#ReferenceElement ::
ElemType : Line2
XiDimension :: 1
NSD : 1
Order : 1
EntityCounts(0) : 2
EntityCounts(1) : 1
EntityCounts(2) : 0
EntityCounts(3) : 0
Node( 1 ) :
------------
-1.00000
0.00000
0.00000
Node( 2 ) :
------------
1.00000
0.00000
0.00000
#Topology( 1 ) :
ElemType : Point1
XiDim : 0
Nptrs :
--------
1
#Topology( 2 ) :
ElemType : Point1
XiDim : 0
Nptrs :
--------
2
#Topology( 3 ) :
ElemType : Line2
XiDim : 1
Nptrs :
--------
1
2

!!! note "" Higher order Lagrange element can be obtained, NNT denotes number of nodes in time element. For line-element order will be equal to NNT-1.

    NNT = 2
    ALLOCATE (ReferenceLine_ :: highOrderElem)
    CALL refelem%LagrangeElement(order=NNT - 1, &
      & HighOrderObj=highOrderElem)

!!! note "" Generate Gauss-Legendre quadrature points on time element.

    CALL Initiate(obj=quad, refelem=refelem, order=refelem%order, &
      & quadratureType="GaussLegendre" )
    CALL display(quad, 'quad for time element :: ')

??? example "Results"

Quad for time element ::!

        Weights    |      Points
-----------------------------------------
    2.0000000        0.0000000
-----------------------------------------

!!! note "" Setting shape FUNCTION for time. This will setup following quantities.

• $T$
• $\frac{dT}{d\theta}$
• $J_t$
• $W_{t}$
• $\theta$
• tiJ it denotes the nodal values of time element.

    tiJ(1, :) = [-1.0, 1.0]
    CALL initiate( &
      & obj=time_elemsd, quad=quad, refelem=refelem, &
      & ContinuityType=typeH1, InterpolType=TypeLagrangeInterpolation)
    CALL Deallocate(quad)
    CALL Set(obj=time_elemsd, val=tiJ, N=time_elemsd%N, &
        & dNdXi=time_elemsd%dNdXi)
    CALL Display(time_elemsd, "time_elemsd :")

??? example "Results"

time_elemsd :

SHAPE FUNCTION IN SPACE ::

Quadrature Point

        Weights    |      Points
-----------------------------------------
    2.0000000        0.0000000
-----------------------------------------

obj%N
--------
0.500000
0.500000

obj%dNdXi( :, :, 1 ) =
-----------------------
    -0.500000
        0.500000

obj%dNdXt( :, :, 1 ) =
-----------------------
    -0.500000
        0.500000

obj%Jacobian( :, :, 1 ) =
--------------------------
        1.00000

obj%Js
-------
1.00000

obj%Thickness
-------------
1.00000

obj%Coord
---------
0.00000

obj%Normal
----------
0.00000
0.00000
0.00000

!!! note "" Now we initiate an instance for storing space-time shape FUNCTION DATA, that is [[STElemshapeData_]] object. This will extract time-shape DATA info from elemsd and put it inside

• obj(i)%T
• obj(i)%dTdTheta
• obj(i)%Jt
• obj(i)%Wt
• obj(i)%Theta

    CALL Initiate(obj=obj, elemsd=time_elemsd)

!!! note "" Generating shape functions for space-elements. Here, we are selecting a triangular element

    ALLOCATE (ReferenceTriangle_ :: refelem)
    refelem = ReferenceTriangle(nsd=nsd)
    CALL Initiate(obj=quad, refelem=refelem, order=1, quadratureType='GaussLegendre' )
    CALL Display(quad, "quad in triangle: ")

??? example "Results"

Quad in triangle:

        Weights    |      Points
-----------------------------------------
0.50000000       0.33333334     0.33333334
-----------------------------------------

!!! note "" Setting local DATA of shape FUNCTION in space. This will set

• N
• dNdXi
• Ws
• Quad

    DO ii = 1, SIZE(obj)
      CALL initiate( &
        & obj=obj(ii), quad=quad, refelem=refelem, &
        & ContinuityType=typeH1, InterpolType=TypeLagrangeInterpolation)
    END DO

!!! note "" Setting the remaining DATA in obj. Here, xiJa are the space-time nodal coordinates.

    ALLOCATE (xiJ(nsd, nns), xiJa(nsd, nns, nnt))
    xiJ = RESHAPE([0, 0, 1, 0, 0, 1], [nsd, nns])
    DO ii = 1, nnt; xiJa(:, :, ii) = xiJ; END DO
    DO ii = 1, SIZE(obj)
        CALL set(obj=obj(ii), val=xiJa, N=obj(ii)%N, &
            & dNdXi=obj(ii)%dNdXi, T=obj(ii)%T )
        CALL Display(obj(ii), "obj("//tostring(ii)//')=' )
    END DO

??? example "Results"

SHAPE FUNCTION IN SPACE ::

Quadrature Point

        Weights    |      Points
-----------------------------------------
0.50000000       0.33333334     0.33333334
-----------------------------------------

obj%N
--------
0.333333
0.333333
0.333333

obj%dNdXi( :, :, 1 ) =
-----------------------
-1.00000  -1.00000
1.00000   0.00000
0.00000   1.00000

obj%dNdXt( :, :, 1 ) =
-----------------------
-1.00000  -1.00000
1.00000   0.00000
0.00000   1.00000

obj%Jacobian( :, :, 1 ) =
--------------------------
    1.00000  0.00000
    0.00000  1.00000

obj%Js
-------
1.00000

obj%Thickness
-------------
1.00000

obj%Coord
---------
0.333333
0.333333

obj%Normal
----------
0.00000
0.00000
0.00000

SHAPE FUNCTION IN TIME ::

obj%Jt :: 1.00000
obj%Theta :: 0.00000
obj%Wt :: 2.00000

obj%T
--------
0.500000
0.500000

obj%dTdTheta
------------
-0.500000
0.500000

obj%dNTdt( :, :, 1 ) =
-----------------------
-0.166667  0.166667
-0.166667  0.166667
-0.166667  0.166667

obj%dNTdXt( :, :, 1, 1 ) =
---------------------------
-0.500000  -0.500000
    0.500000   0.500000
    0.000000   0.000000
obj%dNTdXt( :, :, 2, 1 ) =
---------------------------
-0.500000  -0.500000
    0.000000   0.000000
    0.500000   0.500000

!!! settings "Cleanup"

END PROGRAM