DiffusionMatrix example 4

!!! note "" This example shows how to use the subroutine called DiffusionMatrix to create a Diffusion matrix in space domain.

Here, we want to do the following.

$$\int^{}_{\Omega } \frac{\partial N^{I}}{\partial x_{i}} \frac{\partial N^{J}}{\partial x_{i}} d\Omega$$

• Line2 element

Modules and classes

• [[ElemshapeData_]]
• [[QuadraturePoint_]]
• [[ReferenceLine_]]
• [[FEVariable_]]

Usage

PROGRAM main
    USE easifemBase
    IMPLICIT NONE
    TYPE(elemshapedata_) :: test, trial
    TYPE(quadraturepoint_) :: quad
    TYPE(referenceline_) :: refelem
    TYPE(FEVariable_) :: kvar
    REAL( DFP ), parameter :: xij(1,2) = RESHAPE([-1, 1], [1, 2])
    REAL(DFP), ALLOCATABLE :: mat(:, :)
    integer( I4B ), parameter :: order = 2

!!! note "" Now we create an instance of [[ReferenceLine_]].

    refelem = referenceline(nsd=1)

!!! note "" Here, we create the quadrature points.

    CALL initiate( obj=quad, refelem=refelem, order=order, &
        & quadratureType='GaussLegendre' )

!!! note "" Initiate an instance of [[ElemshapeData_]]. You can learn more about it from [[ElemshapeData_test]]

    CALL initiate(obj=test, &
        & quad=quad, &
        & refelem=refelem, &
        & ContinuityType=typeH1, &
        & InterpolType=typeLagrangeInterpolation)
    CALL Set( obj=test, val=xij, N=test%N, dNdXi=test%dNdXi)

!!! note "" Let us now create the mass matrix.

    kvar = NodalVariable(1.0_DFP, TypeFEVariableScalar, TypeFEVariableConstant)
    mat=DiffusionMatrix(test=test, trial=test, k=kvar)
    CALL Display(mat, "mat:")

??? example "Results"

        mat:        
--------------------
0.500000  -0.500000
-0.500000   0.500000

!!! settings "Cleanup"

END PROGRAM main