DiffusionMatrix example 3

!!! note "" This example shows how to USE the SUBROUTINE called DiffusionMatrix to create a mass matrix in space domain.

Here, we want to DO the following.

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

• Mixed FEM, test on Line2, trial on Line3

Modules and classes

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

Usage

PROGRAM main
    USE easifemBase
    IMPLICIT NONE
    TYPE(Elemshapedata_) :: test, elemsdForsimplex, trial
    TYPE(Quadraturepoint_) :: quad
    TYPE(Referenceline_) :: simplexElem, refElemFortest, refElemFortrial
    REAL(DFP), ALLOCATABLE :: mat(:, :)
    REAL( DFP ), parameter :: xij(1,2) = RESHAPE([-1, 1], [1, 2])
    INTEGER( I4B ), PARAMETER :: orderFortest = 1, orderForTrial = 2, factor=2

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

    simplexElem = referenceline(nsd=1)
    CALL simplexElem%LagrangeElement(order=orderForTest, highOrderObj=refElemForTest)
    CALL simplexElem%LagrangeElement(order=orderForTrial, highOrderObj=refElemForTrial)

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

    CALL Initiate( obj=quad, refelem=simplexElem, &
        & order=factor*refElemForTrial%order, &
        & quadratureType='GaussLegendre' )

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

    CALL Initiate(obj=elemsdForsimplex, &
        & quad=quad, &
        & refelem=simplexElem, &
        & ContinuityType=typeH1, &
        & InterpolType=typeLagrangeInterpolation)

!!! note "" Initiate an instance of [[ElemeshapeData_]] for test function.

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

!!! note "" Initiate an instance of [[ElemeshapeData_]] for trial function.

    CALL Initiate(obj=trial, &
        & quad=quad, &
        & refelem=refElemForTrial, &
        & ContinuityType=typeH1, &
        & InterpolType=typeLagrangeInterpolation)
    CALL Set(obj=trial, val=xij, N=elemsdForSimplex%N, &
        & dNdXi=elemsdForSimplex%dNdXi)

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

    mat=DiffusionMatrix(test=test, trial=trial)
    CALL Display(mat, "mat:")

??? example "Results"

            mat:             
------------------------------
0.500000  -0.500000  0.000000
-0.500000   0.500000  0.000000

!!! settings "Cleanup"

END PROGRAM main