MassMatrix example 2

!!! 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.

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

• Line3 element

Modules and classes

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

Usage

PROGRAM main
    USE easifemBase
    IMPLICIT NONE
    TYPE(Elemshapedata_) :: test, elemsdForsimplex
    TYPE(Quadraturepoint_) :: quad
    TYPE(Referenceline_) :: simplexElem, refElem
    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_]].

    simplexElem = referenceline(nsd=1)
    CALL simplexElem%LagrangeElement(order=order, highOrderObj=refelem)

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

    CALL initiate( obj=quad, refelem=refelem, order=order*refelem%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_]].

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

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

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

??? example "Results"

            mat:            
----------------------------
1.16667   0.16667  -1.33333
0.16667   1.16667  -1.33333
-1.33333  -1.33333   2.66667

!!! settings "Cleanup"

END PROGRAM main