MassMatrix example 4

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

Here, we want to DO the following.

$$\int_{\Omega } N^{I}\rho N^{J}d\Omega$$

!!! warning "" rho can be a constant, or a FUNCTION of spatial coordinates, or some nonlinear FUNCTION.

In this example, following mass matrix is formed for [[ReferenceLine_]] element, [[QuadraturePoint_]] are GaussLegendre.

$$\int_{\Omega } N^{I} N^{J}d\Omega$$

This TYPE of mass matrix is useful when $rho$ is a constant.

Modules and classes

Usage

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

!!! note "" Let us now create the physical coordinate of the line element.

    XiJ = RESHAPE([-1, 1], [1, 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=orderForTest+orderForTrial, &
        & 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=MassMatrix(test=trial, trial=test)
    CALL Display(mat, "mat:")

??? example "Results"

    mat:      
----------------
0.33333  0.00000
0.00000  0.33333
0.66667  0.66667

!!! settings "Cleanup"

END PROGRAM main