MassMatrix example 1

!!! 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, we use

• [[ReferenceLine_]] element,
• [[QuadraturePoint_]] are GaussLegendre
• order of integrand is 2.

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

This type of mass matrix is useful in cases where $rho$ is a constant.

Modules and classes

Usage

PROGRAM main
    USE easifemBase
    IMPLICIT NONE
    TYPE(elemshapedata_) :: test, trial
    TYPE(quadraturepoint_) :: quad
    TYPE(referenceline_) :: refelem
    REAL(DFP), ALLOCATABLE :: mat(:, :), XiJ(:, :)
    integer( I4B ), parameter :: order = 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_]].

    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.

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

??? example "Results"

    mat:       
------------------
0.666667  0.333333
0.333333  0.666667

!!! settings "Cleanup"

END PROGRAM main