ConvectiveMatrix example 24

!!! note "" This example shows how to USE the SUBROUTINE called ConvectiveMatrix to create a convective matrix in space domain for Triangle3 element.

Here, we want to DO the following.

$$M(I,J) = \int_{\Omega} N^I \frac{\partial N^J}{\partial x} d{\Omega}$$ $$M(I,J) = \int_{\Omega} \frac{\partial N^I}{\partial x} N^J d{\Omega}$$ $$M(I,J) = \int_{\Omega} N^I \frac{\partial N^J}{\partial y} d{\Omega}$$ $$M(I,J) = \int_{\Omega} \frac{\partial N^I}{\partial y} N^J d{\Omega}$$ $$M(I,J) = \int_{\Omega} N^I \frac{\partial N^J}{\partial z} d{\Omega}$$ $$M(I,J) = \int_{\Omega} \frac{\partial N^I}{\partial z} N^J d{\Omega}$$

In this example, convective matrix is formed for

• [[ReferenceTriangle_]] element
• [[QuadraturePoint_]] GaussLegendre

Modules and classes

• [[ElemshapeData_]]
• [[QuadraturePoint_]]
• [[ReferenceTriangle_]]
• [[FEVariable_]]

Usage

PROGRAM main
    USE easifemBase
    IMPLICIT NONE
    TYPE(ElemshapeData_) :: test, trial
    TYPE(QuadraturePoint_) :: quad
    TYPE(ReferenceTriangle_) :: refelem
    REAL(DFP), ALLOCATABLE :: mat(:, :)
    REAL(DFP), ALLOCATABLE :: XiJ(:, :)
    INTEGER( I4B ), PARAMETER :: order = 1, nsd=2

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

    XiJ = RESHAPE([0,0, 1,0,0,1], [2, 3])

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

    refelem = referenceTriangle(nsd=nsd)

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

    CALL initiate( obj=quad, refelem=refelem, order=2*order-1, &
        & 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 following convective matrix.

$$M(I,J) = \int_{\Omega} N^{J} \frac{\partial N^{I}}{\partial x} d{\Omega}$$

    mat=ConvectiveMatrix(test=test, trial=test, term1=1, term2=0, dim=1)
    CALL Display(mat, "mat:")

??? example "Results"

            mat:
-------------------------------
-0.166667  -0.166667  -0.166667
0.166667   0.166667   0.166667
0.000000   0.000000   0.000000

!! note "" Let us now create the following convective matrix.

$$M(I,J) = \int_{\Omega} N^{J} \frac{\partial N^{I}}{\partial y} d{\Omega}$$

    mat=ConvectiveMatrix(test=test, trial=test, term1=1, term2=0, dim=2)
    CALL Display(mat, "mat:")

??? example "Results"

            mat:
-------------------------------
-0.166667  -0.166667  -0.166667
0.000000   0.000000   0.000000
0.166667   0.166667   0.166667

!! note "" Let us now create the following convective matrix.

$$M(I,J) = \int_{\Omega} N^{I} \frac{\partial N^{J}}{\partial x} d{\Omega}$$

    mat=ConvectiveMatrix(test=test, trial=test, term1=0, term2=1, dim=1)
    CALL Display(mat, "mat:")

??? example "Results"

            mat:
-----------------------------
-0.166667  0.166667  0.000000
-0.166667  0.166667  0.000000
-0.166667  0.166667  0.000000

!! note "" Let us now create the following convective matrix.

$$M(I,J) = \int_{\Omega} N^{I} \frac{\partial N^{J}}{\partial y} d{\Omega}$$

    mat=ConvectiveMatrix(test=test, trial=test, term1=0, term2=1, dim=2)
    CALL Display(mat, "mat:")

??? example "Results"

            mat:
-----------------------------
-0.166667  0.000000  0.166667
-0.166667  0.000000  0.166667
-0.166667  0.000000  0.166667

!!! settings "Cleanup"

END PROGRAM main