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docs/blog/authors.yml

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socials:
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x: vickysharma0812
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github: vickysharma0812
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linkedin: vickysharma0812
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researchgate: https://www.researchgate.net/profile/Vikas-Sharma-41
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shishiousan:
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name: Shion Shimizu
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image_url: https://raw.githubusercontent.com/easifem/authors/refs/heads/main/images/shishiousan.jpg
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socials:
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github: shishiousan
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linkedin: shion-shimizu-838997340
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researchgate: https://www.researchgate.net/profile/Shion-Shimizu

docs/docs-api/MassMatrix/examples/MassMatrix_test_3.F90

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<<<<<<< HEAD
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---
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title: MassMatrix example 3
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author: Vikas Sharma, Ph.D.
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date: 20 Nov 2021
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update: 20 Nov 2021
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tags:
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- ReferenceLine
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- ReferenceLine/Initiate
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- QuadraturePoint/Initiate
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- ElemshapeData/Initiate
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- MassMatrix
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---
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# MassMatrix example 3
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!!! note ""
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This example shows how to USE the SUBROUTINE called `MassMatrix` to create a mass matrix in space domain.
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Here, we want to DO the following.
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$$
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\int_{\Omega } N^{I}\rho N^{J}d\Omega
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$$
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!!! warning ""
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`rho` can be a constant, or a FUNCTION of spatial coordinates, or some nonlinear FUNCTION.
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In this example, following mass matrix is formed for [[ReferenceLine_]] element, [[QuadraturePoint_]] are `GaussLegendre`.
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$$
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\int_{\Omega } N^{I} N^{J}d\Omega
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$$
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This TYPE of mass matrix is useful when $rho$ is a constant.
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## Modules and classes
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## Usage
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```fortran
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=======
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>>>>>>> 8a747609 (Adding documentation of mass matrix)
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PROGRAM main
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USE easifemBase
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IMPLICIT NONE
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REAL(DFP), ALLOCATABLE :: mat(:, :), XiJ(:, :)
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INTEGER(I4B), PARAMETER :: orderFortest = 1, orderForTrial = 2
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<<<<<<< HEAD
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!!! note ""
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Let us now create the physical coordinate of the line element.
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```fortran
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XiJ = RESHAPE([-1, 1], [1, 2])
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```
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!!! note ""
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Now we create an instance of [[ReferenceLine_]].
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```fortran
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simplexElem = referenceline(nsd=1)
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CALL simplexElem%LagrangeElement(order=orderForTest, highOrderObj=refElemForTest)
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CALL simplexElem%LagrangeElement(order=orderForTrial, highOrderObj=refElemForTrial)
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```
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!!! note ""
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Here, we create the quadrature points.
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```fortran
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CALL initiate( obj=quad, refelem=simplexElem, order=orderForTest+orderForTrial, &
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& quadratureType='GaussLegendre' )
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```
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!!! note ""
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Initiate an instance of [[ElemshapeData_]]. You can learn more about it from [[ElemshapeData_test]].
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```fortran
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CALL initiate(obj=elemsdForsimplex, &
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& quad=quad, &
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& refelem=simplexElem, &
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& ContinuityType=typeH1, &
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& InterpolType=typeLagrangeInterpolation)
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```
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!!! note ""
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Initiate an instance of [[ElemeshapeData_]] for test function.
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```fortran
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CALL initiate(obj=test, &
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& quad=quad, &
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& refelem=refElemForTest, &
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& ContinuityType=typeH1, &
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& InterpolType=typeLagrangeInterpolation)
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CALL Set(obj=test, val=xij, N=elemsdForSimplex%N, &
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& dNdXi=elemsdForSimplex%dNdXi)
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```
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!!! note ""
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Initiate an instance of [[ElemeshapeData_]] for trial function.
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```fortran
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CALL initiate(obj=trial, &
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& quad=quad, &
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& refelem=refElemForTrial, &
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& ContinuityType=typeH1, &
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& InterpolType=typeLagrangeInterpolation)
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CALL Set(obj=trial, val=xij, N=elemsdForSimplex%N, &
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& dNdXi=elemsdForSimplex%dNdXi)
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```
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!!! note ""
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Let us now create the mass matrix.
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```fortran
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mat=MassMatrix(test=test, trial=trial)
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CALL Display(mat, "mat:")
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```
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=======
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! Let us now create the physical coordinate of the line element.
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XiJ = RESHAPE([-1, 1], [1, 2])
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dNdXi=elemsdForSimplex%dNdXi)
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! Initiate an instance of [[ElemeshapeData_]] for trial function.
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>>>>>>> 8a747609 (Adding documentation of mass matrix)
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CALL initiate(obj=trial, &
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quad=quad, &

docs/docs-api/MassMatrix/examples/MassMatrix_test_4.F90

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<<<<<<< HEAD
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---
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title: MassMatrix example 4
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author: Vikas Sharma, Ph.D.
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date: 20 Nov 2021
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update: 20 Nov 2021
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tags:
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- ReferenceLine
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- ReferenceLine/Initiate
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- QuadraturePoint/Initiate
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- ElemshapeData/Initiate
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- MassMatrix
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---
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# MassMatrix example 4
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!!! note ""
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This example shows how to USE the SUBROUTINE called `MassMatrix` to create a mass matrix in space domain.
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Here, we want to DO the following.
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$$
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\int_{\Omega } N^{I}\rho N^{J}d\Omega
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$$
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!!! warning ""
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`rho` can be a constant, or a FUNCTION of spatial coordinates, or some nonlinear FUNCTION.
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In this example, following mass matrix is formed for [[ReferenceLine_]] element, [[QuadraturePoint_]] are `GaussLegendre`.
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$$
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\int_{\Omega } N^{I} N^{J}d\Omega
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$$
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This TYPE of mass matrix is useful when $rho$ is a constant.
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## Modules and classes
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## Usage
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```fortran
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=======
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>>>>>>> 8a747609 (Adding documentation of mass matrix)
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PROGRAM main
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USE easifemBase
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IMPLICIT NONE
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REAL(DFP), ALLOCATABLE :: mat(:, :), XiJ(:, :)
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INTEGER(I4B), PARAMETER :: orderFortest = 1, orderForTrial = 2
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<<<<<<< HEAD
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!!! note ""
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Let us now create the physical coordinate of the line element.
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```fortran
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XiJ = RESHAPE([-1, 1], [1, 2])
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```
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!!! note ""
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Now we create an instance of [[ReferenceLine_]].
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```fortran
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simplexElem = referenceline(nsd=1)
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CALL simplexElem%LagrangeElement(order=orderForTest, highOrderObj=refElemForTest)
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CALL simplexElem%LagrangeElement(order=orderForTrial, highOrderObj=refElemForTrial)
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```
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!!! note ""
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Here, we create the quadrature points.
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```fortran
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CALL initiate( obj=quad, refelem=simplexElem, order=orderForTest+orderForTrial, &
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& quadratureType='GaussLegendre' )
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```
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!!! note ""
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Initiate an instance of [[ElemshapeData_]]. You can learn more about it from [[ElemshapeData_test]].
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```fortran
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=======
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! Let us now create the physical coordinate of the line element.
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XiJ = RESHAPE([-1, 1], [1, 2])
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! Initiate an instance of [[ElemshapeData_]]. You can learn more about it from [[ElemshapeData_test]].
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CALL initiate(obj=elemsdForsimplex, &
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& quad=quad, &
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& refelem=simplexElem, &
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& ContinuityType=typeH1, &
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& InterpolType=typeLagrangeInterpolation)
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<<<<<<< HEAD
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```
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!!! note ""
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Initiate an instance of [[ElemeshapeData_]] for test function.
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```fortran
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CALL initiate(obj=test, &
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& quad=quad, &
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& refelem=refElemForTest, &
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& ContinuityType=typeH1, &
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& InterpolType=typeLagrangeInterpolation)
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CALL Set(obj=test, val=xij, N=elemsdForSimplex%N, &
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& dNdXi=elemsdForSimplex%dNdXi)
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```
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!!! note ""
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Initiate an instance of [[ElemeshapeData_]] for trial function.
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```fortran
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CALL initiate(obj=trial, &
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& quad=quad, &
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& refelem=refElemForTrial, &
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& ContinuityType=typeH1, &
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& InterpolType=typeLagrangeInterpolation)
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CALL Set(obj=trial, val=xij, N=elemsdForSimplex%N, &
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& dNdXi=elemsdForSimplex%dNdXi)
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```
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!!! note ""
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Let us now create the mass matrix.
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```fortran
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mat=MassMatrix(test=trial, trial=test)
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CALL Display(mat, "mat:")
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```
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=======
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! Initiate an instance of [[ElemeshapeData_]] for test function.
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& InterpolType=typeLagrangeInterpolation)
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CALL Set(obj=trial, val=xij, N=elemsdForSimplex%N, &
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& dNdXi=elemsdForSimplex%dNdXi)
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>>>>>>> 8a747609 (Adding documentation of mass matrix)
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! Let us now create the mass matrix.
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