Skip to content

Adding documentation of mass matrix #15

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
vickysharma0812 merged 1 commit into from
Jun 4, 2025
Merged

Adding documentation of mass matrix #15

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
180 changes: 53 additions & 127 deletions docs/docs-api/MassMatrix/examples/MassMatrix_test_3.F90
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,133 +1,59 @@
---
title: MassMatrix example 3
author: Vikas Sharma, Ph.D.
date: 20 Nov 2021
update: 20 Nov 2021
tags:
- ReferenceLine
- ReferenceLine/Initiate
- QuadraturePoint/Initiate
- ElemshapeData/Initiate
- MassMatrix
---

# MassMatrix example 3

!!! 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

```fortran
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.

```fortran
XiJ = RESHAPE([-1, 1], [1, 2])
```

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

```fortran
simplexElem = referenceline(nsd=1)
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

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

XiJ = RESHAPE([-1, 1], [1, 2])

! 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.

```fortran
! 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]].

```fortran
CALL initiate(obj=elemsdForsimplex, &
& quad=quad, &
& refelem=simplexElem, &
& ContinuityType=typeH1, &
& InterpolType=typeLagrangeInterpolation)
```

!!! note ""
Initiate an instance of [[ElemeshapeData_]] for test function.

```fortran
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.

```fortran
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.

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

??? example "Results"

```bash
mat:
-------------------------
0.33333 0.00000 0.66667
0.00000 0.33333 0.66667
```

!!! settings "Cleanup"

```fortran
quadratureType='GaussLegendre')

! 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)

! 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)

! 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)

! Let us now create the mass matrix.

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

END PROGRAM main
```
123 changes: 4 additions & 119 deletions docs/docs-api/MassMatrix/examples/MassMatrix_test_3.md
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,133 +1,18 @@
---
title: MassMatrix example 3
author: Vikas Sharma, Ph.D.
date: 20 Nov 2021
update: 20 Nov 2021
tags:
- ReferenceLine
- ReferenceLine/Initiate
- QuadraturePoint/Initiate
- ElemshapeData/Initiate
- MassMatrix
---
This example shows how to USE the SUBROUTINE called `MassMatrix` to create a mass matrix in space domain.

# MassMatrix example 3

!!! 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`.
`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

```fortran
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.

```fortran
XiJ = RESHAPE([-1, 1], [1, 2])
```

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

```fortran
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.

```fortran
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]].

```fortran
CALL initiate(obj=elemsdForsimplex, &
& quad=quad, &
& refelem=simplexElem, &
& ContinuityType=typeH1, &
& InterpolType=typeLagrangeInterpolation)
```

!!! note ""
Initiate an instance of [[ElemeshapeData_]] for test function.

```fortran
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.

```fortran
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.

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

??? example "Results"

```bash
mat:
-------------------------
0.33333 0.00000 0.66667
0.00000 0.33333 0.66667
```

!!! settings "Cleanup"

```fortran
END PROGRAM main
```
Loading