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docs/docs-api/MassMatrix/MassMatrix_.md

@@ -5,10 +5,11 @@ date: 20 Nov 2021
 update: 20 Nov 2021
 tags:
     - MassMatrix
+category:
+    - MassMatrix
+    - Finite Element
 ---
 
-# MassMatrix
-
 ## Theory
 
 $$
@@ -19,19 +20,27 @@ $$
 \int_{\Omega } \rho N^{I} N^{J}d\Omega
 $$
 
-## Constructor methods
+## Example 1
+
+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. 
+
+$$
+\int_{\Omega } N^{I}\rho N^{J}d\Omega
+$$
+
+`rho` can be a constant, or a function of spatial coordinates, or some nonlinear function.
+
+In this example, we use
 
-!!! note "MassMatrix"
+- ReferenceLine element,  
+- QuadraturePoint are `GaussLegendre`
+- order of integrand is 2.
 
 $$
 \int_{\Omega } N^{I} N^{J}d\Omega
 $$
-
-    You can learn more about this in
-
-    - [[MassMatrix_test_1]] for [[ReferenceLine_]] `Line2`
-    - [[MassMatrix_test_2]] for [[ReferenceLine_]] `Line3`
-    - [[MassMatrix_test_3]] for mixed FEM type, Line2 and Line3 [[ReferenceLine_]] 
 
-- [ ] TODO add examples for creating mass matrix for triangle3 and triangle6 and 3D elements.
+This type of mass matrix is useful in cases where $rho$ is a constant.
 

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

@@ -0,0 +1,133 @@
+---
+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)
+    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
+```