updating triangle utility docs

Author: vickysharma0812

docs/about/easifemBase.md

@@ -3,13 +3,15 @@ title: easifemBase
 sidebar_position: 5
 ---
 
+<!-- markdownlint-disable MD041 MD013 MD033 MD012 -->
+
 `easifemBase` (henceforth read as Base) library is the lowest (or, base) level component of EASIFEM. All other components are built upon `easifemBase`.
 
-It contains a lot of valuable routines and derived types. 
+It contains a lot of valuable routines and derived types.
 
 ## Programming paradigm
 
-The programming paradigm of `easifemBase` is [Multiple dispatch approach](https://en.wikipedia.org/wiki/Multiple_dispatch) and Procedural programming. 
+The programming paradigm of `easifemBase` is [Multiple dispatch approach](https://en.wikipedia.org/wiki/Multiple_dispatch) and Procedural programming.
 
 :::note
 The base library do not use the object-oriented programming concepts. In the Base library `String_Class` is the only exception wherein Object-oriented paradigm has been used.
@@ -22,14 +24,14 @@ import TabItem from '@theme/TabItem';
 
 ## Key features
 
-Currently, easifemBase has interface with 
+Currently, easifemBase has interface with
 
-- `BLAS95` 
-- `Lapack95` 
-- `Sparsekit` 
-- `Metis` 
-- `PlPlot` 
-- `SuperLU` 
+- `BLAS95`
+- `Lapack95`
+- `Sparsekit`
+- `Metis`
+- `PlPlot`
+- `SuperLU`
 - `ARPACK`
 
 - [ ] TODO Add key features in `easifemBase.md`.
@@ -53,11 +55,11 @@ The `easifemBase` library exposes three main modules.
 
 1. `BaseType`, which contains the user-defined data-type
 2. `BaseMethods`, contains the modules (each module defines the routines for data-types defined in `BaseType.F90`.)
-3. `easifemBase` 
+3. `easifemBase`
 
 The structure of source directory is shown in the following figure.
 
-![](./figures/figure-2.svg)
+![easifem-base-design](/img/svg/easifem-base-design.svg)
 
 The source directory has two directories
 
@@ -244,5 +246,3 @@ import {basemethods_columns, basemethods_articles} from "./BaseMethods.table.js"
   columns={basemethods_columns}
   data={basemethods_articles}
 />
-
-###

docs/about/figures/figure-2.svg

@@ -1,7 +1,4 @@
 ---
-id: "index"
-aliases:
-  - "EASIFEM"
 tags:
   - "easifemBase"
   - "easifemClasses"
@@ -10,6 +7,8 @@ sidebar_position: 1
 
 # EASIFEM
 
+<!-- markdownlint-disable MD041 MD013 MD033 -->
+
 Expandable And Scalable Infrastructure for Finite Element Methods, EASIFEM, is [Modern FORTRAN](https://fortran-lang.org) framework for solving partial differential equations (PDEs) using finite element methods. EASIFEM “eases” the efforts to develop scientific programs in FORTRAN. It is meant for researchers, scientists, and engineers using FORTRAN to implement numerical methods for solving the initial-boundary-value problems (IBVPs). EASIFEM is equipped with both low- and high-level datatype and classes for implementing finite element methods.
 
 Following are some features which may interest you.
@@ -26,7 +25,7 @@ Currently, EASIFEM focuses on finite element methods. Eventually, the library wi
 
 ## Structure of EASIFEM
 
-![](/img/what-is-easifem.svg)
+![easifem structure](/img/what-is-easifem.svg)
 
 EASIFEM consists following three hierarchical components:
 
@@ -77,7 +76,6 @@ Currently, `easifemBase` has interface with `HDF5`, `Gmsh`, `PlPlot`, `GTK4`, `P
   </div>
 </div>
 
-
 ## Kernels
 
 `easifemKernels` (henceforth, read as Kernels) contains physics simulators. For example, we have:

docs/about/index.md

@@ -1,15 +1,11 @@
 # BarycentricVertexBasis
 
+<!-- markdownlint-disable MD041 MD013 MD033 MD012 -->
+
 Returns the vertex basis functions on reference Triangle.
 
 ## Interface
 
-import Tabs from '@theme/Tabs';
-import TabItem from '@theme/TabItem';
-
-<Tabs>
-<TabItem value="interface" label="܀ Interface" default>
-
 ```fortran
 INTERFACE
   MODULE PURE FUNCTION BarycentricVertexBasis_Triangle(lambda) &
@@ -22,17 +18,21 @@ INTERFACE
 END INTERFACE
 ```
 
-</TabItem>
+:::info `lambda`
+Barycentric coordinates. The vertex basis function will be evaluated here. The number of rows in lambda is 3 and the number of columns is the number of points. The three rows of lambda dentoe the $\lambda_{i=1,2,3}$.
+:::
 
-<TabItem value="example" label="️܀ See example">
+:::info `ans`
+The number of rows in `ans` is equal to the number of points of evaluation. The number of columns is 3. The three columns of `ans` denote the basis functions of vertex $v=1,2,3$ at all points.
+:::
 
-import EXAMPLE29 from "./_BarycentricVertexBasis_Triangle_test_1.md";
+<details>
+<summary>Example</summary>
+<div>
 
-<EXAMPLE29 />
-
-</TabItem>
+import EXAMPLE29 from "./examples/_BarycentricVertexBasis_Triangle_test_1.md";
 
-<TabItem value="close" label="↢ ">
+<EXAMPLE29 />
 
-</TabItem>
-</Tabs>
+</div>
+</details>

docs/docs-api/TriangleInterpolationUtility/BarycentricVertexBasis_Triangle.md

@@ -1,37 +1,40 @@
-# Dubiner
+# Dubiner_Triangle
 
-Forms Dubiner basis on reference triangle domain.
+<!-- markdownlint-disable MD041 MD013 MD033 MD012 -->
 
-Reference triangle can be "biunit" or "unit".
+Forms Dubiner basis on reference triangle domain. Reference triangle can be "biunit" or "unit".
 
-The shape of `ans` is (M,N), where M=SIZE(xij,2) (number of points) N = 0.5*(order+1)*(order+2).
+:::note It is alias to `OrothogonalBasis_Triangle` method.
+:::
+
+The shape of `ans` is (M,N), where `M=SIZE(xij,2)` (number of points) `N = 0.5*(order+1)*(order+2)`.
+
+- `M` number of points of evaluations.
+- `N` number of degrees of freedom for a given order of approximation.
 
 In this way, `ans(j,:)` denotes the values of all polynomial at jth point.
 
 Polynomials are returned in following way:
 
 $$
- P_{0,0}, P_{0,1}, \cdots , P_{0,order} \\
- P_{1,0}, P_{1,1}, \cdots , P_{1,order-1} \\
- P_{2,0}, P_{2,1}, \cdots , P_{2,order-2} \\
- \cdots
- P_{order,0}
+P_{0,0}, P_{0,1}, \cdots , P_{0,order} \\
+P_{1,0}, P_{1,1}, \cdots , P_{1,order-1} \\
+P_{2,0}, P_{2,1}, \cdots , P_{2,order-2} \\
+\cdots
+P_{order,0}
 $$
 
 For example for order=3, the polynomials are arranged as:
 
 $$
- P_{0,0}, P_{0,1}, P_{0,2}, P_{0,3} \\
- P_{1,0}, P_{1,1}, P_{1,2} \\
- P_{2,0}, P_{2,1} \\
- P_{3,0}
+P_{0,0}, P_{0,1}, P_{0,2}, P_{0,3} \\
+P_{1,0}, P_{1,1}, P_{1,2} \\
+P_{2,0}, P_{2,1} \\
+P_{3,0}
 $$
 
 ## Interface 1
 
-import Tabs from '@theme/Tabs';
-import TabItem from '@theme/TabItem';
-
 <Tabs>
 <TabItem value="interface" label="܀ Interface" default>
 
@@ -44,8 +47,8 @@ INTERFACE
     !! points in reference triangle, shape functions will be evaluated
     !! at these points. SIZE(xij,1) = 2, and SIZE(xij, 2) = number of points
     CHARACTER(*), INTENT(IN) :: refTriangle
-    !! "unit"
-    !! "biunit"
+    !! "UNIT"
+    !! "BIUNIT"
     REAL(DFP) :: ans(SIZE(xij, 2), (order + 1)* (order + 2) / 2)
     !! shape functions
     !! ans(:, j), jth shape functions at all points
@@ -54,19 +57,23 @@ INTERFACE
 END INTERFACE
 ```
 
+:::info `xij`
+Points in reference triangle, shape functions will be evaluated at these points. SIZE(xij,1) = 2, and SIZE(xij, 2) = number of points
+:::
+
 </TabItem>
 
 <TabItem value="example" label="️܀  order=1">
 
-import EXAMPLE61 from "./_Dubiner_Triangle_test_1.md";
+import EXAMPLE61 from "./examples/_Dubiner_Triangle_test_1.md";
 
 <EXAMPLE61 />
 
 </TabItem>
 
 <TabItem value="example2" label="️܀  order=2">
 
-import EXAMPLE100 from "./_Dubiner_Triangle_test_2.md";
+import EXAMPLE100 from "./examples/_Dubiner_Triangle_test_2.md";
 
 <EXAMPLE100 />
 
@@ -100,7 +107,10 @@ INTERFACE
 END INTERFACE
 ```
 
-Forms Dubiner basis on reference triangle domain. Reference triangle can be biunit or unit. Here x and y are the coordinates on the line. xij is given by outerproduct of x and y.
+- Forms Dubiner basis on the reference triangle domain.
+- Reference triangle can be biunit or unit.
+- Here x and y are the coordinates on the line. `xij` is given by outer-product of `x` and `y`.
+
 </TabItem>
 
 <TabItem value="close" label="↢ ">

docs/docs-api/TriangleInterpolationUtility/Dubiner_Triangle.md

@@ -1,4 +1,6 @@
-# EquidistanceInPoint
+# EquidistanceInPoint_Triangle
+
+<!-- markdownlint-disable MD041 MD013 MD033 MD012 -->
 
 This function returns the equidistance points in triangle.
 
@@ -7,9 +9,6 @@ This function returns the equidistance points in triangle.
 
 ## Interface
 
-import Tabs from '@theme/Tabs';
-import TabItem from '@theme/TabItem';
-
 <Tabs>
 <TabItem value="interface" label="܀ Interface" default>
 
@@ -32,7 +31,7 @@ END INTERFACE
 
 <TabItem value="example" label="️܀ See example">
 
-import EXAMPLE35 from "./_EquidistancePoint_Triangle_test_1.md";
+import EXAMPLE35 from "./examples/_EquidistanceInPoint_Triangle_test_1.md";
 
 <EXAMPLE35 />
 

docs/docs-api/TriangleInterpolationUtility/EquidistanceInPoint_Triangle.md

@@ -1,17 +1,25 @@
-# EquidistancePoint
+# EquidistancePoint_Triangle
 
-This function returns the nodal coordinates of higher order triangle element
+<!-- markdownlint-disable MD041 MD013 MD033 MD012 -->
 
-- the layout is always "VEFC"
+This function returns the nodal coordinates of higher order triangle element.
+
+- the layout is always "VEFC", that is, the node numbering is according to GMSH convention, VEFC.
 - coordinates are distributed uniformly
-- these coordinates can be used to construct lagrange polynomials
+- these coordinates can be used to construct Lagrange polynomials
 - the returned coordinates are in $x_{iJ}$ format.
-- the node numbering is according to Gmsh convention, VEFC.
 
-## Interface
+:::info `VEFC` layout
+
+`VEFC` layout is a way to store the nodal coordinates of a triangle element. The layout is as follows:
 
-import Tabs from '@theme/Tabs';
-import TabItem from '@theme/TabItem';
+- First we store the coordinates of the vertices.
+- Then we store the coordinates of the edge midpoints.
+- Finally we store the coordinates of the face center.
+
+:::
+
+## Interface
 
 <Tabs>
 <TabItem value="interface" label="܀ Interface" default>
@@ -20,13 +28,13 @@ import TabItem from '@theme/TabItem';
 INTERFACE
   MODULE RECURSIVE PURE FUNCTION EquidistancePoint_Triangle(order, xij) RESULT(ans)
     INTEGER(I4B), INTENT(IN) :: order
-  !! order
+    !! order
     REAL(DFP), OPTIONAL, INTENT(IN) :: xij(:, :)
-  !! coordinates of point 1 and point 2 in $x_{iJ}$ format
-  !! number of rows = nsd
-  !! number of cols = 3
+    !! coordinates of point 1 and point 2 in $x_{iJ}$ format
+    !! number of rows = nsd
+    !! number of cols = 3
     REAL(DFP), ALLOCATABLE :: ans(:, :)
-  !! returned coordinates in $x_{iJ}$ format
+    !! returned coordinates in $x_{iJ}$ format
   END FUNCTION EquidistancePoint_Triangle
 END INTERFACE
 ```
@@ -35,7 +43,7 @@ END INTERFACE
 
 <TabItem value="example" label="️܀ See example">
 
-import EXAMPLE38 from "./_EquidistancePoint_Triangle_test_1.md";
+import EXAMPLE38 from "./examples/_EquidistancePoint_Triangle_test_1.md";
 
 <EXAMPLE38 />
 

docs/docs-api/TriangleInterpolationUtility/EquidistancePoint_Triangle.md

@@ -1,8 +1,10 @@
-# HeirarchicalBasis
+# HeirarchicalBasis_Triangle
+
+<!-- markdownlint-disable MD041 MD013 MD033 MD012 -->
 
 Evaluate all modal basis (heirarchical polynomial) on Triangle.
 
-# Interface
+## Interface
 
 import Tabs from '@theme/Tabs';
 import TabItem from '@theme/TabItem';