# Meshes

## Mesh Specification

Finite element meshes are specified in the (node,elem) structure due to Long Chen. For the standard elements used in this package, we describe a geometric figure by a triangulation. The nodes are the vertices of the triangle and the elements are the triangles themselves. These are encoded as follows:

Row $i$ of node is an $(x,y)$ (or $(x,y,z)$) pair which specifies the coordinates of the $i$th node.

Row $j$ of elem are the indices of the nodes which make the triangle. Thus in 2D each row has three numbers.

For example, to know the $(x,y)$ locations of the vertices of triangle $j$, we would see that `node[elem[j,i],:]`

are the $(x,y)$ locations of the $i$th vertex for $i=1,2,3$.

For more information, please see Programming of Finite Element Methods by Long Chen.

## Mesh Generation Functions

`DiffEqPDEBase.findboundary`

— Function.`findboundary(elem,bdflag=[])`

`

`findboundary(fem_mesh::FEMMesh,bdflag=[])`

Finds elements which are on the boundary of the domain. If bdflag is given, then those indices are added as nodes for a dirichlet boundary condition (useful for creating cracks and other cutouts of domains).

**Returns**

`bdnode`

= Vector of indices for bdnode. Using node[:,bdnode] returns boundary nodes.

`bdedge`

= Vector of indices for boundary edges.

`is_bdnode`

= Vector of booleans size N which donotes which are on the boundary

`is_bdelem`

= Vector of booleans size NT which denotes which are on the boundary

`DiffEqPDEBase.setboundary`

— Function.`setboundary(node::AbstractArray,elem::AbstractArray,bdtype)`

`setboundary(fem_mesh::FEMMesh,bdtype)`

Takes in the fem_mesh and creates an array bdflag which denotes the boundary types. 1 stands for dirichlet, 2 for neumann, 3 for robin.

`DiffEqPDEBase.fem_squaremesh`

— Function.`fem_squaremesh(square,h)`

Returns the grid in the iFEM form of the two arrays (node,elem)

`DiffEqPDEBase.notime_squaremesh`

— Function.`notime_squaremesh(square,dx,bdtype)`

Computes the (node,elem) square mesh for the square with the chosen `dx`

and boundary settings.

###Example

```
square=[0 1 0 1] #Unit Square
dx=.25
notime_squaremesh(square,dx,"dirichlet")
```

`DiffEqPDEBase.parabolic_squaremesh`

— Function.`parabolic_squaremesh(square,dx,dt,T,bdtype)`

Computes the `(node,elem) x [0,T]`

parabolic square mesh for the square with the chosen `dx`

and boundary settings and with the constant time intervals `dt`

.

###Example

```
square=[0 1 0 1] #Unit Square
dx=.25; dt=.25;T=2
parabolic_squaremesh(square,dx,dt,T,:dirichlet)
```

## Example Meshes

```
DiffEqProblemLibrary.meshExample_bunny
DiffEqProblemLibrary.meshExample_flowpastcylindermesh
DiffEqProblemLibrary.meshExample_lakemesh
DiffEqProblemLibrary.meshExample_Lshapemesh
DiffEqProblemLibrary.meshExample_Lshapeunstructure
DiffEqProblemLibrary.meshExample_oilpump
DiffEqProblemLibrary.meshExample_wavymesh
DiffEqProblemLibrary.meshExample_wavyperturbmesh
```

## Plot Functions

The plot functionality is provided by a Plots.jl recipe. What is plotted is a "trisurf" of the mesh. To plot a mesh, simply use:

`plot(mesh::Mesh)`

All of the functionality (keyword arguments) provided by Plots.jl are able to be used in this command. Please see the Plots.jl documentation for more information.