(fem)=
# FEM

The {py:mod}`EasyFEA.FEM` module provides essential tools for creating and managing finite element meshes, which are crucial for numerical simulations using the [Finite Element Method](https://en.wikipedia.org/wiki/Finite_element_method) (FEM).

In the simulation workflow, `FEM` is the **second step**: geometry objects from {py:mod}`~EasyFEA.Geoms` are passed to {py:class}`~EasyFEA.FEM.Mesher` to produce the {py:class}`~EasyFEA.FEM.Mesh`.

```{seealso}
- {ref}`howto-mesh`
- {ref}`howto-import-mesh`
- {ref}`easyfea-examples-meshes` examples
```

---

## What is a mesh in EasyFEA?

A {py:class}`~EasyFEA.FEM.Mesh` object in EasyFEA represents a collection of elements used to define the geometry and structure for finite element analysis. It contains multiple {py:class}`~EasyFEA.FEM._GroupElem` instances, which are groups of {py:class}`~EasyFEA.FEM.ElemType` that collectively define the spatial discretization of the domain for numerical simulations.

For example, a {py:class}`~EasyFEA.FEM.Elems.HEXA8` mesh includes the following element types:

- {py:class}`~EasyFEA.FEM.Elems.POINT` (0D element)
- {py:class}`~EasyFEA.FEM.Elems.SEG2` (1D element)
- {py:class}`~EasyFEA.FEM.Elems.QUAD4` (2D element)
- {py:class}`~EasyFEA.FEM.Elems.HEXA8` (3D element)

All implemented element types, along with their corresponding shape functions and derivatives, are defined in the {py:mod}`EasyFEA.FEM.Elems` module and were defined in {ref}`examples-meshes-shape-functions`.
The Gauss point quadratures are implemented in the {py:class}`~EasyFEA.FEM.Gauss` class.

---

## Creating or importing a Mesh

To construct a {py:class}`~EasyFEA.FEM.Mesh` using the {py:class}`~EasyFEA.FEM.Mesher`, you must first create {py:class}`~EasyFEA.Geoms._Geom` objects (see {ref}`geoms` for some examples). The {py:class}`~EasyFEA.FEM.Mesher` class serves as an interface to [Gmsh](https://gmsh.info/), a powerful meshing tool, and includes the following primary functions for mesh generation:

- {py:meth}`~EasyFEA.FEM.Mesher.Mesh_2D`: Generates a 2D mesh.
- {py:meth}`~EasyFEA.FEM.Mesher.Mesh_Extrude`: Creates a mesh by extruding a 2D shape.
- {py:meth}`~EasyFEA.FEM.Mesher.Mesh_Revolve`: Generates a mesh by revolving a 2D shape around an axis.
- {py:meth}`~EasyFEA.FEM.Mesher.Mesh_Import_part`: Imports a CAD part (e.g., .stp) to create a mesh.
- {py:meth}`~EasyFEA.FEM.Mesher.Mesh_Import_mesh`: Imports an existing Gmsh mesh. EasyFEA is also linked to meshio and can be used through the following functions:
- {py:meth}`~EasyFEA.Utilities.MeshIO.Medit_to_EasyFEA`: Imports a Medit mesh.
- {py:meth}`~EasyFEA.Utilities.MeshIO.Gmsh_to_EasyFEA`: Imports a Gmsh mesh.
- {py:meth}`~EasyFEA.Utilities.MeshIO.PyVista_to_EasyFEA`: Imports a PyVista mesh (UnstructuredGrid or MultiBlock).
- {py:meth}`~EasyFEA.Utilities.MeshIO.Ensight_to_EasyFEA`: Imports an EnSight mesh.

```{seealso}
- {ref}`howto-geom`
- {ref}`howto-mesh`
- {ref}`howto-import-mesh`
- {ref}`easyfea-examples-meshes` examples
```

## FEM API

```{eval-rst}
.. automodule:: EasyFEA.FEM
.. automodule:: EasyFEA.FEM.Elems
```