Meshing
Meshes are stored as an ExtendableGrid, see ExtendableGrids.jl for details and constructors. Grid generators for simplex grids can be found e.g. in the external module SimplexGridFactory.jl
Cells, faces and edges of the mesh are associated to AbstractElementGeometries (defined by ExtendableGrids.jl) that are used to dispatch functionality (local/global transformation, enumeration rules, set of basis functions, volume calculation, refinements etc.). See further below for a list of recognized element geometries.
Recognized Geometries and Reference Domains
The following list contains all subtypes of ExtendableGrids.AbstractElementGeometries and their reference domains for which the package offers finite elements on them.
Edge1D <: AbstractElementGeometry1D
[1]-----[2] [1] = [0]
[2] = [1]Triangle2D
[3]
| \
| \ [1] = [0,0]
| \ [2] = [1,0]
| \ [3] = [0,1]
| \
[1]--------[2]Parallelogram2D <: Quadrilateral2D
[4]--------[3]
| | [1] = [0,0]
| | [2] = [1,0]
| | [3] = [1,1]
| | [4] = [0,1]
[1]--------[2]
Note: most finite elements only work as intended on Parallelogram2D
since the local<>global map stays affine in this caseTetrahedron3D
[4]
|\\
| \ \ [1] = [0,0,0]
| \ \ [2] = [1,0,0]
| \ \ [3] = [0,1,0]
| _-[3]-_ \ [4] = [0,0,1]
[1]--------[2]Parallelepiped3D <: Hexahedron3D
[8]--------[7] [1] = [0,0,0]
/ | / | [2] = [1,0,0]
[5]--------[6] | [3] = [1,1,0]
| | | | [4] = [0,1,0]
| | | | [5] = [0,0,1]
| [4]-----|--[3] [6] = [1,0,1]
| / | / [7] = [1,1,1]
[1]--------[2] [8] = [0,1,1]
Note: most finite elements only work as intended on Parallelepiped3D
since the local<>global map stays affine in this case