Quadrature rules for finite element applications

### 4 releases

 0.0.4 Sep 1, 2022 Sep 1, 2022 Oct 26, 2021 Oct 8, 2021

#7 in #fenris

Used in 2 crates (via fenris)

MIT/Apache

265KB
3.5K SLoC

Quadrature rules for finite element reference domains.

The main purpose of this crate is to support the `fenris` FEM library. However, it has been designed so that the quadrature rules available here may be used completely independently of `fenris`.

# Reference domains

## Segment (1D)

The reference domain in 1D is the interval `[-1, 1]`.

## Triangle (2D)

The reference triangle is comprised of the vertices `(-1, -1)`, `(1, -1)` and `(-1, 1)`.

![Reference triangle][ref_tri]

The reference quadrilateral is the square `[-1, 1]^2`, comprised of the vertices `(-1, -1)`, `(1, -1)`, `(1, 1)` and `(-1, 1)`.

## Hexahedron (3D)

The reference hexahedron is the box `[-1, 1]^3`.

![Reference hexahedron][ref_hex]

## Tetrahedron (3D)

The reference tetrahedron is comprised of the vertices `(-1, -1, -1)`, `(1, -1, -1)`, `(-1, 1, -1)` and `(-1, -1, 1)`.

![Reference tetrahedron][ref_tet]

## Pyramid (3D)

The reference pyramid is comprised of the vertices `(-1, -1, -1)`, `(1, -1, -1)`, `(1, 1, -1)`, `(-1, 1, -1)` and `(0, 0, 1)`.

![Reference pyramid][ref_pyramid]

## Prism (3D)

The reference prism is comprised of the vertices `(-1, -1, -1)`, `(1, -1, -1)`, `(-1, 1, -1)`, `(-1, -1, 1)`, `(1, -1, 1)` and `(-1, 1, 1)`.

![Reference prism][ref_prism]

TODO: Document how quadratures work, e.g. the concept of a reference domain and that quadrature rules are specific to a reference domain