### 4 releases

0.0.4 | Sep 1, 2022 |
---|---|

0.0.3 | Sep 1, 2022 |

0.0.2 | Oct 26, 2021 |

0.0.1 | Oct 8, 2021 |

#**253** in Science

**65** downloads per month

Used in **2** crates
(via fenris)

**MIT/Apache**

170KB

3.5K
SLoC

Quadrature rules for finite element reference domains.

The main purpose of this crate is to support the

FEM library. However, it has been
designed so that the quadrature rules available here may be used completely independently
of `fenris`

.`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``)`

and `(``1``,` `-``1``)`

.`(``-``1``,` `1``)`

![Reference triangle][ref_tri]

## Quadrilateral (2D)

The reference quadrilateral is the square

, comprised of the vertices
`[``-``1``,` `1``]``^``2`

, `(``-``1``,` `-``1``)`

, `(``1``,` `-``1``)`

and `(``1``,` `1``)`

.`(``-``1``,` `1``)`

![Reference quadrilateral][ref_quad]

## 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``)`

and `(``-``1``,` `1``,` `-``1``)`

.`(``-``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``)`

and `(``-``1``,` `1``,` `-``1``)`

.`(``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``)`

and `(``1``,` `-``1``,` `1``)`

.`(``-``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