#quadrature #finite #element #rules

fenris-quadrature

Quadrature rules for finite element applications

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

Download history 14/week @ 2023-02-03 9/week @ 2023-02-10 25/week @ 2023-02-17 65/week @ 2023-02-24 17/week @ 2023-03-03 12/week @ 2023-03-10 16/week @ 2023-03-17 32/week @ 2023-03-24 5/week @ 2023-03-31 19/week @ 2023-04-07 6/week @ 2023-04-14 2/week @ 2023-04-21 15/week @ 2023-04-28 19/week @ 2023-05-05 20/week @ 2023-05-12 11/week @ 2023-05-19

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 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]

Quadrilateral (2D)

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

Dependencies