conspire/domain/fem/block/element/quadratic/tetrahedron/
mod.rs

1#[cfg(test)]
2pub mod test;
3
4use crate::{
5    fem::block::element::{
6        FiniteElement, IntegrationWeights, ParametricCoordinate, ParametricCoordinates,
7        ParametricReference, ShapeFunctions, ShapeFunctionsGradients,
8        quadratic::{M, QuadraticElement, QuadraticFiniteElement},
9    },
10    math::ScalarList,
11    units::Volume,
12};
13
14const G: usize = 4;
15const N: usize = 10;
16const P: usize = N;
17
18pub type Tetrahedron = QuadraticElement<G, N>;
19
20impl FiniteElement<G, M, N, P> for Tetrahedron {
21    fn integration_points() -> ParametricCoordinates<G, M> {
22        let alpha = (1.0 + 3.0 / 5.0_f64.sqrt()) / 4.0;
23        let beta = (1.0 - 1.0 / 5.0_f64.sqrt()) / 4.0;
24        [
25            [beta, beta, beta],
26            [alpha, beta, beta],
27            [beta, alpha, beta],
28            [beta, beta, alpha],
29        ]
30        .into()
31    }
32    fn integration_weights(&self) -> &IntegrationWeights<G, Volume> {
33        &self.integration_weights
34    }
35    fn parametric_reference() -> ParametricReference<M, N> {
36        [
37            [0.0, 0.0, 0.0],
38            [1.0, 0.0, 0.0],
39            [0.0, 1.0, 0.0],
40            [0.0, 0.0, 1.0],
41            [0.5, 0.0, 0.0],
42            [0.5, 0.5, 0.0],
43            [0.0, 0.5, 0.0],
44            [0.0, 0.0, 0.5],
45            [0.5, 0.0, 0.5],
46            [0.0, 0.5, 0.5],
47        ]
48        .into()
49    }
50    fn parametric_weights() -> ScalarList<G> {
51        [1.0 / 24.0; G].into()
52    }
53    fn shape_functions(parametric_coordinate: ParametricCoordinate<M>) -> ShapeFunctions<N> {
54        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
55        let xi_0 = 1.0 - xi_1 - xi_2 - xi_3;
56        [
57            xi_0 * (2.0 * xi_0 - 1.0),
58            xi_1 * (2.0 * xi_1 - 1.0),
59            xi_2 * (2.0 * xi_2 - 1.0),
60            xi_3 * (2.0 * xi_3 - 1.0),
61            4.0 * xi_0 * xi_1,
62            4.0 * xi_1 * xi_2,
63            4.0 * xi_0 * xi_2,
64            4.0 * xi_0 * xi_3,
65            4.0 * xi_1 * xi_3,
66            4.0 * xi_2 * xi_3,
67        ]
68        .into()
69    }
70    fn shape_functions_gradients(
71        parametric_coordinate: ParametricCoordinate<M>,
72    ) -> ShapeFunctionsGradients<M, N> {
73        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
74        let xi_0 = 1.0 - xi_1 - xi_2 - xi_3;
75        [
76            [-4.0 * xi_0 + 1.0, -4.0 * xi_0 + 1.0, -4.0 * xi_0 + 1.0],
77            [4.0 * xi_1 - 1.0, 0.0, 0.0],
78            [0.0, 4.0 * xi_2 - 1.0, 0.0],
79            [0.0, 0.0, 4.0 * xi_3 - 1.0],
80            [4.0 * (xi_0 - xi_1), -4.0 * xi_1, -4.0 * xi_1],
81            [4.0 * xi_2, 4.0 * xi_1, 0.0],
82            [-4.0 * xi_2, 4.0 * (xi_0 - xi_2), -4.0 * xi_2],
83            [-4.0 * xi_3, -4.0 * xi_3, 4.0 * (xi_0 - xi_3)],
84            [4.0 * xi_3, 0.0, 4.0 * xi_1],
85            [0.0, 4.0 * xi_3, 4.0 * xi_2],
86        ]
87        .into()
88    }
89}
90
91impl QuadraticFiniteElement<G, N> for Tetrahedron {}
conspire/domain/fem/block/element/quadratic/tetrahedron/mod.rs

conspire/domain/fem/block/element/quadratic/tetrahedron/
mod.rs
