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

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

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