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

1#[cfg(test)]
2pub mod test;
3
4use crate::{
5    fem::block::element::{
6        ElementNodalEitherCoordinates, FiniteElement, ParametricCoordinate, ParametricCoordinates,
7        ParametricReference, 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 scaled_jacobians<const I: usize>(
53        _nodal_coordinates: ElementNodalEitherCoordinates<I, N>,
54    ) -> ScalarList<P> {
55        todo!()
56    }
57    fn shape_functions(parametric_coordinate: ParametricCoordinate<M>) -> ShapeFunctions<N> {
58        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
59        let xi_0 = 1.0 - xi_1 - xi_2 - xi_3;
60        [
61            xi_0 * (2.0 * xi_0 - 1.0),
62            xi_1 * (2.0 * xi_1 - 1.0),
63            xi_2 * (2.0 * xi_2 - 1.0),
64            xi_3 * (2.0 * xi_3 - 1.0),
65            4.0 * xi_0 * xi_1,
66            4.0 * xi_1 * xi_2,
67            4.0 * xi_0 * xi_2,
68            4.0 * xi_0 * xi_3,
69            4.0 * xi_1 * xi_3,
70            4.0 * xi_2 * xi_3,
71        ]
72        .into()
73    }
74    fn shape_functions_gradients(
75        parametric_coordinate: ParametricCoordinate<M>,
76    ) -> ShapeFunctionsGradients<M, N> {
77        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
78        let xi_0 = 1.0 - xi_1 - xi_2 - xi_3;
79        [
80            [-4.0 * xi_0 + 1.0, -4.0 * xi_0 + 1.0, -4.0 * xi_0 + 1.0],
81            [4.0 * xi_1 - 1.0, 0.0, 0.0],
82            [0.0, 4.0 * xi_2 - 1.0, 0.0],
83            [0.0, 0.0, 4.0 * xi_3 - 1.0],
84            [4.0 * (xi_0 - xi_1), -4.0 * xi_1, -4.0 * xi_1],
85            [4.0 * xi_2, 4.0 * xi_1, 0.0],
86            [-4.0 * xi_2, 4.0 * (xi_0 - xi_2), -4.0 * xi_2],
87            [-4.0 * xi_3, -4.0 * xi_3, 4.0 * (xi_0 - xi_3)],
88            [4.0 * xi_3, 0.0, 4.0 * xi_1],
89            [0.0, 4.0 * xi_3, 4.0 * xi_2],
90        ]
91        .into()
92    }
93}
94
95impl QuadraticFiniteElement<G, N> for Tetrahedron {}
conspire/domain/fem/block/element/quadratic/tetrahedron/mod.rs

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