conspire/domain/fem/block/element/linear/hexahedron/
mod.rs

1#[cfg(test)]
2mod test;
3
4use crate::{
5    fem::block::element::{
6        FRAC_1_SQRT_3, FiniteElement, ParametricCoordinate, ParametricCoordinates,
7        ParametricReference, ShapeFunctions, ShapeFunctionsGradients,
8        linear::{LinearElement, LinearFiniteElement, M},
9    },
10    math::ScalarList,
11};
12
13const G: usize = 8;
14const N: usize = 8;
15const P: usize = N;
16
17pub type Hexahedron = LinearElement<G, N>;
18
19impl FiniteElement<G, M, N, P> for Hexahedron {
20    fn integration_points() -> ParametricCoordinates<G, M> {
21        [
22            [-FRAC_1_SQRT_3, -FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
23            [-FRAC_1_SQRT_3, -FRAC_1_SQRT_3, FRAC_1_SQRT_3],
24            [-FRAC_1_SQRT_3, FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
25            [-FRAC_1_SQRT_3, FRAC_1_SQRT_3, FRAC_1_SQRT_3],
26            [FRAC_1_SQRT_3, -FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
27            [FRAC_1_SQRT_3, -FRAC_1_SQRT_3, FRAC_1_SQRT_3],
28            [FRAC_1_SQRT_3, FRAC_1_SQRT_3, -FRAC_1_SQRT_3],
29            [FRAC_1_SQRT_3, FRAC_1_SQRT_3, FRAC_1_SQRT_3],
30        ]
31        .into()
32    }
33    fn integration_weights(&self) -> &ScalarList<G> {
34        &self.integration_weights
35    }
36    fn parametric_reference() -> ParametricReference<M, N> {
37        [
38            [-1.0, -1.0, -1.0],
39            [1.0, -1.0, -1.0],
40            [1.0, 1.0, -1.0],
41            [-1.0, 1.0, -1.0],
42            [-1.0, -1.0, 1.0],
43            [1.0, -1.0, 1.0],
44            [1.0, 1.0, 1.0],
45            [-1.0, 1.0, 1.0],
46        ]
47        .into()
48    }
49    fn parametric_weights() -> ScalarList<G> {
50        [1.0; 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        [
55            (1.0 - xi_1) * (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
56            (1.0 + xi_1) * (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
57            (1.0 + xi_1) * (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
58            (1.0 - xi_1) * (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
59            (1.0 - xi_1) * (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
60            (1.0 + xi_1) * (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
61            (1.0 + xi_1) * (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
62            (1.0 - xi_1) * (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
63        ]
64        .into()
65    }
66    fn shape_functions_gradients(
67        parametric_coordinate: ParametricCoordinate<M>,
68    ) -> ShapeFunctionsGradients<M, N> {
69        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
70        [
71            [
72                -(1.0 - xi_2) * (1.0 - xi_3) / 8.0,
73                -(1.0 - xi_1) * (1.0 - xi_3) / 8.0,
74                -(1.0 - xi_1) * (1.0 - xi_2) / 8.0,
75            ],
76            [
77                (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
78                -(1.0 + xi_1) * (1.0 - xi_3) / 8.0,
79                -(1.0 + xi_1) * (1.0 - xi_2) / 8.0,
80            ],
81            [
82                (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
83                (1.0 + xi_1) * (1.0 - xi_3) / 8.0,
84                -(1.0 + xi_1) * (1.0 + xi_2) / 8.0,
85            ],
86            [
87                -(1.0 + xi_2) * (1.0 - xi_3) / 8.0,
88                (1.0 - xi_1) * (1.0 - xi_3) / 8.0,
89                -(1.0 - xi_1) * (1.0 + xi_2) / 8.0,
90            ],
91            [
92                -(1.0 - xi_2) * (1.0 + xi_3) / 8.0,
93                -(1.0 - xi_1) * (1.0 + xi_3) / 8.0,
94                (1.0 - xi_1) * (1.0 - xi_2) / 8.0,
95            ],
96            [
97                (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
98                -(1.0 + xi_1) * (1.0 + xi_3) / 8.0,
99                (1.0 + xi_1) * (1.0 - xi_2) / 8.0,
100            ],
101            [
102                (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
103                (1.0 + xi_1) * (1.0 + xi_3) / 8.0,
104                (1.0 + xi_1) * (1.0 + xi_2) / 8.0,
105            ],
106            [
107                -(1.0 + xi_2) * (1.0 + xi_3) / 8.0,
108                (1.0 - xi_1) * (1.0 + xi_3) / 8.0,
109                (1.0 - xi_1) * (1.0 + xi_2) / 8.0,
110            ],
111        ]
112        .into()
113    }
114}
115
116impl LinearFiniteElement<G, N> for Hexahedron {}
conspire/domain/fem/block/element/linear/hexahedron/mod.rs

conspire/domain/fem/block/element/linear/hexahedron/
mod.rs
