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, IntegrationWeights, ParametricCoordinate,
7        ParametricCoordinates, ParametricReference, ShapeFunctions, ShapeFunctionsGradients,
8        linear::{LinearElement, LinearFiniteElement, M},
9    },
10    math::ScalarList,
11    units::Volume,
12};
13
14const G: usize = 8;
15const N: usize = 8;
16const P: usize = N;
17
18pub type Hexahedron = LinearElement<G, N>;
19
20impl FiniteElement<G, M, N, P> for Hexahedron {
21    fn integration_points() -> ParametricCoordinates<G, M> {
22        [
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            [FRAC_1_SQRT_3, FRAC_1_SQRT_3, FRAC_1_SQRT_3],
31        ]
32        .into()
33    }
34    fn integration_weights(&self) -> &IntegrationWeights<G, Volume> {
35        &self.integration_weights
36    }
37    fn parametric_reference() -> ParametricReference<M, N> {
38        [
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            [-1.0, 1.0, 1.0],
47        ]
48        .into()
49    }
50    fn parametric_weights() -> ScalarList<G> {
51        [1.0; 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        [
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            (1.0 - xi_1) * (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
64        ]
65        .into()
66    }
67    fn shape_functions_gradients(
68        parametric_coordinate: ParametricCoordinate<M>,
69    ) -> ShapeFunctionsGradients<M, N> {
70        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
71        [
72            [
73                -(1.0 - xi_2) * (1.0 - xi_3) / 8.0,
74                -(1.0 - xi_1) * (1.0 - xi_3) / 8.0,
75                -(1.0 - xi_1) * (1.0 - xi_2) / 8.0,
76            ],
77            [
78                (1.0 - xi_2) * (1.0 - xi_3) / 8.0,
79                -(1.0 + xi_1) * (1.0 - xi_3) / 8.0,
80                -(1.0 + xi_1) * (1.0 - xi_2) / 8.0,
81            ],
82            [
83                (1.0 + xi_2) * (1.0 - xi_3) / 8.0,
84                (1.0 + xi_1) * (1.0 - xi_3) / 8.0,
85                -(1.0 + xi_1) * (1.0 + xi_2) / 8.0,
86            ],
87            [
88                -(1.0 + xi_2) * (1.0 - xi_3) / 8.0,
89                (1.0 - xi_1) * (1.0 - xi_3) / 8.0,
90                -(1.0 - xi_1) * (1.0 + xi_2) / 8.0,
91            ],
92            [
93                -(1.0 - xi_2) * (1.0 + xi_3) / 8.0,
94                -(1.0 - xi_1) * (1.0 + xi_3) / 8.0,
95                (1.0 - xi_1) * (1.0 - xi_2) / 8.0,
96            ],
97            [
98                (1.0 - xi_2) * (1.0 + xi_3) / 8.0,
99                -(1.0 + xi_1) * (1.0 + xi_3) / 8.0,
100                (1.0 + xi_1) * (1.0 - xi_2) / 8.0,
101            ],
102            [
103                (1.0 + xi_2) * (1.0 + xi_3) / 8.0,
104                (1.0 + xi_1) * (1.0 + xi_3) / 8.0,
105                (1.0 + xi_1) * (1.0 + xi_2) / 8.0,
106            ],
107            [
108                -(1.0 + xi_2) * (1.0 + xi_3) / 8.0,
109                (1.0 - xi_1) * (1.0 + xi_3) / 8.0,
110                (1.0 - xi_1) * (1.0 + xi_2) / 8.0,
111            ],
112        ]
113        .into()
114    }
115}
116
117impl LinearFiniteElement<G, N> for Hexahedron {}
conspire/domain/fem/block/element/linear/hexahedron/mod.rs

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