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

1#[cfg(test)]
2mod test;
3
4use crate::{
5    fem::block::element::{
6        ElementNodalEitherCoordinates, FiniteElement, ParametricCoordinate, ParametricCoordinates,
7        ParametricReference, ShapeFunctions, ShapeFunctionsGradients,
8        linear::{LinearElement, LinearFiniteElement, M},
9    },
10    math::{ScalarList, Tensor},
11};
12use std::f64::consts::SQRT_2;
13
14const G: usize = 1;
15const N: usize = 4;
16const P: usize = N;
17
18const EDGES: usize = 6;
19
20pub type Tetrahedron = LinearElement<G, N>;
21
22impl FiniteElement<G, M, N, P> for Tetrahedron {
23    fn integration_points() -> ParametricCoordinates<G, M> {
24        [[0.25; M]].into()
25    }
26    fn integration_weights(&self) -> &ScalarList<G> {
27        &self.integration_weights
28    }
29    fn parametric_reference() -> ParametricReference<M, N> {
30        [
31            [0.0, 0.0, 0.0],
32            [1.0, 0.0, 0.0],
33            [0.0, 1.0, 0.0],
34            [0.0, 0.0, 1.0],
35        ]
36        .into()
37    }
38    fn parametric_weights() -> ScalarList<G> {
39        [1.0 / 6.0; G].into()
40    }
41    fn scaled_jacobians<const I: usize>(
42        nodal_coordinates: ElementNodalEitherCoordinates<I, N>,
43    ) -> ScalarList<P> {
44        let numerator = ((&nodal_coordinates[1] - &nodal_coordinates[0])
45            .cross(&(&nodal_coordinates[2] - &nodal_coordinates[0]))
46            * (&nodal_coordinates[3] - &nodal_coordinates[0]))
47            * SQRT_2;
48        let lengths = lengths(nodal_coordinates);
49        [
50            numerator / (lengths[0] * lengths[2] * lengths[3]),
51            numerator / (lengths[0] * lengths[1] * lengths[4]),
52            numerator / (lengths[1] * lengths[2] * lengths[5]),
53            numerator / (lengths[3] * lengths[4] * lengths[5]),
54        ]
55        .into()
56    }
57    fn shape_functions(parametric_coordinate: ParametricCoordinate<M>) -> ShapeFunctions<N> {
58        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
59        [1.0 - xi_1 - xi_2 - xi_3, xi_1, xi_2, xi_3].into()
60    }
61    fn shape_functions_gradients(
62        _parametric_coordinate: ParametricCoordinate<M>,
63    ) -> ShapeFunctionsGradients<M, N> {
64        [
65            [-1.0, -1.0, -1.0],
66            [1.0, 0.0, 0.0],
67            [0.0, 1.0, 0.0],
68            [0.0, 0.0, 1.0],
69        ]
70        .into()
71    }
72}
73
74impl LinearFiniteElement<G, N> for Tetrahedron {}
75
76fn edges<const I: usize>(
77    nodal_coordinates: ElementNodalEitherCoordinates<I, N>,
78) -> ElementNodalEitherCoordinates<I, 6> {
79    [
80        &nodal_coordinates[1] - &nodal_coordinates[0],
81        &nodal_coordinates[2] - &nodal_coordinates[1],
82        &nodal_coordinates[0] - &nodal_coordinates[2],
83        &nodal_coordinates[3] - &nodal_coordinates[0],
84        &nodal_coordinates[3] - &nodal_coordinates[1],
85        &nodal_coordinates[3] - &nodal_coordinates[2],
86    ]
87    .into()
88}
89
90fn lengths<const I: usize>(
91    nodal_coordinates: ElementNodalEitherCoordinates<I, N>,
92) -> ScalarList<EDGES> {
93    edges(nodal_coordinates)
94        .into_iter()
95        .map(|edge| edge.norm())
96        .collect()
97}
conspire/domain/fem/block/element/linear/tetrahedron/mod.rs

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