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

1#[cfg(test)]
2mod test;
3
4use crate::{
5    fem::block::element::{
6        FRAC_SQRT_3_5, FiniteElement, ParametricCoordinate, ParametricCoordinates,
7        ParametricReference, ShapeFunctions, ShapeFunctionsGradients,
8        quadratic::{M, QuadraticElement, QuadraticFiniteElement},
9    },
10    math::{Scalar, ScalarList},
11};
12
13const G: usize = 18;
14const N: usize = 15;
15const P: usize = N;
16
17pub type Wedge = QuadraticElement<G, N>;
18
19impl FiniteElement<G, M, N, P> for Wedge {
20    fn integration_points() -> ParametricCoordinates<G, M> {
21        const ONE_SIXTH: Scalar = 1.0 / 12.0;
22        const TWO_THIRDS: Scalar = 2.0 / 3.0;
23        [
24            [ONE_SIXTH, ONE_SIXTH, FRAC_SQRT_3_5],
25            [ONE_SIXTH, TWO_THIRDS, FRAC_SQRT_3_5],
26            [TWO_THIRDS, ONE_SIXTH, FRAC_SQRT_3_5],
27            [ONE_SIXTH, ONE_SIXTH, -FRAC_SQRT_3_5],
28            [ONE_SIXTH, TWO_THIRDS, -FRAC_SQRT_3_5],
29            [TWO_THIRDS, ONE_SIXTH, -FRAC_SQRT_3_5],
30            [ONE_SIXTH, ONE_SIXTH, 0.0],
31            [ONE_SIXTH, TWO_THIRDS, 0.0],
32            [TWO_THIRDS, ONE_SIXTH, 0.0],
33            [0.5, 0.5, FRAC_SQRT_3_5],
34            [0.5, 0.0, FRAC_SQRT_3_5],
35            [0.0, 0.5, FRAC_SQRT_3_5],
36            [0.5, 0.5, -FRAC_SQRT_3_5],
37            [0.5, 0.0, -FRAC_SQRT_3_5],
38            [0.0, 0.5, -FRAC_SQRT_3_5],
39            [0.5, 0.5, 0.0],
40            [0.5, 0.0, 0.0],
41            [0.0, 0.5, 0.0],
42        ]
43        .into()
44    }
45    fn integration_weights(&self) -> &ScalarList<G> {
46        &self.integration_weights
47    }
48    fn parametric_reference() -> ParametricReference<M, N> {
49        [
50            [0.0, 0.0, -1.0],
51            [1.0, 0.0, -1.0],
52            [0.0, 1.0, -1.0],
53            [0.0, 0.0, 1.0],
54            [1.0, 0.0, 1.0],
55            [0.0, 1.0, 1.0],
56            [0.5, 0.0, -1.0],
57            [0.5, 0.5, -1.0],
58            [0.0, 0.5, -1.0],
59            [0.0, 0.0, 0.0],
60            [1.0, 0.0, 0.0],
61            [0.0, 1.0, 0.0],
62            [0.5, 0.0, 1.0],
63            [0.5, 0.5, 1.0],
64            [0.0, 0.5, 1.0],
65        ]
66        .into()
67    }
68    fn parametric_weights() -> ScalarList<G> {
69        const ONE_TWELFTH: Scalar = 1.0 / 12.0;
70        const TWO_FIFTEENTHS: Scalar = 2.0 / 15.0;
71        const ONE_ONE_HUNDRED_EIGHTH: Scalar = 1.0 / 108.0;
72        const TWO_ONE_HUNDRED_THIRTY_FIFTHS: Scalar = 2.0 / 135.0;
73        [
74            ONE_TWELFTH,
75            ONE_TWELFTH,
76            ONE_TWELFTH,
77            ONE_TWELFTH,
78            ONE_TWELFTH,
79            ONE_TWELFTH,
80            TWO_FIFTEENTHS,
81            TWO_FIFTEENTHS,
82            TWO_FIFTEENTHS,
83            ONE_ONE_HUNDRED_EIGHTH,
84            ONE_ONE_HUNDRED_EIGHTH,
85            ONE_ONE_HUNDRED_EIGHTH,
86            ONE_ONE_HUNDRED_EIGHTH,
87            ONE_ONE_HUNDRED_EIGHTH,
88            ONE_ONE_HUNDRED_EIGHTH,
89            TWO_ONE_HUNDRED_THIRTY_FIFTHS,
90            TWO_ONE_HUNDRED_THIRTY_FIFTHS,
91            TWO_ONE_HUNDRED_THIRTY_FIFTHS,
92        ]
93        .into()
94    }
95    fn shape_functions(parametric_coordinate: ParametricCoordinate<M>) -> ShapeFunctions<N> {
96        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
97        let xi_0 = 1.0 - xi_1 - xi_2;
98        [
99            -0.5 * xi_0 * (1.0 - xi_3) * (2.0 * xi_1 + 2.0 * xi_2 + xi_3),
100            0.5 * xi_1 * (1.0 - xi_3) * (2.0 * xi_1 - 2.0 - xi_3),
101            0.5 * xi_2 * (1.0 - xi_3) * (2.0 * xi_2 - 2.0 - xi_3),
102            -0.5 * xi_0 * (1.0 + xi_3) * (2.0 * xi_1 + 2.0 * xi_2 - xi_3),
103            0.5 * xi_1 * (1.0 + xi_3) * (2.0 * xi_1 - 2.0 + xi_3),
104            0.5 * xi_2 * (1.0 + xi_3) * (2.0 * xi_2 - 2.0 + xi_3),
105            2.0 * xi_0 * xi_1 * (1.0 - xi_3),
106            2.0 * xi_1 * xi_2 * (1.0 - xi_3),
107            2.0 * xi_0 * xi_2 * (1.0 - xi_3),
108            xi_0 * (1.0 - xi_3 * xi_3),
109            xi_1 * (1.0 - xi_3 * xi_3),
110            xi_2 * (1.0 - xi_3 * xi_3),
111            2.0 * xi_0 * xi_1 * (1.0 + xi_3),
112            2.0 * xi_1 * xi_2 * (1.0 + xi_3),
113            2.0 * xi_0 * xi_2 * (1.0 + xi_3),
114        ]
115        .into()
116    }
117    fn shape_functions_gradients(
118        parametric_coordinate: ParametricCoordinate<M>,
119    ) -> ShapeFunctionsGradients<M, N> {
120        let [xi_1, xi_2, xi_3] = parametric_coordinate.into();
121        let xi_0 = 1.0 - xi_1 - xi_2;
122        [
123            [
124                0.5 * (1.0 - xi_3) * (4.0 * xi_1 + 4.0 * xi_2 + xi_3 - 2.0),
125                0.5 * (1.0 - xi_3) * (4.0 * xi_1 + 4.0 * xi_2 + xi_3 - 2.0),
126                xi_0 * (xi_1 + xi_2 + xi_3 - 0.5),
127            ],
128            [
129                0.5 * (1.0 - xi_3) * (4.0 * xi_1 - 2.0 - xi_3),
130                0.0,
131                xi_1 * (xi_3 - xi_1 + 0.5),
132            ],
133            [
134                0.0,
135                0.5 * (1.0 - xi_3) * (4.0 * xi_2 - xi_3 - 2.0),
136                xi_2 * (xi_3 - xi_2 + 0.5),
137            ],
138            [
139                0.5 * (1.0 + xi_3) * (4.0 * xi_1 + 4.0 * xi_2 - xi_3 - 2.0),
140                0.5 * (1.0 + xi_3) * (4.0 * xi_1 + 4.0 * xi_2 - xi_3 - 2.0),
141                xi_0 * (-xi_1 - xi_2 + xi_3 + 0.5),
142            ],
143            [
144                0.5 * (1.0 + xi_3) * (4.0 * xi_1 - 2.0 + xi_3),
145                0.0,
146                xi_1 * (xi_3 + xi_1 - 0.5),
147            ],
148            [
149                0.0,
150                0.5 * (1.0 + xi_3) * (4.0 * xi_2 + xi_3 - 2.0),
151                xi_2 * (xi_3 + xi_2 - 0.5),
152            ],
153            [
154                2.0 * (1.0 - xi_3) * (1.0 - 2.0 * xi_1 - xi_2),
155                -2.0 * xi_1 * (1.0 - xi_3),
156                -2.0 * xi_0 * xi_1,
157            ],
158            [
159                2.0 * xi_2 * (1.0 - xi_3),
160                2.0 * xi_1 * (1.0 - xi_3),
161                -2.0 * xi_1 * xi_2,
162            ],
163            [
164                -2.0 * xi_2 * (1.0 - xi_3),
165                2.0 * (1.0 - xi_3) * (xi_0 - xi_2),
166                -2.0 * xi_0 * xi_2,
167            ],
168            [xi_3 * xi_3 - 1.0, xi_3 * xi_3 - 1.0, -2.0 * xi_0 * xi_3],
169            [1.0 - xi_3 * xi_3, 0.0, -2.0 * xi_1 * xi_3],
170            [0.0, 1.0 - xi_3 * xi_3, -2.0 * xi_2 * xi_3],
171            [
172                2.0 * (1.0 + xi_3) * (1.0 - 2.0 * xi_1 - xi_2),
173                -2.0 * xi_1 * (1.0 + xi_3),
174                2.0 * xi_0 * xi_1,
175            ],
176            [
177                2.0 * xi_2 * (1.0 + xi_3),
178                2.0 * xi_1 * (1.0 + xi_3),
179                2.0 * xi_1 * xi_2,
180            ],
181            [
182                -2.0 * xi_2 * (1.0 + xi_3),
183                2.0 * (1.0 + xi_3) * (1.0 - xi_1 - 2.0 * xi_2),
184                2.0 * xi_0 * xi_2,
185            ],
186        ]
187        .into()
188    }
189}
190
191impl QuadraticFiniteElement<G, N> for Wedge {}
conspire/domain/fem/block/element/quadratic/wedge/mod.rs

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