pub fn create<T: RlstScalar + Getrf + Getri, TGeo: RlstScalar>(
cell_type: ReferenceCellType,
degree: usize,
continuity: Continuity,
) -> CiarletElement<T, ContravariantPiolaMap, TGeo>Expand description
Create a Raviart-Thomas element
Examples found in repository?
ndgrid/examples/test_push_forward.rs (line 84)
73fn test_rt_push_forward() {
74 let mut b = SingleElementGridBuilder::<f64>::new(3, (ReferenceCellType::Triangle, 1));
75 b.add_point(0, &[0.0, 0.0, 0.0]);
76 b.add_point(1, &[1.0, 0.0, 0.0]);
77 b.add_point(2, &[2.0, 0.0, 1.0]);
78 b.add_point(3, &[0.0, 1.0, 0.0]);
79 b.add_cell(0, &[0, 1, 3]);
80 b.add_cell(1, &[1, 2, 3]);
81 let grid = b.create_grid();
82
83 let e =
84 raviart_thomas::create::<f64, f64>(ReferenceCellType::Triangle, 4, Continuity::Standard);
85
86 let npts = 5;
87
88 let mut cell0_points = rlst_dynamic_array!(f64, [2, npts]);
89 for i in 0..npts {
90 cell0_points[[1, i]] = i as f64 / (npts - 1) as f64;
91 cell0_points[[0, i]] = 1.0 - cell0_points[[1, i]];
92 }
93 let mut cell0_table = DynArray::<f64, 4>::from_shape(e.tabulate_array_shape(0, npts));
94 e.tabulate(&cell0_points, 0, &mut cell0_table);
95
96 let mut points = rlst_dynamic_array!(f64, [2, npts]);
97 for i in 0..npts {
98 points[[0, i]] = 0.0;
99 points[[1, i]] = i as f64 / (npts - 1) as f64;
100 }
101
102 let mut table = DynArray::<f64, 4>::from_shape(e.tabulate_array_shape(0, npts));
103 e.tabulate(&points, 0, &mut table);
104
105 let gmap = grid.geometry_map(ReferenceCellType::Triangle, 1, &points);
106
107 let mut jacobians = rlst_dynamic_array!(f64, [grid.geometry_dim(), grid.topology_dim(), npts]);
108 let mut jinv = rlst_dynamic_array!(f64, [grid.topology_dim(), grid.geometry_dim(), npts]);
109 let mut jdets = vec![0.0; npts];
110
111 gmap.jacobians_inverses_dets(1, &mut jacobians, &mut jinv, &mut jdets);
112
113 let mut cell1_table =
114 DynArray::<f64, 4>::from_shape([table.shape()[0], table.shape()[1], table.shape()[2], 3]);
115 e.push_forward(&table, 0, &jacobians, &jdets, &jinv, &mut cell1_table);
116
117 // Check that basis functions dotted with normal to edge are continuous between cells
118 for (cell0_dof, cell1_dof) in izip!(
119 e.entity_closure_dofs(1, 0).unwrap(),
120 e.entity_closure_dofs(1, 1).unwrap()
121 ) {
122 for i in 0..npts {
123 assert_relative_eq!(
124 (cell0_table[[0, i, *cell0_dof, 0]] + cell0_table[[0, i, *cell0_dof, 1]])
125 / f64::sqrt(2.0),
126 (cell1_table[[0, i, *cell1_dof, 0]]
127 + cell1_table[[0, i, *cell1_dof, 1]]
128 + 2.0 * cell1_table[[0, i, *cell1_dof, 2]])
129 / f64::sqrt(6.0),
130 epsilon = 1e-10
131 );
132 }
133 }
134}