DUNE-FEM (unstable)

raviartthomas3cube2dlocalinterpolation.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
4// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
5#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
7
8#include <vector>
9
11
12namespace Dune
13{
14
23 template<class LB>
25 {
26
27 public:
28
34 RT3Cube2DLocalInterpolation (std::bitset<4> s = 0)
35 {
36 for (size_t i=0; i<4; i++)
37 sign_[i] = (s[i]) ? -1.0 : 1.0;
38
39 n_[0] = {-1.0, 0.0};
40 n_[1] = { 1.0, 0.0};
41 n_[2] = { 0.0, -1.0};
42 n_[3] = { 0.0, 1.0};
43 }
44
53 template<typename F, typename C>
54 void interpolate (const F& f, std::vector<C>& out) const
55 {
56 // f gives v*outer normal at a point on the edge!
57 typedef typename LB::Traits::RangeFieldType Scalar;
58 typedef typename LB::Traits::DomainFieldType Vector;
59
60 out.resize(40);
61 fill(out.begin(), out.end(), 0.0);
62
63 const int qOrder = 9;
64 const auto& rule1 = QuadratureRules<Scalar,1>::rule(GeometryTypes::cube(1), qOrder);
65
66 for (auto&& qp : rule1)
67 {
68 Scalar qPos = qp.position();
69 typename LB::Traits::DomainType localPos;
70
71 localPos = {0.0, qPos};
72 auto y = f(localPos);
73 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
74 out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
75 out[2] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[0];
76 out[3] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
77
78 localPos = {1.0, qPos};
79 y = f(localPos);
80 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
81 out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
82 out[6] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
83 out[7] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
84
85 localPos = {qPos, 0.0};
86 y = f(localPos);
87 out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
88 out[9] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
89 out[10] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
90 out[11] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
91
92 localPos = {qPos, 1.0};
93 y = f(localPos);
94 out[12] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
95 out[13] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
96 out[14] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
97 out[15] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
98 }
99
100 const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
101
102 for (auto&& qp : rule2)
103 {
104 auto qPos = qp.position();
105
106 auto y = f(qPos);
107 double l0_x=1.0;
108 double l1_x=2.0*qPos[0]-1.0;
109 double l2_x=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
110 double l3_x=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
111 double l0_y=1.0;
112 double l1_y=2.0*qPos[1]-1.0;
113 double l2_y=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
114 double l3_y=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
115
116 out[16] += y[0]*l0_x*l0_y*qp.weight();
117 out[17] += y[0]*l0_x*l1_y*qp.weight();
118 out[18] += y[0]*l0_x*l2_y*qp.weight();
119 out[19] += y[0]*l0_x*l3_y*qp.weight();
120 out[20] += y[0]*l1_x*l0_y*qp.weight();
121 out[21] += y[0]*l1_x*l1_y*qp.weight();
122 out[22] += y[0]*l1_x*l2_y*qp.weight();
123 out[23] += y[0]*l1_x*l3_y*qp.weight();
124 out[24] += y[0]*l2_x*l0_y*qp.weight();
125 out[25] += y[0]*l2_x*l1_y*qp.weight();
126 out[26] += y[0]*l2_x*l2_y*qp.weight();
127 out[27] += y[0]*l2_x*l3_y*qp.weight();
128
129 out[28] += y[1]*l0_x*l0_y*qp.weight();
130 out[29] += y[1]*l0_x*l1_y*qp.weight();
131 out[30] += y[1]*l0_x*l2_y*qp.weight();
132 out[31] += y[1]*l1_x*l0_y*qp.weight();
133 out[32] += y[1]*l1_x*l1_y*qp.weight();
134 out[33] += y[1]*l1_x*l2_y*qp.weight();
135 out[34] += y[1]*l2_x*l0_y*qp.weight();
136 out[35] += y[1]*l2_x*l1_y*qp.weight();
137 out[36] += y[1]*l2_x*l2_y*qp.weight();
138 out[37] += y[1]*l3_x*l0_y*qp.weight();
139 out[38] += y[1]*l3_x*l1_y*qp.weight();
140 out[39] += y[1]*l3_x*l2_y*qp.weight();
141 }
142 }
143
144 private:
145 // Edge orientations
146 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
147
148 // Edge normals
149 std::array<typename LB::Traits::DomainType, 4> n_;
150 };
151}
152
153#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
static const QuadratureRule & rule(const GeometryType &t, int p, QuadratureType::Enum qt=QuadratureType::GaussLegendre)
select the appropriate QuadratureRule for GeometryType t and order p
Definition: quadraturerules.hh:326
Second order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas3cube2dlocalinterpolation.hh:25
RT3Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas3cube2dlocalinterpolation.hh:34
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas3cube2dlocalinterpolation.hh:54
constexpr GeometryType cube(unsigned int dim)
Returns a GeometryType representing a hypercube of dimension dim.
Definition: type.hh:462
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:235
Dune namespace.
Definition: alignedallocator.hh:13
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