DUNE-FEM (unstable)

raviartthomas12dlocalinterpolation.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_RAVIARTTHOMAS12DLOCALINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALINTERPOLATION_HH
7
8#include <vector>
9
11
12namespace Dune
13{
14
23 template<class LB>
25 {
26
27 public:
28
34 RT12DLocalInterpolation (std::bitset<3> s = 0)
35 {
36 using std::sqrt;
37 for (size_t i=0; i<3; i++)
38 sign_[i] = (s[i]) ? -1.0 : 1.0;
39
40 n_[0] = { 0.0, -1.0};
41 n_[1] = {-1.0, 0.0};
42 n_[2] = { 1.0/sqrt(2.0), 1.0/sqrt(2.0)};
43
44 c_ = { 0.5*n_[0][0] - 1.0*n_[0][1],
45 -1.0*n_[1][0] + 0.5*n_[1][1],
46 0.5*n_[2][0] + 0.5*n_[2][1]};
47 }
48
57 template<typename F, typename C>
58 void interpolate (const F& f, std::vector<C>& out) const
59 {
60 // f gives v*outer normal at a point on the edge!
61 typedef typename LB::Traits::RangeFieldType Scalar;
62 typedef typename LB::Traits::DomainFieldType Vector;
63
64 out.resize(8);
65 fill(out.begin(), out.end(), 0.0);
66
67 const int qOrder1 = 4;
69
70 for (auto&& qp : rule1)
71 {
72 Scalar qPos = qp.position();
73 typename LB::Traits::DomainType localPos;
74
75 localPos = {qPos, 0.0};
76 auto y = f(localPos);
77 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0]/c_[0];
78 out[3] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight()/c_[0];
79
80 localPos = {0.0, qPos};
81 y = f(localPos);
82 out[1] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1]/c_[1];
83 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight()/c_[1];
84
85 localPos = {1.0 - qPos, qPos};
86 y = f(localPos);
87 out[2] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2]/c_[2];
88 out[5] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(2.0*qPos - 1.0)*qp.weight()/c_[2];
89 }
90
91 const int qOrder2 = 8;
93
94 for (auto&& qp : rule2)
95 {
96 auto qPos = qp.position();
97
98 auto y = f(qPos);
99 out[6] += y[0]*qp.weight();
100 out[7] += y[1]*qp.weight();
101 }
102 }
103
104 private:
105 // Edge orientations
106 std::array<typename LB::Traits::RangeFieldType, 3> sign_;
107
108 // Edge normals
109 std::array<typename LB::Traits::DomainType, 3> n_;
110
111 std::array<typename LB::Traits::RangeFieldType, 3> c_;
112 };
113}
114#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALINTERPOLATION_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
First order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas12dlocalinterpolation.hh:25
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas12dlocalinterpolation.hh:58
RT12DLocalInterpolation(std::bitset< 3 > s=0)
Make set number s, where 0 <= s < 8.
Definition: raviartthomas12dlocalinterpolation.hh:34
constexpr GeometryType simplex(unsigned int dim)
Returns a GeometryType representing a simplex of dimension dim.
Definition: type.hh:453
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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