DUNE-FEM (unstable)

raviartthomas2cube2dlocalinterpolation.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_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
6#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
7
8#include <vector>
9
11
12namespace Dune
13{
14
23 template<class LB>
25 {
26
27 public:
28
34 RT2Cube2DLocalInterpolation (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(24);
61 fill(out.begin(), out.end(), 0.0);
62
63 const int qOrder = 6;
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
77 localPos = {1.0, qPos};
78 y = f(localPos);
79 out[3] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
80 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
81 out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
82
83 localPos = {qPos, 0.0};
84 y = f(localPos);
85 out[6] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
86 out[7] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
87 out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
88
89 localPos = {qPos, 1.0};
90 y = f(localPos);
91 out[9] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
92 out[10] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
93 out[11] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
94 }
95
96 const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
97
98 for (auto&& qp : rule2)
99 {
100 FieldVector<double,2> qPos = qp.position();
101
102 auto y = f(qPos);
103 out[12] += y[0]*qp.weight();
104 out[13] += y[1]*qp.weight();
105 out[14] += y[0]*qPos[0]*qp.weight();
106 out[15] += y[1]*qPos[0]*qp.weight();
107 out[16] += y[0]*qPos[1]*qp.weight();
108 out[17] += y[1]*qPos[1]*qp.weight();
109 out[18] += y[0]*qPos[0]*qPos[1]*qp.weight();
110 out[19] += y[1]*qPos[0]*qPos[1]*qp.weight();
111 out[20] += y[0]*qPos[1]*qPos[1]*qp.weight();
112 out[21] += y[1]*qPos[0]*qPos[0]*qp.weight();
113 out[22] += y[0]*qPos[0]*qPos[1]*qPos[1]*qp.weight();
114 out[23] += y[1]*qPos[0]*qPos[0]*qPos[1]*qp.weight();
115 }
116 }
117
118 private:
119 // Edge orientations
120 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
121
122 // Edge normals
123 std::array<typename LB::Traits::DomainType, 4> n_;
124 };
125}
126#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
vector space out of a tensor product of fields.
Definition: fvector.hh:91
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 triangle.
Definition: raviartthomas2cube2dlocalinterpolation.hh:25
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas2cube2dlocalinterpolation.hh:54
RT2Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas2cube2dlocalinterpolation.hh:34
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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