Dune Core Modules (2.8.0)

raviartthomas1cube2dlocalinterpolation.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALINTERPOLATION_HH
5
6#include <vector>
7
9#include <dune/localfunctions/common/localinterpolation.hh>
10
11
12namespace Dune
13{
14
23 template<class LB>
25 {
26
27 public:
33 RT1Cube2DLocalInterpolation (std::bitset<4> s = 0)
34 {
35 for (size_t i=0; i<4; i++)
36 sign_[i] = (s[i]) ? -1.0 : 1.0;
37
38 n_[0] = {-1.0, 0.0};
39 n_[1] = { 1.0, 0.0};
40 n_[2] = { 0.0, -1.0};
41 n_[3] = { 0.0, 1.0};
42 }
43
52 template<class F, class C>
53 void interpolate (const F& ff, std::vector<C>& out) const
54 {
55 // f gives v*outer normal at a point on the edge!
56 typedef typename LB::Traits::RangeFieldType Scalar;
57 typedef typename LB::Traits::DomainFieldType Vector;
58
59 auto&& f = Impl::makeFunctionWithCallOperator<typename LB::Traits::DomainType>(ff);
60
61 out.resize(12);
62 fill(out.begin(), out.end(), 0.0);
63
64 const int qOrder = 3;
65 const auto& rule1 = QuadratureRules<Scalar,1>::rule(GeometryTypes::cube(1), qOrder);
66
67 for (auto&& qp : rule1)
68 {
69 Scalar qPos = qp.position();
70 typename LB::Traits::DomainType localPos = {0.0, qPos};
71
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
76 localPos = {1.0, qPos};
77 y = f(localPos);
78 out[2] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
79 out[3] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
80
81 localPos = {qPos, 0.0};
82 y = f(localPos);
83 out[4] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
84 out[5] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
85
86 localPos = {qPos, 1.0};
87 y = f(localPos);
88 out[6] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
89 out[7] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
90 }
91
92 const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
93
94 for (auto&& qp : rule2)
95 {
96 auto qPos = qp.position();
97
98 auto y = f(qPos);
99 out[8] += y[0]*qp.weight();
100 out[9] += y[1]*qp.weight();
101 out[10] += y[0]*qPos[1]*qp.weight();
102 out[11] += y[1]*qPos[0]*qp.weight();
103 }
104 }
105
106 private:
107 // Edge orientations
108 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
109
110 // Edge normals
111 std::array<typename LB::Traits::DomainType, 4> n_;
112 };
113}
114#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_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:280
First order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas1cube2dlocalinterpolation.hh:25
RT1Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas1cube2dlocalinterpolation.hh:33
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas1cube2dlocalinterpolation.hh:53
constexpr GeometryType cube(unsigned int dim)
Returns a GeometryType representing a hypercube of dimension dim.
Definition: type.hh:470
typename Overloads::ScalarType< std::decay_t< V > >::type Scalar
Element type of some SIMD type.
Definition: interface.hh:233
Dune namespace.
Definition: alignedallocator.hh:11
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