Dune Core Modules (2.8.0)

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#ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
4#define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
5
6#include <vector>
7
9#include <dune/localfunctions/common/localinterpolation.hh>
10
11namespace Dune
12{
13
22 template<class LB>
24 {
25
26 public:
27
33 RT2Cube2DLocalInterpolation (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<typename F, typename 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(24);
62 fill(out.begin(), out.end(), 0.0);
63
64 const int qOrder = 6;
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;
71
72 localPos = {0.0, qPos};
73 auto y = f(localPos);
74 out[0] += (y[0]*n_[0][0] + y[1]*n_[0][1])*qp.weight()*sign_[0];
75 out[1] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(2.0*qPos - 1.0)*qp.weight();
76 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];
77
78 localPos = {1.0, qPos};
79 y = f(localPos);
80 out[3] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
81 out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
82 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];
83
84 localPos = {qPos, 0.0};
85 y = f(localPos);
86 out[6] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
87 out[7] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
88 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];
89
90 localPos = {qPos, 1.0};
91 y = f(localPos);
92 out[9] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
93 out[10] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
94 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];
95 }
96
97 const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
98
99 for (auto&& qp : rule2)
100 {
101 FieldVector<double,2> qPos = qp.position();
102
103 auto y = f(qPos);
104 out[12] += y[0]*qp.weight();
105 out[13] += y[1]*qp.weight();
106 out[14] += y[0]*qPos[0]*qp.weight();
107 out[15] += y[1]*qPos[0]*qp.weight();
108 out[16] += y[0]*qPos[1]*qp.weight();
109 out[17] += y[1]*qPos[1]*qp.weight();
110 out[18] += y[0]*qPos[0]*qPos[1]*qp.weight();
111 out[19] += y[1]*qPos[0]*qPos[1]*qp.weight();
112 out[20] += y[0]*qPos[1]*qPos[1]*qp.weight();
113 out[21] += y[1]*qPos[0]*qPos[0]*qp.weight();
114 out[22] += y[0]*qPos[0]*qPos[1]*qPos[1]*qp.weight();
115 out[23] += y[1]*qPos[0]*qPos[0]*qPos[1]*qp.weight();
116 }
117 }
118
119 private:
120 // Edge orientations
121 std::array<typename LB::Traits::RangeFieldType, 4> sign_;
122
123 // Edge normals
124 std::array<typename LB::Traits::DomainType, 4> n_;
125 };
126}
127#endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
vector space out of a tensor product of fields.
Definition: fvector.hh:95
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
Second order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas2cube2dlocalinterpolation.hh:24
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas2cube2dlocalinterpolation.hh:53
RT2Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas2cube2dlocalinterpolation.hh:33
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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