dune-localfunctions  2.8.0
raviartthomas1cube2dlocalinterpolation.hh
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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 
8 #include <dune/geometry/quadraturerules.hh>
10 
11 
12 namespace 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
Definition: bdfmcube.hh:16
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