dune-localfunctions  2.8.0
raviartthomas2cube2dlocalinterpolation.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_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS2_CUBE2D_LOCALINTERPOLATION_HH
5 
6 #include <vector>
7 
8 #include <dune/geometry/quadraturerules.hh>
10 
11 namespace 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
Definition: bdfmcube.hh:16
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