dune-localfunctions  2.8.0
raviartthomas3cube2dlocalinterpolation.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_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_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  RT3Cube2DLocalInterpolation (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(40);
62  fill(out.begin(), out.end(), 0.0);
63 
64  const int qOrder = 9;
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  out[3] += (y[0]*n_[0][0] + y[1]*n_[0][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
78 
79  localPos = {1.0, qPos};
80  y = f(localPos);
81  out[4] += (y[0]*n_[1][0] + y[1]*n_[1][1])*qp.weight()*sign_[1];
82  out[5] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(1.0 - 2.0*qPos)*qp.weight();
83  out[6] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[1];
84  out[7] += (y[0]*n_[1][0] + y[1]*n_[1][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
85 
86  localPos = {qPos, 0.0};
87  y = f(localPos);
88  out[8] += (y[0]*n_[2][0] + y[1]*n_[2][1])*qp.weight()*sign_[2];
89  out[9] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(1.0 - 2.0*qPos)*qp.weight();
90  out[10] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[2];
91  out[11] += (y[0]*n_[2][0] + y[1]*n_[2][1])*(-20.0*qPos*qPos*qPos + 30.0*qPos*qPos - 12.0*qPos + 1.0)*qp.weight();
92 
93  localPos = {qPos, 1.0};
94  y = f(localPos);
95  out[12] += (y[0]*n_[3][0] + y[1]*n_[3][1])*qp.weight()*sign_[3];
96  out[13] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(2.0*qPos - 1.0)*qp.weight();
97  out[14] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(6.0*qPos*qPos - 6.0*qPos + 1.0)*qp.weight()*sign_[3];
98  out[15] += (y[0]*n_[3][0] + y[1]*n_[3][1])*(20.0*qPos*qPos*qPos - 30.0*qPos*qPos + 12.0*qPos - 1.0)*qp.weight();
99  }
100 
101  const auto& rule2 = QuadratureRules<Vector,2>::rule(GeometryTypes::cube(2), qOrder);
102 
103  for (auto&& qp : rule2)
104  {
105  auto qPos = qp.position();
106 
107  auto y = f(qPos);
108  double l0_x=1.0;
109  double l1_x=2.0*qPos[0]-1.0;
110  double l2_x=6.0*qPos[0]*qPos[0]-6.0*qPos[0]+1.0;
111  double l3_x=20.0*qPos[0]*qPos[0]*qPos[0] - 30.0*qPos[0]*qPos[0] + 12.0*qPos[0] - 1.0;
112  double l0_y=1.0;
113  double l1_y=2.0*qPos[1]-1.0;
114  double l2_y=6.0*qPos[1]*qPos[1]-6.0*qPos[1]+1.0;
115  double l3_y=20.0*qPos[1]*qPos[1]*qPos[1] - 30.0*qPos[1]*qPos[1] + 12.0*qPos[1] - 1.0;
116 
117  out[16] += y[0]*l0_x*l0_y*qp.weight();
118  out[17] += y[0]*l0_x*l1_y*qp.weight();
119  out[18] += y[0]*l0_x*l2_y*qp.weight();
120  out[19] += y[0]*l0_x*l3_y*qp.weight();
121  out[20] += y[0]*l1_x*l0_y*qp.weight();
122  out[21] += y[0]*l1_x*l1_y*qp.weight();
123  out[22] += y[0]*l1_x*l2_y*qp.weight();
124  out[23] += y[0]*l1_x*l3_y*qp.weight();
125  out[24] += y[0]*l2_x*l0_y*qp.weight();
126  out[25] += y[0]*l2_x*l1_y*qp.weight();
127  out[26] += y[0]*l2_x*l2_y*qp.weight();
128  out[27] += y[0]*l2_x*l3_y*qp.weight();
129 
130  out[28] += y[1]*l0_x*l0_y*qp.weight();
131  out[29] += y[1]*l0_x*l1_y*qp.weight();
132  out[30] += y[1]*l0_x*l2_y*qp.weight();
133  out[31] += y[1]*l1_x*l0_y*qp.weight();
134  out[32] += y[1]*l1_x*l1_y*qp.weight();
135  out[33] += y[1]*l1_x*l2_y*qp.weight();
136  out[34] += y[1]*l2_x*l0_y*qp.weight();
137  out[35] += y[1]*l2_x*l1_y*qp.weight();
138  out[36] += y[1]*l2_x*l2_y*qp.weight();
139  out[37] += y[1]*l3_x*l0_y*qp.weight();
140  out[38] += y[1]*l3_x*l1_y*qp.weight();
141  out[39] += y[1]*l3_x*l2_y*qp.weight();
142  }
143  }
144 
145  private:
146  // Edge orientations
147  std::array<typename LB::Traits::RangeFieldType, 4> sign_;
148 
149  // Edge normals
150  std::array<typename LB::Traits::DomainType, 4> n_;
151  };
152 }
153 
154 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS3_CUBE2D_LOCALINTERPOLATION_HH
Definition: bdfmcube.hh:16
Second order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas3cube2dlocalinterpolation.hh:24
RT3Cube2DLocalInterpolation(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas3cube2dlocalinterpolation.hh:33
void interpolate(const F &ff, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas3cube2dlocalinterpolation.hh:53