dune-localfunctions  2.3.1-rc1
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>
9 
10 
11 namespace Dune
12 {
13 
22  template<class LB>
24  {
25 
26  public:
29  {
30  sign0 = sign1 = sign2 = sign3 = 1.0;
31  }
32 
38  RT1Cube2DLocalInterpolation (unsigned int s)
39  {
40  sign0 = sign1 = sign2 = sign3 = 1.0;
41  if (s & 1)
42  {
43  sign0 = -1.0;
44  }
45  if (s & 2)
46  {
47  sign1 = -1.0;
48  }
49  if (s & 4)
50  {
51  sign2 = -1.0;
52  }
53  if (s & 8)
54  {
55  sign3 = -1.0;
56  }
57 
58  n0[0] = -1.0;
59  n0[1] = 0.0;
60  n1[0] = 1.0;
61  n1[1] = 0.0;
62  n2[0] = 0.0;
63  n2[1] = -1.0;
64  n3[0] = 0.0;
65  n3[1] = 1.0;
66  }
67 
76  template<class F, class C>
77  void interpolate (const F& f, std::vector<C>& out) const
78  {
79  // f gives v*outer normal at a point on the edge!
80  typedef typename LB::Traits::RangeFieldType Scalar;
81  typedef typename LB::Traits::DomainFieldType Vector;
82  typename F::Traits::RangeType y;
83 
84  out.resize(12);
85  fill(out.begin(), out.end(), 0.0);
86 
87  const int qOrder = 3;
88  const QuadratureRule<Scalar,1>& rule1 = QuadratureRules<Scalar,1>::rule(GeometryType(GeometryType::cube,1), qOrder);
89 
90  for (typename QuadratureRule<Scalar,1>::const_iterator it = rule1.begin();
91  it != rule1.end(); ++it)
92  {
93  Scalar qPos = it->position();
94  typename LB::Traits::DomainType localPos;
95 
96  localPos[0] = 0.0;
97  localPos[1] = qPos;
98  f.evaluate(localPos, y);
99  out[0] += (y[0]*n0[0] + y[1]*n0[1])*it->weight()*sign0;
100  out[1] += (y[0]*n0[0] + y[1]*n0[1])*(2.0*qPos - 1.0)*it->weight();
101 
102  localPos[0] = 1.0;
103  localPos[1] = qPos;
104  f.evaluate(localPos, y);
105  out[2] += (y[0]*n1[0] + y[1]*n1[1])*it->weight()*sign1;
106  out[3] += (y[0]*n1[0] + y[1]*n1[1])*(1.0 - 2.0*qPos)*it->weight();
107 
108  localPos[0] = qPos;
109  localPos[1] = 0.0;
110  f.evaluate(localPos, y);
111  out[4] += (y[0]*n2[0] + y[1]*n2[1])*it->weight()*sign2;
112  out[5] += (y[0]*n2[0] + y[1]*n2[1])*(1.0 - 2.0*qPos)*it->weight();
113 
114  localPos[0] = qPos;
115  localPos[1] = 1.0;
116  f.evaluate(localPos, y);
117  out[6] += (y[0]*n3[0] + y[1]*n3[1])*it->weight()*sign3;
118  out[7] += (y[0]*n3[0] + y[1]*n3[1])*(2.0*qPos - 1.0)*it->weight();
119  }
120 
121  const QuadratureRule<Vector,2>& rule2 = QuadratureRules<Vector,2>::rule(GeometryType(GeometryType::cube,2), qOrder);
122 
123  for (typename QuadratureRule<Vector,2>::const_iterator it=rule2.begin(); it!=rule2.end(); ++it)
124  {
125  FieldVector<double,2> qPos = it->position();
126 
127  f.evaluate(qPos, y);
128  out[8] += y[0]*it->weight();
129  out[9] += y[1]*it->weight();
130  out[10] += y[0]*qPos[1]*it->weight();
131  out[11] += y[1]*qPos[0]*it->weight();
132  }
133  }
134 
135  private:
136  typename LB::Traits::RangeFieldType sign0, sign1, sign2, sign3;
137  typename LB::Traits::DomainType n0, n1, n2, n3;
138  };
139 }
140 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS1_CUBE2D_LOCALINTERPOLATION_HH
RT1Cube2DLocalInterpolation(unsigned int s)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas1cube2dlocalinterpolation.hh:38
First order Raviart-Thomas shape functions on the reference quadrilateral.
Definition: raviartthomas1cube2dlocalinterpolation.hh:23
RT1Cube2DLocalInterpolation()
Standard constructor.
Definition: raviartthomas1cube2dlocalinterpolation.hh:28
void interpolate(const F &f, std::vector< C > &out) const
Interpolate a given function with shape functions.
Definition: raviartthomas1cube2dlocalinterpolation.hh:77