dune-localfunctions  2.8.0
raviartthomas03dlocalbasis.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_RAVIARTTHOMAS_RAVIARTTHOMAS03D_RAVIARTTHOMAS03DLOCALBASIS_HH
4 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS_RAVIARTTHOMAS03D_RAVIARTTHOMAS03DLOCALBASIS_HH
5 
6 #include <numeric>
7 
8 #include <dune/common/fmatrix.hh>
9 
11 
12 namespace Dune
13 {
22  template<class D, class R>
24  {
25  public:
26  typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,3,Dune::FieldVector<R,3>,
27  Dune::FieldMatrix<R,3,3> > Traits;
28 
30  RT03DLocalBasis (std::bitset<4> s = 0)
31  {
32  for (int i=0; i<4; i++)
33  sign_[i] = s[i] ? -1.0 : 1.0;
34  }
35 
37  unsigned int size () const
38  {
39  return 4;
40  }
41 
43  inline void evaluateFunction (const typename Traits::DomainType& in,
44  std::vector<typename Traits::RangeType>& out) const
45  {
46  out.resize(4);
47  auto c = std::sqrt(2.0);
48  out[0] = {sign_[0]*c* in[0], sign_[0]*c* in[1], sign_[0]*c*(in[2]-D(1))};
49  out[1] = {sign_[1]*c* in[0], sign_[1]*c*(in[1]-D(1)), sign_[1]*c* in[2] };
50  out[2] = {sign_[2]*c*(in[0]-D(1)), sign_[2]*c* in[1], sign_[2]*c* in[2] };
51  out[3] = {sign_[3]*c* in[0], sign_[3]*c* in[1], sign_[3]*c* in[2] };
52  }
53 
55  inline void
56  evaluateJacobian (const typename Traits::DomainType& in, // position
57  std::vector<typename Traits::JacobianType>& out) const // return value
58  {
59  out.resize(4);
60  for (int i=0; i<4; i++)
61  {
62  auto c = std::sqrt(2.0);
63  out[i][0] = {c*sign_[i], 0, 0};
64  out[i][1] = { 0,c*sign_[i], 0};
65  out[i][2] = { 0, 0,c*sign_[i]};
66  }
67  }
68 
70  void partial (const std::array<unsigned int, 3>& order,
71  const typename Traits::DomainType& in, // position
72  std::vector<typename Traits::RangeType>& out) const // return value
73  {
74  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
75  if (totalOrder == 0) {
76  evaluateFunction(in, out);
77  } else if (totalOrder == 1) {
78  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
79  out.resize(size());
80 
81  for (int i=0; i<size(); i++)
82  {
83  out[i][direction] = sign_[i]* std::sqrt(2.0) ;
84  out[i][(direction+1)%3] = 0;
85  out[i][(direction+2)%3] = 0;
86  }
87  } else {
88  out.resize(size());
89  for (std::size_t i = 0; i < size(); ++i)
90  for (std::size_t j = 0; j < 3; ++j)
91  out[i][j] = 0;
92  }
93 
94  }
95 
97  unsigned int order () const
98  {
99  return 1;
100  }
101 
102  private:
103 
104  // Signs of the face normals
105  std::array<R,4> sign_;
106  };
107 }
108 #endif
Definition: bdfmcube.hh:16
Type traits for LocalBasisVirtualInterface.
Definition: common/localbasis.hh:32
D DomainType
domain type
Definition: common/localbasis.hh:43
Lowest order Raviart-Thomas shape functions on the reference tetrahedron.
Definition: raviartthomas03dlocalbasis.hh:24
RT03DLocalBasis(std::bitset< 4 > s=0)
Make set number s, where 0 <= s < 16.
Definition: raviartthomas03dlocalbasis.hh:30
void partial(const std::array< unsigned int, 3 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: raviartthomas03dlocalbasis.hh:70
unsigned int order() const
Polynomial order of the shape functions.
Definition: raviartthomas03dlocalbasis.hh:97
unsigned int size() const
number of shape functions
Definition: raviartthomas03dlocalbasis.hh:37
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: raviartthomas03dlocalbasis.hh:56
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: raviartthomas03dlocalbasis.hh:43
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 3, Dune::FieldVector< R, 3 >, Dune::FieldMatrix< R, 3, 3 > > Traits
Definition: raviartthomas03dlocalbasis.hh:27