Dune Core Modules (unstable)

raviartthomas12dlocalbasis.hh
1 // -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2 // vi: set et ts=4 sw=2 sts=2:
3 // SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
4 // SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
5 #ifndef DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALBASIS_HH
6 #define DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALBASIS_HH
7 
8 #include <numeric>
9 #include <vector>
10 
11 #include <dune/common/fmatrix.hh>
12 
13 #include "../../common/localbasis.hh"
14 
15 namespace Dune
16 {
26  template<class D, class R>
27  class RT12DLocalBasis
28  {
29 
30  public:
31  typedef LocalBasisTraits<D,2,Dune::FieldVector<D,2>,R,2,Dune::FieldVector<R,2>,
32  Dune::FieldMatrix<R,2,2> > Traits;
33 
39  RT12DLocalBasis (std::bitset<3> s = 0)
40  {
41  for (size_t i=0; i<3; i++)
42  sign_[i] = (s[i]) ? -1.0 : 1.0;
43  }
44 
46  unsigned int size () const
47  {
48  return 8;
49  }
50 
57  inline void evaluateFunction (const typename Traits::DomainType& in,
58  std::vector<typename Traits::RangeType>& out) const
59  {
60  out.resize(8);
61  out[0][0] = sign_[0]*(in[0] - 4.0*in[0]*in[1]);
62  out[0][1] = sign_[0]*(-1.0 + 5.0*in[1] - 4.0*in[1]*in[1]);
63  out[1][0] = sign_[1]*(-1.0 + 5.0*in[0] - 4.0*in[0]*in[0]);
64  out[1][1] = sign_[1]*(in[1] - 4.0*in[0]*in[1]);
65  out[2][0] = sign_[2]*(-3.0*in[0] + 4.0*in[0]*in[0] + 4.0*in[1]*in[0]);
66  out[2][1] = sign_[2]*(-3.0*in[1] + 4.0*in[0]*in[1] + 4.0*in[1]*in[1]);
67  out[3][0] = -5.0*in[0] + 8.0*in[0]*in[0] + 4.0*in[1]*in[0];
68  out[3][1] = 3.0 - 6.0*in[0] - 7.0*in[1] + 8.0*in[0]*in[1] + 4.0*in[1]*in[1];
69  out[4][0] = -3.0 + 7.0*in[0] + 6.0*in[1] - 4.0*in[0]*in[0] - 8.0*in[1]*in[0];
70  out[4][1] = 5.0*in[1] - 4.0*in[0]*in[1] - 8.0*in[1]*in[1];
71  out[5][0] = in[0] - 4.0*in[0]*in[0] + 4.0*in[1]*in[0];
72  out[5][1] = -1.0*in[1] - 4.0*in[0]*in[1] + 4.0*in[1]*in[1];
73  out[6][0] = 16.0*in[0] - 16.0*in[0]*in[0] - 8.0*in[1]*in[0];
74  out[6][1] = 8.0*in[1] - 16.0*in[0]*in[1] - 8.0*in[1]*in[1];
75  out[7][0] = 8.0*in[0] - 8.0*in[0]*in[0] - 16.0*in[1]*in[0];
76  out[7][1] = 16.0*in[1] - 8.0*in[0]*in[1] - 16.0*in[1]*in[1];
77  }
78 
85  inline void evaluateJacobian (const typename Traits::DomainType& in,
86  std::vector<typename Traits::JacobianType>& out) const
87  {
88  out.resize(8);
89 
90  out[0][0][0] = sign_[0]*(1.0 - 4.0*in[1]);
91  out[0][0][1] = sign_[0]*(-4.0*in[0]);
92  out[0][1][0] = 0.0;
93  out[0][1][1] = sign_[0]*(5.0 - 8.0*in[1]);
94 
95  out[1][0][0] = sign_[1]*(5.0 - 8.0*in[0]);
96  out[1][0][1] = 0.0;
97  out[1][1][0] = sign_[1]*(-4.0*in[1]);
98  out[1][1][1] = sign_[1]*(1.0 - 4.0*in[0]);
99 
100  out[2][0][0] = sign_[2]*(-3.0 + 8.0*in[0] + 4.0*in[1]);
101  out[2][0][1] = sign_[2]*(4.0*in[0]);
102  out[2][1][0] = sign_[2]*(4.0*in[1]);
103  out[2][1][1] = sign_[2]*(-3.0 + 4.0*in[0] + 8.0*in[1]);
104 
105  out[3][0][0] = -5.0 + 16.0*in[0] + 4.0*in[1];
106  out[3][0][1] = 4.0*in[0];
107  out[3][1][0] = -6.0 + 8.0*in[1];
108  out[3][1][1] = -7.0 + 8.0*in[0] + 8.0*in[1];
109 
110  out[4][0][0] = 7.0 - 8.0*in[0] - 8.0*in[1];
111  out[4][0][1] = 6.0 - 8.0*in[0];
112  out[4][1][0] = -4.0*in[1];
113  out[4][1][1] = 5.0 - 4.0*in[0] - 16.0*in[1];
114 
115  out[5][0][0] = 1.0 - 8.0*in[0] + 4*in[1];
116  out[5][0][1] = 4.0*in[0];
117  out[5][1][0] = -4.0*in[1];
118  out[5][1][1] = -1.0 - 4.0*in[0] + 8.0*in[1];
119 
120  out[6][0][0] = 16.0 - 32.0*in[0] - 8.0*in[1];
121  out[6][0][1] = -8.0*in[0];
122  out[6][1][0] = -16.0*in[1];
123  out[6][1][1] = 8.0 - 16.0*in[0] - 16.0*in[1];
124 
125  out[7][0][0] = 8.0 - 16.0*in[0] - 16.0*in[1];
126  out[7][0][1] = -16.0*in[0];
127  out[7][1][0] = -8.0*in[1];
128  out[7][1][1] = 16.0 - 8.0*in[0] - 32.0*in[1];
129  }
130 
132  void partial (const std::array<unsigned int, 2>& order,
133  const typename Traits::DomainType& in, // position
134  std::vector<typename Traits::RangeType>& out) const // return value
135  {
136  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
137  if (totalOrder == 0) {
138  evaluateFunction(in, out);
139  } else if (totalOrder == 1) {
140  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
141  out.resize(size());
142 
143  switch (direction) {
144  case 0:
145  out[0][0] = sign_[0]*(1.0 - 4.0*in[1]);
146  out[0][1] = 0.0;
147  out[1][0] = sign_[1]*(5.0 - 8.0*in[0]);
148  out[1][1] = sign_[1]*(-4.0*in[1]);
149  out[2][0] = sign_[2]*(-3.0 + 8.0*in[0] + 4.0*in[1]);
150  out[2][1] = sign_[2]*(4.0*in[1]);
151  out[3][0] = -5.0 + 16.0*in[0] + 4.0*in[1];
152  out[3][1] = -6.0 + 8.0*in[1];
153  out[4][0] = 7.0 - 8.0*in[0] - 8.0*in[1];
154  out[4][1] = -4.0*in[1];
155  out[5][0] = 1.0 - 8.0*in[0] + 4*in[1];
156  out[5][1] = -4.0*in[1];
157  out[6][0] = 16.0 - 32.0*in[0] - 8.0*in[1];
158  out[6][1] = -16.0*in[1];
159  out[7][0] = 8.0 - 16.0*in[0] - 16.0*in[1];
160  out[7][1] = -8.0*in[1];
161  break;
162  case 1:
163  out[2][1] = sign_[2]*(-3.0 + 4.0*in[0] + 8.0*in[1]);
164  out[2][0] = sign_[2]*(4.0*in[0]);
165  out[1][1] = sign_[1]*(1.0 - 4.0*in[0]);
166  out[1][0] = 0.0;
167  out[0][0] = sign_[0]*(-4.0*in[0]);
168  out[0][1] = sign_[0]*(5.0 - 8.0*in[1]);
169  out[3][0] = 4.0*in[0];
170  out[3][1] = -7.0 + 8.0*in[0] + 8.0*in[1];
171  out[4][0] = 6.0 - 8.0*in[0];
172  out[4][1] = 5.0 - 4.0*in[0] - 16.0*in[1];
173  out[5][0] = 4.0*in[0];
174  out[5][1] = -1.0 - 4.0*in[0] + 8.0*in[1];
175  out[6][0] = -8.0*in[0];
176  out[6][1] = 8.0 - 16.0*in[0] - 16.0*in[1];
177  out[7][0] = -16.0*in[0];
178  out[7][1] = 16.0 - 8.0*in[0] - 32.0*in[1];
179  break;
180  default:
181  DUNE_THROW(RangeError, "Component out of range.");
182  }
183  } else {
184  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
185  }
186  }
187 
189  unsigned int order () const
190  {
191  return 2;
192  }
193 
194  private:
195  std::array<R,3> sign_;
196  };
197 }
198 #endif // DUNE_LOCALFUNCTIONS_RAVIARTTHOMAS12DLOCALBASIS_HH
Dune::FieldMatrix
A dense n x m matrix.
Definition: fmatrix.hh:117
Dune::FieldVector
vector space out of a tensor product of fields.
Definition: fvector.hh:95
Dune::NotImplemented
Default exception for dummy implementations.
Definition: exceptions.hh:263
Dune::RT12DLocalBasis
First order Raviart-Thomas shape functions on the reference triangle.
Definition: raviartthomas12dlocalbasis.hh:28
Dune::RT12DLocalBasis::RT12DLocalBasis
RT12DLocalBasis(std::bitset< 3 > s=0)
Make set number s, where 0 <= s < 8.
Definition: raviartthomas12dlocalbasis.hh:39
Dune::RT12DLocalBasis::size
unsigned int size() const
number of shape functions
Definition: raviartthomas12dlocalbasis.hh:46
Dune::RT12DLocalBasis::partial
void partial(const std::array< unsigned int, 2 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: raviartthomas12dlocalbasis.hh:132
Dune::RT12DLocalBasis::evaluateJacobian
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: raviartthomas12dlocalbasis.hh:85
Dune::RT12DLocalBasis::order
unsigned int order() const
Polynomial order of the shape functions.
Definition: raviartthomas12dlocalbasis.hh:189
Dune::RT12DLocalBasis::evaluateFunction
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: raviartthomas12dlocalbasis.hh:57
Dune::RangeError
Default exception class for range errors.
Definition: exceptions.hh:254
fmatrix.hh
Implements a matrix constructed from a given type representing a field and compile-time given number ...
DUNE_THROW
#define DUNE_THROW(E, m)
Definition: exceptions.hh:218
Dune::Hybrid::accumulate
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:279
Dune
Dune namespace.
Definition: alignedallocator.hh:13
Dune::LocalBasisTraits
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:35
Dune::LocalBasisTraits::DomainType
D DomainType
domain type
Definition: localbasis.hh:43
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