dune-localfunctions  2.5.0
hierarchicalprismp2localbasis.hh
Go to the documentation of this file.
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_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
4 #define DUNE_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
5 
10 #include <numeric>
11 
12 #include <dune/common/fvector.hh>
13 #include <dune/common/fmatrix.hh>
14 
16 
17 namespace Dune
18 {
19  template<class D, class R>
21  {
22  public:
24  typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,3> > Traits;
25 
27  unsigned int size () const
28  {
29  return 18;
30  }
31 
33  void evaluateFunction (const typename Traits::DomainType& in,
34  std::vector<typename Traits::RangeType> & out) const
35  {
36  out.resize(18);
37 
38  out[0]=(1.0-in[0]-in[1])*(1.0-in[2]);
39  out[1]= in[0]*(1-in[2]);
40  out[2]=in[1]*(1-in[2]);
41  out[3]=in[2]*(1.0-in[0]-in[1]);
42  out[4]=in[0]*in[2];
43  out[5]=in[1]*in[2];
44 
45  //edges
46  out[6]=2*(1.0-in[0]-in[1])*(0.5-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
47  out[7]=2*in[0]*(-0.5+in[0])*(4*in[2]-4*in[2]*in[2]);
48  out[8]=2*in[1]*(-0.5+in[1])*(4*in[2]-4*in[2]*in[2]);
49  out[9]=4*in[0]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
50  out[10]=4*in[1]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
51  out[11]=4*in[0]*in[1]*(1-3*in[2]+2*in[2]*in[2]);
52  out[12]=4*in[0]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
53  out[13]=4*in[1]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
54  out[14]=4*in[0]*in[1]*(-in[2]+2*in[2]*in[2]);
55 
56  //faces
57  out[15]=4*in[0]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
58  out[16]=4*in[1]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
59  out[17]=4*in[0]*in[1]*(4*in[2]-4*in[2]*in[2]);
60  }
61 
62 
63 
65  void evaluateJacobian (const typename Traits::DomainType& in, //position
66  std::vector<typename Traits::JacobianType>& out) const //return value
67  {
68  out.resize(18);
69 
70  //vertices
71  out[0][0][0] = in[2]-1;
72  out[0][0][1] = in[2]-1;
73  out[0][0][2] = in[0]+in[1]-1;
74 
75  out[1][0][0] = 1-in[2];
76  out[1][0][1] = 0;
77  out[1][0][2] =-in[0];
78 
79  out[2][0][0] = 0;
80  out[2][0][1] = 1-in[2];
81  out[2][0][2] = -in[1];
82 
83  out[3][0][0] = -in[2];
84  out[3][0][1] = -in[2];
85  out[3][0][2] = 1-in[0]-in[1];
86 
87  out[4][0][0] = in[2];
88  out[4][0][1] = 0;
89  out[4][0][2] = in[0];
90 
91  out[5][0][0] = 0;
92  out[5][0][1] = in[2];
93  out[5][0][2] = in[1];
94 
95  //edges
96  out[6][0][0] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
97  out[6][0][1] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
98  out[6][0][2] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
99 
100  out[7][0][0] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
101  out[7][0][1] = 0;
102  out[7][0][2] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
103 
104  out[8][0][0] = 0;
105  out[8][0][1] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
106  out[8][0][2] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
107 
108  out[9][0][0] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
109  out[9][0][1] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
110  out[9][0][2] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
111 
112  out[10][0][0] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
113  out[10][0][1] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
114  out[10][0][2] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
115 
116  out[11][0][0] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
117  out[11][0][1] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
118  out[11][0][2] = 4*in[0]*in[1]*(-3+4*in[2]);
119 
120  out[12][0][0] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
121  out[12][0][1] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
122  out[12][0][2] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
123 
124  out[13][0][0] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
125  out[13][0][1] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
126  out[13][0][2] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
127 
128  out[14][0][0] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
129  out[14][0][1] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
130  out[14][0][2] = 4*in[0]*in[1]*(-1+4*in[2]);
131 
132  //faces
133  out[15][0][0] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
134  out[15][0][1] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
135  out[15][0][2] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
136 
137  out[16][0][0] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
138  out[16][0][1] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
139  out[16][0][2] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
140 
141  out[17][0][0] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
142  out[17][0][1] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
143  out[17][0][2] = 4*in[0]*in[1]*(4-8*in[2]);
144  }
145 
147  void partial (const std::array<unsigned int, 3>& order,
148  const typename Traits::DomainType& in, // position
149  std::vector<typename Traits::RangeType>& out) const // return value
150  {
151  auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
152  if (totalOrder == 0) {
153  evaluateFunction(in, out);
154  } else if (totalOrder == 1) {
155  out.resize(size());
156  auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
157 
158  switch (direction) {
159  case 0:
160  out[0] = in[2]-1;
161  out[1] = 1-in[2];
162  out[2] = 0;
163  out[3] = -in[2];
164  out[4] = in[2];
165  out[5] = 0;
166  out[6] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
167  out[7] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
168  out[8] = 0;
169  out[9] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
170  out[10] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
171  out[11] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
172  out[12] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
173  out[13] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
174  out[14] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
175  out[15] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
176  out[16] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
177  out[17] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
178  break;
179  case 1:
180  out[0] = in[2]-1;
181  out[1] = 0;
182  out[2] = 1-in[2];
183  out[3] = -in[2];
184  out[4] = 0;
185  out[5] = in[2];
186  out[6] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
187  out[7] = 0;
188  out[8] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
189  out[9] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
190  out[10] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
191  out[11] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
192  out[12] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
193  out[13] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
194  out[14] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
195  out[15] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
196  out[16] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
197  out[17] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
198  break;
199  case 2:
200  out[0] = in[0]+in[1]-1;
201  out[1] =-in[0];
202  out[2] = -in[1];
203  out[3] = 1-in[0]-in[1];
204  out[4] = in[0];
205  out[5] = in[1];
206  out[6] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
207  out[7] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
208  out[8] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
209  out[9] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
210  out[10] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
211  out[11] = 4*in[0]*in[1]*(-3+4*in[2]);
212  out[12] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
213  out[13] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
214  out[14] = 4*in[0]*in[1]*(-1+4*in[2]);
215  out[15] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
216  out[16] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
217  out[17] = 4*in[0]*in[1]*(4-8*in[2]);
218  break;
219  default:
220  DUNE_THROW(RangeError, "Component out of range.");
221  }
222  } else {
223  DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
224  }
225  }
226 
229  unsigned int order() const
230  {
231  return 2;
232  }
233 
234  };
235 }
236 #endif
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: hierarchicalprismp2localbasis.hh:65
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: hierarchicalprismp2localbasis.hh:147
unsigned int size() const
number of shape functions
Definition: hierarchicalprismp2localbasis.hh:27
Definition: brezzidouglasmarini1cube2dlocalbasis.hh:15
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: hierarchicalprismp2localbasis.hh:33
D DomainType
domain type
Definition: localbasis.hh:49
unsigned int order() const
Polynomial order of the shape functions.
Definition: hierarchicalprismp2localbasis.hh:229
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 3 > > Traits
export type traits for function signature
Definition: hierarchicalprismp2localbasis.hh:24
Definition: hierarchicalprismp2localbasis.hh:20
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:37