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hierarchicalprismp2localbasis.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// 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_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
6#define DUNE_HIERARCHICAL_PRISM_P2_LOCALBASIS_HH
7
12#include <numeric>
13
14#include <dune/common/fvector.hh>
15#include <dune/common/fmatrix.hh>
16
17#include <dune/localfunctions/common/localbasis.hh>
18
19namespace Dune
20{
21 template<class D, class R>
22 class HierarchicalPrismP2LocalBasis
23 {
24 public:
26 typedef LocalBasisTraits<D,3,Dune::FieldVector<D,3>,R,1,Dune::FieldVector<R,1>, Dune::FieldMatrix<R,1,3> > Traits;
27
29 unsigned int size () const
30 {
31 return 18;
32 }
33
35 void evaluateFunction (const typename Traits::DomainType& in,
36 std::vector<typename Traits::RangeType> & out) const
37 {
38 out.resize(18);
39
40 out[0]=(1.0-in[0]-in[1])*(1.0-in[2]);
41 out[1]= in[0]*(1-in[2]);
42 out[2]=in[1]*(1-in[2]);
43 out[3]=in[2]*(1.0-in[0]-in[1]);
44 out[4]=in[0]*in[2];
45 out[5]=in[1]*in[2];
46
47 //edges
48 out[6]=2*(1.0-in[0]-in[1])*(0.5-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
49 out[7]=2*in[0]*(-0.5+in[0])*(4*in[2]-4*in[2]*in[2]);
50 out[8]=2*in[1]*(-0.5+in[1])*(4*in[2]-4*in[2]*in[2]);
51 out[9]=4*in[0]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
52 out[10]=4*in[1]*(1-in[0]-in[1])*(1-3*in[2]+2*in[2]*in[2]);
53 out[11]=4*in[0]*in[1]*(1-3*in[2]+2*in[2]*in[2]);
54 out[12]=4*in[0]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
55 out[13]=4*in[1]*(1-in[0]-in[1])*(-in[2]+2*in[2]*in[2]);
56 out[14]=4*in[0]*in[1]*(-in[2]+2*in[2]*in[2]);
57
58 //faces
59 out[15]=4*in[0]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
60 out[16]=4*in[1]*(1-in[0]-in[1])*(4*in[2]-4*in[2]*in[2]);
61 out[17]=4*in[0]*in[1]*(4*in[2]-4*in[2]*in[2]);
62 }
63
64
65
67 void evaluateJacobian (const typename Traits::DomainType& in, //position
68 std::vector<typename Traits::JacobianType>& out) const //return value
69 {
70 out.resize(18);
71
72 //vertices
73 out[0][0][0] = in[2]-1;
74 out[0][0][1] = in[2]-1;
75 out[0][0][2] = in[0]+in[1]-1;
76
77 out[1][0][0] = 1-in[2];
78 out[1][0][1] = 0;
79 out[1][0][2] =-in[0];
80
81 out[2][0][0] = 0;
82 out[2][0][1] = 1-in[2];
83 out[2][0][2] = -in[1];
84
85 out[3][0][0] = -in[2];
86 out[3][0][1] = -in[2];
87 out[3][0][2] = 1-in[0]-in[1];
88
89 out[4][0][0] = in[2];
90 out[4][0][1] = 0;
91 out[4][0][2] = in[0];
92
93 out[5][0][0] = 0;
94 out[5][0][1] = in[2];
95 out[5][0][2] = in[1];
96
97 //edges
98 out[6][0][0] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
99 out[6][0][1] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
100 out[6][0][2] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
101
102 out[7][0][0] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
103 out[7][0][1] = 0;
104 out[7][0][2] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
105
106 out[8][0][0] = 0;
107 out[8][0][1] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
108 out[8][0][2] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
109
110 out[9][0][0] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
111 out[9][0][1] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
112 out[9][0][2] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
113
114 out[10][0][0] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
115 out[10][0][1] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
116 out[10][0][2] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
117
118 out[11][0][0] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
119 out[11][0][1] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
120 out[11][0][2] = 4*in[0]*in[1]*(-3+4*in[2]);
121
122 out[12][0][0] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
123 out[12][0][1] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
124 out[12][0][2] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
125
126 out[13][0][0] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
127 out[13][0][1] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
128 out[13][0][2] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
129
130 out[14][0][0] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
131 out[14][0][1] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
132 out[14][0][2] = 4*in[0]*in[1]*(-1+4*in[2]);
133
134 //faces
135 out[15][0][0] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
136 out[15][0][1] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
137 out[15][0][2] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
138
139 out[16][0][0] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
140 out[16][0][1] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
141 out[16][0][2] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
142
143 out[17][0][0] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
144 out[17][0][1] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
145 out[17][0][2] = 4*in[0]*in[1]*(4-8*in[2]);
146 }
147
149 void partial (const std::array<unsigned int, 3>& order,
150 const typename Traits::DomainType& in, // position
151 std::vector<typename Traits::RangeType>& out) const // return value
152 {
153 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
154 if (totalOrder == 0) {
155 evaluateFunction(in, out);
156 } else if (totalOrder == 1) {
157 out.resize(size());
158 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
159
160 switch (direction) {
161 case 0:
162 out[0] = in[2]-1;
163 out[1] = 1-in[2];
164 out[2] = 0;
165 out[3] = -in[2];
166 out[4] = in[2];
167 out[5] = 0;
168 out[6] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
169 out[7] = (-1+4*in[0])*(4*in[2]-4*in[2]*in[2]);
170 out[8] = 0;
171 out[9] = (4-8*in[0]-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
172 out[10] = (-4*in[1])*(1-3*in[2]+2*in[2]*in[2]);
173 out[11] = 4*in[1]*(1-3*in[2]+2*in[2]*in[2]);
174 out[12] = (4-8*in[0]-4*in[1])*(-in[2]+2*in[2]*in[2]);
175 out[13] = -4*in[1]*(-in[2]+2*in[2]*in[2]);
176 out[14] = 4*in[1]*(-in[2]+2*in[2]*in[2]);
177 out[15] = (4-8*in[0]-4*in[1])*(4*in[2]-4*in[2]*in[2]);
178 out[16] = -4*in[1]*(4*in[2]-4*in[2]*in[2]);
179 out[17] = 4*in[1]*(4*in[2]-4*in[2]*in[2]);
180 break;
181 case 1:
182 out[0] = in[2]-1;
183 out[1] = 0;
184 out[2] = 1-in[2];
185 out[3] = -in[2];
186 out[4] = 0;
187 out[5] = in[2];
188 out[6] = (-3+4*in[0]+4*in[1])*(4*in[2]-4*in[2]*in[2]);
189 out[7] = 0;
190 out[8] = (-1+4*in[1])*(4*in[2]-4*in[2]*in[2]);
191 out[9] = -4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
192 out[10] = (4-4*in[0]-8*in[1])*(1-3*in[2]+2*in[2]*in[2]);
193 out[11] = 4*in[0]*(1-3*in[2]+2*in[2]*in[2]);
194 out[12] = (-4*in[0])*(-in[2]+2*in[2]*in[2]);
195 out[13] = (4-4*in[0]-8*in[1])*(-in[2]+2*in[2]*in[2]);
196 out[14] = 4*in[0]*(-in[2]+2*in[2]*in[2]);
197 out[15] = -4*in[0]*(4*in[2]-4*in[2]*in[2]);
198 out[16] = (4-4*in[0]-8*in[1])*(4*in[2]-4*in[2]*in[2]);
199 out[17] = 4*in[0]*(4*in[2]-4*in[2]*in[2]);
200 break;
201 case 2:
202 out[0] = in[0]+in[1]-1;
203 out[1] =-in[0];
204 out[2] = -in[1];
205 out[3] = 1-in[0]-in[1];
206 out[4] = in[0];
207 out[5] = in[1];
208 out[6] = 2*(1-in[0]-in[1])*(0.5-in[0]-in[1])*(4-8*in[2]);
209 out[7] = 2*in[0]*(-0.5+in[0])*(4-8*in[2]);
210 out[8] = 2*in[1]*(-0.5+in[1])*(4-8*in[2]);
211 out[9] = 4*in[0]*(1-in[0]-in[1])*(-3+4*in[2]);
212 out[10] = 4*in[1]*(1-in[0]-in[1])*(-3+4*in[2]);
213 out[11] = 4*in[0]*in[1]*(-3+4*in[2]);
214 out[12] = 4*in[0]*(1-in[0]-in[1])*(-1+4*in[2]);
215 out[13] = 4*in[1]*(1-in[0]-in[1])*(-1+4*in[2]);
216 out[14] = 4*in[0]*in[1]*(-1+4*in[2]);
217 out[15] = 4*in[0]*(1-in[0]-in[1])*(4-8*in[2]);
218 out[16] = 4*in[1]*(1-in[0]-in[1])*(4-8*in[2]);
219 out[17] = 4*in[0]*in[1]*(4-8*in[2]);
220 break;
221 default:
222 DUNE_THROW(RangeError, "Component out of range.");
223 }
224 } else {
225 DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
226 }
227 }
228
231 unsigned int order() const
232 {
233 return 2;
234 }
235
236 };
237}
238#endif
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:91
fmatrix.hh
Implements a matrix constructed from a given type representing a field and compile-time given number ...
fvector.hh
Implements a vector constructed from a given type representing a field and a compile-time given size.
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::size
constexpr std::integral_constant< std::size_t, sizeof...(II)> size(std::integer_sequence< T, II... >)
Return the size of the sequence.
Definition: integersequence.hh:75
Dune::LocalBasisTraits::DomainType
D DomainType
domain type
Definition: localbasis.hh:43
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