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5#ifndef DUNE_LOCALFUNCTIONS_NEDELEC_NEDELEC1STKINDCUBE_HH \n-
6#define DUNE_LOCALFUNCTIONS_NEDELEC_NEDELEC1STKINDCUBE_HH \n+
5#ifndef DUNE_RANNACHER_TUREK_3D_LOCALBASIS_HH \n+
6#define DUNE_RANNACHER_TUREK_3D_LOCALBASIS_HH \n
\n
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10#include <dune/common/fmatrix.hh> \n+
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11#include <dune/common/fvector.hh> \n-
12#include <dune/common/math.hh> \n+
12#include <dune/common/fmatrix.hh> \n
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14#include <dune/geometry/referenceelements.hh> \n-
15#include <dune/geometry/type.hh> \n-
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37 template<
class D,
class R,
int dim,
int k>
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38 class Nedelec1stKindCubeLocalBasis
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41 constexpr static std::size_t numberOfEdges = power(2,dim-1)*dim;
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44 using Traits = LocalBasisTraits<D,dim,FieldVector<D,dim>,
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45 R,dim,FieldVector<R,dim>,
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46 FieldMatrix<R,dim,dim> >;
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54 Nedelec1stKindCubeLocalBasis()
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56 std::fill(edgeOrientation_.begin(), edgeOrientation_.end(), 1.0);
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61 Nedelec1stKindCubeLocalBasis(std::bitset<numberOfEdges> edgeOrientation)
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62 : Nedelec1stKindCubeLocalBasis()
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64 for (std::size_t i=0; i<edgeOrientation_.size(); i++)
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65 edgeOrientation_[i] *= edgeOrientation[i] ? -1.0 : 1.0;
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69 static constexpr unsigned int size()
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71 static_assert(dim==2 || dim==3,
"Nedelec shape functions are implemented only for 2d and 3d cubes.");
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75 return 3*k * (k+1) * (k+1);
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84 std::vector<typename Traits::RangeType>& out)
const \n-
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86 static_assert(k==1,
"Evaluating N\u00e9d\u00e9lec shape functions is implemented only for first order.");
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103 out[0] = { 0, D(1) - in[0]};
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104 out[1] = { 0, in[0]};
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105 out[2] = { D(1) - in[1], 0};
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106 out[3] = { in[1], 0};
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109 if constexpr (dim==3)
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22 template<
class D,
class R >
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25 static const int coefficients[ 6 ][ 6 ];
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29 R, 1, FieldVector< R, 1 >,
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40 std::vector< typename Traits::RangeType > &out )
const \n+
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43 RangeFieldType y[ 6 ] = { 1, in[ 0 ], in[ 1 ], in[ 2 ],
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44 in[ 0 ]*in[ 0 ] - in[ 1 ]*in[ 1 ],
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45 in[ 1 ]*in[ 1 ] - in[ 2 ]*in[ 2 ] };
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47 for(
unsigned int i = 0; i <
size(); ++i )
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49 out[ i ] = RangeFieldType( 0 );
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50 for(
unsigned int j = 0; j < 6; ++j )
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51 out[ i ] += coefficients[ i ][ j ]*y[ j ];
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52 out[ i ] /= RangeFieldType( 3 );
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58 std::vector< typename Traits::JacobianType > &out )
const \n+
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61 RangeFieldType y0[ 5 ] = { 1, 0, 0, 2*in[ 0 ], 0 };
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62 RangeFieldType y1[ 5 ] = { 0, 1, 0, -2*in[ 1 ], 2*in[ 1 ] };
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63 RangeFieldType y2[ 5 ] = { 0, 0, 1, 0, -2*in[ 2 ] };
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66 for(
unsigned int i = 0; i <
size(); ++i )
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68 out[ i ] = RangeFieldType( 0 );
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69 for(
unsigned int j = 0; j < 5; ++j )
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71 out[ i ][ 0 ][ 0 ] += coefficients[ i ][ j+1 ]*y0[ j ];
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72 out[ i ][ 0 ][ 1 ] += coefficients[ i ][ j+1 ]*y1[ j ];
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73 out[ i ][ 0 ][ 2 ] += coefficients[ i ][ j+1 ]*y2[ j ];
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75 out[ i ] /= RangeFieldType( 3 );
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82 std::vector<typename Traits::RangeType>& out)
const \n+
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84 auto totalOrder = std::accumulate(
order.begin(),
order.end(), 0);
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85 if (totalOrder == 0) {
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87 }
else if (totalOrder == 1) {
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89 auto const direction = std::distance(
order.begin(), std::find(
order.begin(),
order.end(), 1));
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92 RangeFieldType y[3][5] = { { 1.0, 0.0, 0.0, 2*in[0], 0.0 },
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93 { 0.0, 1.0, 0.0, -2*in[1], 2*in[1] },
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94 { 0.0, 0.0, 1.0, 0.0, -2*in[2] } };
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96 for (std::size_t i = 0; i <
size(); ++i) {
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97 out[i] = RangeFieldType{0};
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98 for (std::size_t j = 0; j < 5; ++j)
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99 out[i] += coefficients[i][j+1] * y[direction][j];
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100 out[i] /= RangeFieldType{3};
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103 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
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119 template<
class D,
class R >
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120 const int RannacherTurek3DLocalBasis< D, R >
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121 ::coefficients[ 6 ][ 6 ] = {{ 2, -7, 2, 2, 4, 2 },
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122 { -1, -1, 2, 2, 4, 2 },
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123 { 2, 2, -7, 2, -2, 2 },
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124 { -1, 2, -1, 2, -2, 2 },
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125 { 2, 2, 2, -7, -2, -4 },
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126 { -1, 2, 2, -1, -2, -4 }};
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128 for (std::size_t i=0; i<out.size(); i++)
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131 out[0][2] = { 1 - in[0] - in[1] + in[0]*in[1]};
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132 out[1][2] = { in[0] - in[0]*in[1]};
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133 out[2][2] = { in[1] - in[0]*in[1]};
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134 out[3][2] = { in[0]*in[1]};
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136 out[4][1] = { 1 - in[0] - in[2] + in[0]*in[2]};
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137 out[5][1] = { in[0] - in[0]*in[2]};
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138 out[8][1] = { in[2] - in[0]*in[2]};
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139 out[9][1] = { in[0]*in[2]};
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141 out[6][0] = { 1 - in[1] - in[2] + in[1]*in[2]};
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142 out[7][0] = { in[1] - in[1]*in[2]};
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143 out[10][0] = { in[2] - in[1]*in[2]};
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144 out[11][0] = { in[1]*in[2]};
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147 for (std::size_t i=0; i<out.size(); i++)
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148 out[i] *= edgeOrientation_[i];
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157 std::vector<typename Traits::JacobianType>& out)
const \n-
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162 for (std::size_t i=0; i<out.size(); i++)
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163 for (std::size_t j=0; j<dim; j++)
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166 out[0][1] = { -1, 0};
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169 out[2][0] = { 0, -1};
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174 for (std::size_t i=0; i<out.size(); i++)
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175 for(std::size_t j=0;j<dim; j++)
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179 out[0][2] = {-1 +in[1], -1 + in[0], 0};
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180 out[1][2] = { 1 -in[1], - in[0], 0};
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181 out[2][2] = { -in[1], 1 - in[0], 0};
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182 out[3][2] = { in[1], in[0], 0};
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184 out[4][1] = {-1 +in[2], 0, -1 + in[0]};
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185 out[5][1] = { 1 -in[2], 0, - in[0]};
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186 out[8][1] = { -in[2], 0, 1 - in[0]};
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187 out[9][1] = { in[2], 0, in[0]};
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189 out[6][0] = { 0, -1 + in[2], -1 + in[1]};
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190 out[7][0] = { 0, 1 - in[2], - in[1]};
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191 out[10][0] = { 0, - in[2], 1 - in[1]};
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192 out[11][0] = { 0, in[2], in[1]};
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196 for (std::size_t i=0; i<out.size(); i++)
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197 out[i] *= edgeOrientation_[i];
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207 void partial(
const std::array<unsigned int, dim>& order,
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209 std::vector<typename Traits::RangeType>& out)
const \n-
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211 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
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212 if (totalOrder == 0) {
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213 evaluateFunction(in, out);
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214 }
else if (totalOrder == 1) {
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215 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
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241 out[0] = { 0, 0, -1 +in[1]};
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242 out[1] = { 0, 0, 1 -in[1]};
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243 out[2] = { 0, 0, -in[1]};
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244 out[3] = { 0, 0, in[1]};
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246 out[4] = { 0, -1 +in[2], 0};
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247 out[5] = { 0, 1 -in[2], 0};
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248 out[8] = { 0, -in[2], 0};
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249 out[9] = { 0, in[2], 0};
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258 out[0] = { 0, 0, -1 + in[0]};
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259 out[1] = { 0, 0, - in[0]};
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260 out[2] = { 0, 0, 1 - in[0]};
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261 out[3] = { 0, 0, in[0]};
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268 out[6] = { -1 + in[2], 0, 0};
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269 out[7] = { 1 - in[2], 0, 0};
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270 out[10] = { - in[2], 0, 0};
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271 out[11] = { in[2], 0, 0};
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280 out[4] = { 0, -1 + in[0], 0};
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281 out[5] = { 0, - in[0], 0};
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282 out[8] = { 0, 1 - in[0], 0};
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283 out[9] = { 0, in[0], 0};
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285 out[6] = { -1 + in[1], 0, 0};
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286 out[7] = { - in[1], 0, 0};
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287 out[10] = { 1 - in[1], 0, 0};
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288 out[11] = { in[1], 0, 0};
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293 for (std::size_t i=0; i<out.size(); i++)
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294 out[i] *= edgeOrientation_[i];
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296 }
else if (totalOrder == 2) {
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300 for (std::size_t i = 0; i < size(); ++i)
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301 for (std::size_t j = 0; j < dim; ++j)
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306 for(
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310 if( order[0] == 1 and order[1]==1)
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313 out[1] = { 0, 0, -1};
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314 out[2] = { 0, 0, -1};
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319 if( order[0] == 1 and order[2]==1)
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322 out[5] = { 0, -1, 0};
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323 out[8] = { 0, -1, 0};
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328 if( order[1] == 1 and order[2]==1)
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331 out[7] = { -1, 0, 0};
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332 out[10] = { -1, 0, 0};
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333 out[11] = { 1, 0, 0};
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336 for (std::size_t i=0; i<out.size(); i++)
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337 out[i] *= edgeOrientation_[i];
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343 for (std::size_t i = 0; i < size(); ++i)
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344 for (std::size_t j = 0; j < dim; ++j)
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351 unsigned int order()
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362 std::array<R,numberOfEdges> edgeOrientation_;
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370 template <
int dim,
int k>
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371 class Nedelec1stKindCubeLocalCoefficients
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375 Nedelec1stKindCubeLocalCoefficients ()
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378 static_assert(k==1,
"Only first-order N\u00e9d\u00e9lec local coefficients are implemented.");
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381 for (std::size_t i=0; i<size(); i++)
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382 localKey_[i] = LocalKey(i,dim-1,0);
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386 std::size_t size()
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388 static_assert(dim==2 || dim==3,
"N\u00e9d\u00e9lec shape functions are implemented only for 2d and 3d cubes.");
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389 return (dim==2) ? 2*k * (k+1)
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390 : 3*k * (k+1) * (k+1);
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395 const LocalKey& localKey (std::size_t i)
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401 std::vector<LocalKey> localKey_;
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409 class Nedelec1stKindCubeLocalInterpolation
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411 static constexpr auto dim = LB::Traits::dimDomain;
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412 static constexpr auto size = LB::size();
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415 constexpr static std::size_t numberOfEdges = power(2,dim-1)*dim;
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420 Nedelec1stKindCubeLocalInterpolation (std::bitset<numberOfEdges> s = 0)
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422 auto refElement = Dune::referenceElement<double,dim>(GeometryTypes::cube(dim));
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424 for (std::size_t i=0; i<numberOfEdges; i++)
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425 m_[i] = refElement.position(i,dim-1);
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427 for (std::size_t i=0; i<numberOfEdges; i++)
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429 auto vertexIterator = refElement.subEntities(i,dim-1,dim).begin();
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430 auto v0 = *vertexIterator;
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431 auto v1 = *(++vertexIterator);
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437 edge_[i] = refElement.position(v1,dim) - refElement.position(v0,dim);
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438 edge_[i] *= (s[i]) ? -1.0 : 1.0;
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447 template<
typename F,
typename C>
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448 void interpolate (
const F& f, std::vector<C>& out)
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452 for (std::size_t i=0; i<size; i++)
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456 for (
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457 out[i] += y[j]*edge_[i][j];
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463 std::array<typename LB::Traits::DomainType, numberOfEdges> m_;
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465 std::array<typename LB::Traits::DomainType, numberOfEdges> edge_;
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494 template<
class D,
class R,
int dim,
int k>
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499 Impl::Nedelec1stKindCubeLocalCoefficients<dim,k>,
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500 Impl::Nedelec1stKindCubeLocalInterpolation<Impl::Nedelec1stKindCubeLocalBasis<D,R,dim,k> > >;
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502 static_assert(dim==2 || dim==3,
"Nedelec elements are only implemented for 2d and 3d elements.");
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503 static_assert(k==1,
"Nedelec elements of the first kind are currently only implemented for order k==1.");
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526 return coefficients_;
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531 return interpolation_;
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534 static constexpr unsigned int size ()
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536 return Traits::LocalBasisType::size();
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539 static constexpr GeometryType
type ()
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541 return GeometryTypes::cube(dim);
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Definition bdfmcube.hh:18
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Type traits for LocalBasisVirtualInterface.
Definition common/localbasis.hh:35
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D DomainType
domain type
Definition common/localbasis.hh:43
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traits helper struct
Definition localfiniteelementtraits.hh:13
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LB LocalBasisType
Definition localfiniteelementtraits.hh:16
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LC LocalCoefficientsType
Definition localfiniteelementtraits.hh:20
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LI LocalInterpolationType
Definition localfiniteelementtraits.hh:24
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N\u00e9d\u00e9lec elements of the first kind for cube elements.
Definition nedelec1stkindcube.hh:496
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const Traits::LocalInterpolationType & localInterpolation() const
Definition nedelec1stkindcube.hh:529
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static constexpr unsigned int size()
Definition nedelec1stkindcube.hh:534
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Nedelec1stKindCubeLocalFiniteElement()=default
Default constructor.
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static constexpr GeometryType type()
Definition nedelec1stkindcube.hh:539
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const Traits::LocalCoefficientsType & localCoefficients() const
Definition nedelec1stkindcube.hh:524
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const Traits::LocalBasisType & localBasis() const
Definition nedelec1stkindcube.hh:519
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Nedelec1stKindCubeLocalFiniteElement(std::bitset< power(2, dim-1) *dim > s)
Constructor with explicitly given edge orientations.
Definition nedelec1stkindcube.hh:514
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RF RangeFieldType
Export type for range field.
Definition common/localbasis.hh:46
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Definition rannacherturek3dlocalbasis.hh:24
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LocalBasisTraits< D, 3, FieldVector< D, 3 >, R, 1, FieldVector< R, 1 >, FieldMatrix< R, 1, 3 > > Traits
Definition rannacherturek3dlocalbasis.hh:30
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void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
evaluate all shape functions
Definition rannacherturek3dlocalbasis.hh:39
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unsigned int size() const
number of shape functions
Definition rannacherturek3dlocalbasis.hh:33
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void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
evaluate jacobian of all shape functions
Definition rannacherturek3dlocalbasis.hh:57
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unsigned int order() const
polynomial order of the shape functions
Definition rannacherturek3dlocalbasis.hh:108
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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 rannacherturek3dlocalbasis.hh:80
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1.9.8\n \n \n \n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -1,26 +1,12 @@\n dune-localfunctions\u00a02.10\n Loading...\n Searching...\n No Matches\n * _\bd_\bu_\bn_\be\n * _\bl_\bo_\bc_\ba_\bl_\bf_\bu_\bn_\bc_\bt_\bi_\bo_\bn_\bs\n- * _\br_\be_\bf_\bi_\bn_\be_\bd\n- * _\br_\be_\bf_\bi_\bn_\be_\bd_\bp_\b0\n-_\bC_\bl_\ba_\bs_\bs_\be_\bs | _\bN_\ba_\bm_\be_\bs_\bp_\ba_\bc_\be_\bs\n-refinedp0localbasis.hh File Reference\n-#include