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5#ifndef DUNE_LOCALFUNCTIONS_BREZZIDOUGLASFORTINMARINI_BDFMCUBE_HH \n-
6#define DUNE_LOCALFUNCTIONS_BREZZIDOUGLASFORTINMARINI_BDFMCUBE_HH \n+
5#ifndef DUNE_LOCALFUNCTIONS_LAGRANGE_LAGRANGEPYRAMID_HH \n+
6#define DUNE_LOCALFUNCTIONS_LAGRANGE_LAGRANGEPYRAMID_HH \n
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8#include <dune/geometry/type.hh> \n-
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11#include <dune/common/fmatrix.hh> \n+
12#include <dune/common/fvector.hh> \n+
13#include <dune/common/math.hh> \n+
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15#include <dune/geometry/referenceelements.hh> \n
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43 template<
class D,
class R,
unsigned int dim,
unsigned int order>
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62 : basis( s ), interpolation( s )
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70 unsigned int size ()
const {
return basis.size(); }
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71 static constexpr auto type () -> GeometryType {
return GeometryTypes::cube(dim); }
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75 LocalCoefficients coefficients;
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76 LocalInterpolation interpolation;
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22namespace Dune {
namespace Impl
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33 template<
class D,
class R,
unsigned int k>
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34 class LagrangePyramidLocalBasis
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37 using Traits = LocalBasisTraits<D,3,FieldVector<D,3>,R,1,FieldVector<R,1>,FieldMatrix<R,1,3> >;
\n+
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41 static constexpr std::size_t size ()
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43 std::size_t result = 0;
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44 for (
unsigned int i=0; i<=k; i++)
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45 result += power(i+1,2);
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51 std::vector<typename Traits::RangeType>& out)
const \n+
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66 out[0] = (1-in[0])*(1-in[1])-in[2]*(1-in[1]);
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67 out[1] = in[0]*(1-in[1])-in[2]*in[1];
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68 out[2] = (1-in[0])*in[1]-in[2]*in[1];
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69 out[3] = in[0]*in[1]+in[2]*in[1];
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73 out[0] = (1-in[0])*(1-in[1])-in[2]*(1-in[0]);
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74 out[1] = in[0]*(1-in[1])-in[2]*in[0];
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75 out[2] = (1-in[0])*in[1]-in[2]*in[0];
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76 out[3] = in[0]*in[1]+in[2]*in[0];
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87 const R x = 2.0*in[0] + in[2] - 1.0;
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88 const R y = 2.0*in[1] + in[2] - 1.0;
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94 out[0] = 0.25*(x + z)*(x + z - 1)*(y - z - 1)*(y - z);
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95 out[1] = -0.25*(x + z)*(y - z)*((x + z + 1)*(-y + z + 1) - 4*z) - z*(x - y);
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96 out[2] = 0.25*(x + z)*(y - z)*(y - z + 1)*(x + z - 1);
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97 out[3] = 0.25*(y - z)*(x + z)*(y - z + 1)*(x + z + 1);
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101 out[5] = -0.5*(y - z + 1)*(x + z - 1)*(y - 1)*x;
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102 out[6] = -0.5*(y - z + 1)*(((x + z + 1)*(y - 1)*x - z) + z*(2*y + 1));
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103 out[7] = -0.5*(x + z - 1)*(((y - z - 1)*(x + 1)*y - z) + z*(2*x + 1));
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104 out[8] = -0.5*(y - z + 1)*(x + z - 1)*(x + 1)*y;
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107 out[9] = z*(x + z - 1)*(y - z - 1);
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108 out[10] = -z*((x + z + 1)*(y - z - 1) + 4*z);
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109 out[11] = -z*(y - z + 1)*(x + z - 1);
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110 out[12] = z*(y - z + 1)*(x + z + 1);
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113 out[13] = (y - z + 1)*(x + z - 1)*((y - 1)*(x + 1) + z*(x - y + z + 1));
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118 out[0] = 0.25*(y + z)*(y + z - 1)*(x - z - 1)*(x - z);
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119 out[1] = -0.25*(x - z)*(y + z)*(x - z + 1)*(-y - z + 1);
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120 out[2] = 0.25*(x - z)*(y + z)*((x - z - 1)*(y + z + 1) + 4*z) + z*(x - y);
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121 out[3] = 0.25*(y + z)*(x - z)*(x - z + 1)*(y + z + 1);
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122 out[4] = z*(2*z - 1);
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125 out[5] = -0.5*(y + z - 1)*(((x - z - 1)*(y + 1)*x - z) + z*(2*y + 1));
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126 out[6] = -0.5*(x - z + 1)*(y + z - 1)*(y + 1)*x;
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127 out[7] = -0.5*(x - z + 1)*(y + z - 1)*(x - 1)*y;
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128 out[8] = -0.5*(x - z + 1)*(((y + z + 1)*(x - 1)*y - z) + z*(2*x + 1));
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131 out[9] = z*(y + z - 1)*(x - z - 1);
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132 out[10] = -z*(x - z + 1)*(y + z - 1);
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133 out[11] = -z*((y + z + 1)*(x - z - 1) + 4*z);
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134 out[12] = z*(x - z + 1)*(y + z + 1);
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137 out[13] = (x - z + 1)*(y + z - 1)*((y + 1)*(x - 1) - z*(x - y - z - 1));
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143 DUNE_THROW(NotImplemented,
"LagrangePyramidLocalBasis::evaluateFunction for order " << k);
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152 std::vector<typename Traits::JacobianType>& out)
const \n+
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159 std::fill(out[0][0].begin(), out[0][0].end(), 0);
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167 out[0][0] = {-1 + in[1], -1 + in[0] + in[2], -1 + in[1]};
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168 out[1][0] = { 1 - in[1], -in[0] - in[2], -in[1]};
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169 out[2][0] = { -in[1], 1 - in[0] - in[2], -in[1]};
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170 out[3][0] = { in[1], in[0] + in[2], in[1]};
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174 out[0][0] = {-1 + in[1] + in[2], -1 + in[0], -1 + in[0]};
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175 out[1][0] = { 1 - in[1] - in[2], -in[0], -in[0]};
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176 out[2][0] = { -in[1] - in[2], 1 - in[0], -in[0]};
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177 out[3][0] = { in[1] + in[2], in[0], in[0]};
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180 out[4][0] = {0, 0, 1};
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187 const R x = 2.0*in[0] + in[2] - 1.0;
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188 const R y = 2.0*in[1] + in[2] - 1.0;
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196 out[0][0][0] = 0.5*(y - z - 1)*(y - z)*(2*x + 2*z - 1);
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197 out[0][0][1] = 0.5*(x + z)*(x + z - 1)*(2*y - 2*z - 1);
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198 out[0][0][2] = 0.5*(out[0][0][0] + out[0][0][1])
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199 + 0.25*((2*x + 2*z - 1)*(y - z - 1)*(y - z)
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200 + (x + z)*(x + z - 1)*(-2*y + 2*z + 1));
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202 out[1][0][0] = 2*(-0.25*((y - z)*((x + z + 1)*(-y + z + 1) - 4*z)
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203 + (x + z)*(y - z)*(-y + z + 1)) - z);
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204 out[1][0][1] = 2*(-0.25*((x + z)*((x + z + 1)*(-y + z + 1) - 4*z)
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205 + (x + z)*(y - z)*(-(x + z + 1))) + z);
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206 out[1][0][2] = 0.5*(out[1][0][0] + out[1][0][1])
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207 - 0.25*((y - z)*((x + z + 1)*(-y + z + 1) - 4*z)
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208 - (x + z)*((x + z + 1)*(-y + z + 1) - 4*z)
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209 + (x + z)*(y - z)*(x - y + 2*z - 2))
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212 out[2][0][0] = 0.5*(y - z)*(y - z + 1)*(2*x + 2*z - 1);
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213 out[2][0][1] = 0.5*(x + z)*(2*y - 2*z + 1)*(x + z - 1);
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214 out[2][0][2] = 0.5*(out[2][0][0] + out[2][0][1])
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215 + 0.25*((y - x - 2*z)*(y - z + 1)*(x + z - 1)
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216 + (x + z)*(y - z)*(y - x - 2*z + 2));
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218 out[3][0][0] = 0.5*(y - z)*(2*x + 2*z + 1)*(y - z + 1);
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219 out[3][0][1] = 0.5*(2*y - 2*z + 1)*(x + z)*(x + z + 1);
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220 out[3][0][2] = 0.5*(out[3][0][0] + out[3][0][1])
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221 + 0.25*((y - x - 2*z)*(y - z + 1)*(x + z + 1)
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222 + (y - z)*(x + z)*(y - x - 2*z));
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226 out[4][0][2] = 4*z - 1;
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229 out[5][0][0] = -(y - z + 1)*(y - 1)*(2*x + z - 1);
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230 out[5][0][1] = -(x + z - 1)*(y - 1)*x - (y - z + 1)*(x + z - 1)*x;
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231 out[5][0][2] = 0.5*(out[5][0][0] + out[5][0][1])
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232 + 0.5*(x + z - 1)*(y - 1)*x - 0.5*(y - z + 1)*(y - 1)*x;
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234 out[6][0][0] = -(y - z + 1)*(2*x + z + 1)*(y - 1);
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235 out[6][0][1] = -(((x + z + 1)*(y - 1)*x - z) + z*(2*y + 1)
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236 + (y - z + 1)*((x + z + 1)*x + 2*z));
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237 out[6][0][2] = 0.5*(out[6][0][0] + out[6][0][1])
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238 - 0.5*(-(((x + z + 1)*(y - 1)*x - z) + z*(2*y + 1))
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239 + (y - z + 1)*(((y - 1)*x - 1) + 2*y + 1));
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241 out[7][0][0] = -(((y - z - 1)*(x + 1)*y - z) + z*(2*x + 1)
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242 + (x + z - 1)*((y - z - 1)*y + 2*z));
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243 out[7][0][1] = -(x + z - 1)*(2*y - z - 1)*(x + 1);
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244 out[7][0][2] = 0.5*(out[7][0][0] + out[7][0][1])
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245 - 0.5*(((y - z - 1)*(x + 1)*y - z) + z*(2*x + 1)
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246 + (x + z - 1)*((-(x + 1)*y - 1) + 2*x + 1));
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248 out[8][0][0] = -(y - z + 1)*(2*x + z)*y;
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249 out[8][0][1] = -(2*y - z + 1)*(x + z - 1)*(x + 1);
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250 out[8][0][2] = 0.5*(out[8][0][0] + out[8][0][1])
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251 - 0.5*(-x + y - 2*z + 2)*(x + 1)*y;
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254 out[9][0][0] = 2*z*(y - z - 1);
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255 out[9][0][1] = 2*z*(x + z - 1);
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256 out[9][0][2] = 0.5*(out[9][0][0] + out[9][0][1])
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257 + (x + z - 1)*(y - z - 1) + z*(-x + y - 2*z);
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259 out[10][0][0] = -2*z*(y - z - 1);
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260 out[10][0][1] = -2*z*(x + z + 1);
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261 out[10][0][2] = 0.5*(out[10][0][0] + out[10][0][1])
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262 - ((x + z + 1)*(y - z - 1) + 4*z)
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263 - z*(-x + y - 2*z + 2);
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265 out[11][0][0] = -2*z*(y - z + 1);
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266 out[11][0][1] = -2*z*(x + z - 1);
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267 out[11][0][2] = 0.5*(out[11][0][0] + out[11][0][1])
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268 - (y - z + 1)*(x + z - 1) - z*(-x + y - 2*z + 2);
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270 out[12][0][0] = 2*z*(y - z + 1);
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271 out[12][0][1] = 2*z*(x + z + 1);
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272 out[12][0][2] = 0.5*(out[12][0][0] + out[12][0][1])
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273 + (y - z + 1)*(x + z + 1) + z*(-x + y - 2*z);
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276 out[13][0][0] = 2*((y - z + 1)*((y - 1)*(x + 1) + z*(x - y + z + 1))
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277 + (y - z + 1)*(x + z - 1)*(y - 1 + z));
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278 out[13][0][1] = 2*((x + z - 1)*((y - 1)*(x + 1) + z*(x - y + z + 1))
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279 + (y - z + 1)*(x + z - 1)*(x + 1 - z));
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280 out[13][0][2] = 0.5*(out[13][0][0] + out[13][0][1])
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281 + ((-x + y - 2*z + 2)*((y - 1)*(x + 1) + z*(x - y + z + 1))
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282 + (y - z + 1)*(x + z - 1)*(x - y + 2*z + 1));
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287 out[0][0][0] = 0.5*(y + z)*(y + z - 1)*(2*x - 2*z - 1);
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288 out[0][0][1] = 0.5*(2*y + 2*z - 1)*(x - z - 1)*(x - z);
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289 out[0][0][2] = 0.5*(out[0][0][0] + out[0][0][1])
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290 + 0.25*((2*y + 2*z - 1)*(x - z - 1)*(x - z)
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291 + (y + z)*(y + z - 1)*(-2*x + 2*z + 1));
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293 out[1][0][0] = -0.5*(y + z)*(2*x - 2*z + 1)*(-y - z + 1);
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294 out[1][0][1] = -0.5*(x - z)*(x - z + 1)*(-2*y - 2*z + 1);
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295 out[1][0][2] = 0.5*(out[1][0][0] + out[1][0][1])
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296 - 0.25*((x - y - 2*z)*(x - z + 1)*(-y - z + 1)
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297 + (x - z)*(y + z)*(-x + y + 2*z - 2));
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299 out[2][0][0] = 0.5*((y + z)*((x - z - 1)*(y + z + 1) + 4*z)
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300 + (x - z)*(y + z)*(y + z + 1) + 4*z);
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301 out[2][0][1] = 0.5*((x - z)*((x - z - 1)*(y + z + 1) + 4*z)
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302 + (x - z)*(y + z)*(x - z - 1) - 4*z);
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303 out[2][0][2] = 0.5*(out[2][0][0] + out[2][0][1])
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304 + 0.25*((x - y - 2*z)*((x - z - 1)*(y + z + 1) + 4*z)
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305 + (x - z)*(y + z)*(x - y - 2*z + 2) + 4*(x - y));
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307 out[3][0][0] = 0.5*(y + z)*(2*x - 2*z + 1)*(y + z + 1);
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308 out[3][0][1] = 0.5*(x - z)*(x - z + 1)*(2*y + 2*z + 1);
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309 out[3][0][2] = 0.5*(out[3][0][0] + out[3][0][1])
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310 + 0.25*((x - y - 2*z)*(x - z + 1)*(y + z + 1)
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311 + (y + z)*(x - z)*(x - y - 2*z));
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315 out[4][0][2] = 4*z - 1;
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318 out[5][0][0] = -(y + z - 1)*(2*x - z - 1)*(y + 1);
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319 out[5][0][1] = -(((x - z - 1)*(y + 1)*x - z) + z*(2*y + 1)
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320 + (y + z - 1)*((x - z - 1)*x + 2*z));
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321 out[5][0][2] = 0.5*(out[5][0][0] + out[5][0][1])
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322 - 0.5*((((x - z - 1)*(y + 1)*x - z) + z*(2*y + 1))
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323 + (y + z - 1)*((-(y + 1)*x - 1) + 2*y + 1));
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325 out[6][0][0] = -(2*x - z + 1)*(y + z - 1)*(y + 1);
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326 out[6][0][1] = -(x - z + 1)*(2*y + z)*x;
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327 out[6][0][2] = 0.5*(out[6][0][0] + out[6][0][1])
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328 - 0.5*(x - y - 2*z + 2)*(y + 1)*x;
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330 out[7][0][0] = -(2*x - z)*(y + z - 1)*y;
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331 out[7][0][1] = -(x - z + 1)*(2*y + z - 1)*(x - 1);
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332 out[7][0][2] = 0.5*(out[7][0][0] + out[7][0][1])
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333 - 0.5*(x - y - 2*z + 2)*(x - 1)*y;
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335 out[8][0][0] = -(((y + z + 1)*(x - 1)*y - z) + z*(2*x + 1)
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336 + (x - z + 1)*((y + z + 1)*y + 2*z));
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337 out[8][0][1] = -(x - z + 1)*(2*y + z + 1)*(x - 1);
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338 out[8][0][2] = 0.5*(out[8][0][0] + out[8][0][1])
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339 - 0.5*(-(((y + z + 1)*(x - 1)*y - z) + z*(2*x + 1))
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340 + (x - z + 1)*(((x - 1)*y - 1) + 2*x + 1));
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343 out[9][0][0] = 2*z*(y + z - 1);
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344 out[9][0][1] = 2*z*(x - z - 1);
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345 out[9][0][2] = 0.5*(out[9][0][0] + out[9][0][1])
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346 + (y + z - 1)*(x - z - 1) + z*(x - y - 2*z);
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348 out[10][0][0] = -2*z*(y + z - 1);
\n+
349 out[10][0][1] = -2*z*(x - z + 1);
\n+
350 out[10][0][2] = 0.5*(out[10][0][0] + out[10][0][1])
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351 - (x - z + 1)*(y + z - 1) - z*(x - y - 2*z + 2);
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353 out[11][0][0] = -2*z*(y + z + 1);
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354 out[11][0][1] = -2*z*(x - z - 1);
\n+
355 out[11][0][2] = 0.5*(out[11][0][0] + out[11][0][1])
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356 - ((y + z + 1)*(x - z - 1) + 4*z) - z*(x - y - 2*z + 2);
\n+
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358 out[12][0][0] = 2*z*(y + z + 1);
\n+
359 out[12][0][1] = 2*z*(x - z + 1);
\n+
360 out[12][0][2] = 0.5*(out[12][0][0] + out[12][0][1])
\n+
361 + (x - z + 1)*(y + z + 1) + z*(x - y - 2*z);
\n+
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364 out[13][0][0] = 2*((y + z - 1)*((y + 1)*(x - 1) - z*(x - y - z - 1))
\n+
365 + (x - z + 1)*(y + z - 1)*(y + 1 - z));
\n+
366 out[13][0][1] = 2*((x - z + 1)*((y + 1)*(x - 1) - z*(x - y - z - 1))
\n+
367 + (x - z + 1)*(y + z - 1)*(x - 1 + z));
\n+
368 out[13][0][2] = 0.5*(out[13][0][0] + out[13][0][1])
\n+
369 + (x - y - 2*z + 2)*((y + 1)*(x - 1) - z*(x - y - z - 1))
\n+
370 + (x - z + 1)*(y + z - 1)*(-(x - y - 2*z - 1));
\n+
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376 DUNE_THROW(NotImplemented,
"LagrangePyramidLocalBasis::evaluateJacobian for order " << k);
\n+
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385 void partial(
const std::array<unsigned int,3>& order,
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387 std::vector<typename Traits::RangeType>& out)
const \n+
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389 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
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395 evaluateFunction(in, out);
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
409 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
422 out[0] = -1 + in[0] + in[2];
\n+
423 out[1] = -in[0] - in[2];
\n+
424 out[2] = 1 - in[0] - in[2];
\n+
425 out[3] = in[0]+in[2];
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
436 DUNE_THROW(RangeError,
"Component out of range.");
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
444 out[0] = -1 + in[1] + in[2];
\n+
445 out[1] = 1 - in[1] - in[2];
\n+
446 out[2] = -in[1] - in[2];
\n+
447 out[3] = in[1] + in[2];
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
465 DUNE_THROW(RangeError,
"Component out of range.");
\n+
\n+
\n+
468 }
else if (totalOrder == 2)
\n+
\n+
470 if ((order[0] == 1 && order[1] == 1) ||
\n+
471 (order[1] == 1 && order[2] == 1 && in[0] > in[1]) ||
\n+
472 (order[0] == 1 && order[2] == 1 && in[0] <=in[1]))
\n+
\n+
474 out = {1, -1, -1, 1, 0};
\n+
\n+
\n+
477 out = {0, 0, 0, 0, 0};
\n+
\n+
\n+
\n+
\n+
482 out = {0, 0, 0, 0, 0};
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
493 const R x = 2.0*in[0] + in[2] - 1.0;
\n+
494 const R y = 2.0*in[1] + in[2] - 1.0;
\n+
\n+
\n+
497 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
506 out[0] = 0.5*(y - z - 1)*(y - z)*(2*x + 2*z - 1);
\n+
507 out[1] = 2*(-0.25*((y - z)*((x + z + 1)*(-y + z + 1) - 4*z) + (x + z)*(y - z)*(-y + z + 1)) - z);
\n+
508 out[2] = 0.5*(y - z)*(y - z + 1)*(2*x + 2*z - 1);
\n+
509 out[3] = 0.5*(y - z)*(2*x + 2*z + 1)*(y - z + 1);
\n+
\n+
511 out[5] = -(y - z + 1)*(2*x + z - 1)*(y - 1);
\n+
512 out[6] = -(y - z + 1)*(2*x + z + 1)*(y - 1);
\n+
513 out[7] = -(((y - z - 1)*(x + 1)*y - z) + z*(2*x + 1) + (x + z - 1)*((y - z - 1)*y + 2*z));
\n+
514 out[8] = -(y - z + 1)*(2*x + z)*y;
\n+
515 out[9] = 2*z*(y - z - 1);
\n+
516 out[10] = -2*z*(y - z - 1);
\n+
517 out[11] = -2*z*(y - z + 1);
\n+
518 out[12] = 2*z*(y - z + 1);
\n+
519 out[13] = 2*((y - z + 1)*((y - 1)*(x + 1) + z*(x - y + z + 1)) + (y - z + 1)*(x + z - 1)*(y - 1 + z));
\n+
\n+
\n+
522 out[0] = 0.5*(x + z)*(x + z - 1)*(2*y - 2*z - 1);
\n+
523 out[1] = 2*(-0.25*((x + z)*((x + z + 1)*(-y + z + 1) - 4*z) + (x + z)*(y - z)*(-(x + z + 1))) + z);
\n+
524 out[2] = 0.5*(x + z)*(2*y - 2*z + 1)*(x + z - 1);
\n+
525 out[3] = 0.5*(2*y - 2*z + 1)*(x + z)*(x + z + 1);
\n+
\n+
527 out[5] = -(x + z - 1)*(y - 1)*x - (y - z + 1)*(x + z - 1)*x;
\n+
528 out[6] = -(((x + z + 1)*(y - 1)*x - z) + z*(2*y + 1) + (y - z + 1)*((x + z + 1)*x + 2*z));
\n+
529 out[7] = -(x + z - 1)*(2*y - z - 1)*(x + 1);
\n+
530 out[8] = -(2*y - z + 1)*(x + z - 1)*(x + 1);
\n+
531 out[9] = 2*z*(x + z - 1);
\n+
532 out[10] = -2*z*(x + z + 1);
\n+
533 out[11] = -2*z*(x + z - 1);
\n+
534 out[12] = 2*z*(x + z + 1);
\n+
535 out[13] = 2*((x + z - 1)*((y - 1)*(x + 1) + z*(x - y + z + 1)) + (y - z + 1)*(x + z - 1)*(x + 1 - z));
\n+
\n+
\n+
538 out[0] = -((y - z)*(2*x + 2*z - 1)*(z - y + 1))/2;
\n+
539 out[1] = ((y - z + 1)*(y - 2*x + z + 2*x*y - 2*x*z + 2*y*z - 2*z*z))/2;
\n+
540 out[2] = ((y - z)*(2*x + 2*z - 1)*(y - z + 1))/2;
\n+
541 out[3] = ((y - z)*(2*x + 2*z + 1)*(y - z + 1))/2;
\n+
\n+
543 out[5] = (-(y - z + 1)*(2*x + z - 1)*(y - 1) - (x + z - 1)*(y - 1)*x - (y - z + 1)*(x + z - 1)*x + (x + z - 1)*(y - 1)*x - (y - z + 1)*(y - 1)*x)/2;
\n+
544 out[6] = -((y - z + 1)*(3*y - 2*x + z + 3*x*y + x*z + y*z + x*x - 1))/2;
\n+
545 out[7] = z - z*(2*x + 1) - ((2*z - y*(z - y + 1))*(x + z - 1))/2 - ((2*x - y*(x + 1))*(x + z - 1))/2 + ((x + 1)*(x + z - 1)*(z - 2*y + 1))/2 + y*(x + 1)*(z - y + 1);
\n+
546 out[8] = -((y - z + 1)*(y + z + 3*x*y + x*z + y*z + x*x - 1))/2;
\n+
547 out[9] = -(x + 3*z - 1)*(z - y + 1);
\n+
548 out[10] = (x + z + 1)*(z - y + 1) - 2*y*z - 6*z + 2*z*z;
\n+
549 out[11] = -(x + 3*z - 1)*(y - z + 1);
\n+
550 out[12] = (x + 3*z + 1)*(y - z + 1);
\n+
551 out[13] = (y - z + 1)*(2*y - 3*x + z + 2*x*y + 6*x*z - 2*y*z + 2*x*x + 4*z*z - 3);
\n+
\n+
\n+
554 DUNE_THROW(RangeError,
"Component out of range.");
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
562 out[0] = -((y + z)*(2*z - 2*x + 1)*(y + z - 1))/2;
\n+
563 out[1] = ((y + z)*(2*x - 2*z + 1)*(y + z - 1))/2;
\n+
564 out[2] = -((y + z + 1)*(y - 3*z - 2*x*y - 2*x*z + 2*y*z + 2*z*z))/2;
\n+
565 out[3] = ((y + z)*(2*x - 2*z + 1)*(y + z + 1))/2;
\n+
\n+
567 out[5] = (y + 1)*(y + z - 1)*(z - 2*x + 1);
\n+
568 out[6] = -(y + 1)*(2*x - z + 1)*(y + z - 1);
\n+
569 out[7] = -y*(2*x - z)*(y + z - 1);
\n+
570 out[8] = z - z*(2*x + 1) - (2*z + y*(y + z + 1))*(x - z + 1) - y*(x - 1)*(y + z + 1);
\n+
571 out[9] = 2*z*(y + z - 1);
\n+
572 out[10] = -2*z*(y + z - 1);
\n+
573 out[11] = -2*z*(y + z + 1);
\n+
574 out[12] = 2*z*(y + z + 1);
\n+
575 out[13] = 2*(y + z - 1)*(2*x - z + 2*x*y - 2*x*z + 2*z*z);
\n+
\n+
\n+
578 out[0] = -(x - z)*(y + z - 0.5)*(z - x + 1);
\n+
579 out[1] = ((x - z)*(2*y + 2*z - 1)*(x - z + 1))/2;
\n+
580 out[2] = -((z - x + 1)*(x + 3*z + 2*x*y + 2*x*z - 2*y*z - 2*z*z))/2;
\n+
581 out[3] = ((x - z)*(2*y + 2*z + 1)*(x - z + 1))/2;
\n+
\n+
583 out[5] = z - z*(2*y + 1) - (2*z - x*(z - x + 1))*(y + z - 1) + x*(y + 1)*(z - x + 1);
\n+
584 out[6] = -x*(2*y + z)*(x - z + 1);
\n+
585 out[7] = -(x - 1)*(x - z + 1)*(2*y + z - 1);
\n+
586 out[8] = -(x - 1)*(x - z + 1)*(2*y + z + 1);
\n+
587 out[9] = -2*z*(z - x + 1);
\n+
588 out[10] = -2*z*(x - z + 1);
\n+
589 out[11] = 2*z*(z - x + 1);
\n+
590 out[12] = 2*z*(x - z + 1);
\n+
591 out[13] = 2*(x - z + 1)*(2*x*y - z - 2*y + 2*y*z + 2*z*z);
\n+
\n+
\n+
594 out[0] = -((x - z)*(2*y + 2*z - 1)*(z - x + 1))/2;
\n+
595 out[1] = ((x - z)*(2*y + 2*z - 1)*(x - z + 1))/2;
\n+
596 out[2] = ((x - z + 1)*(x - 2*y + z + 2*x*y + 2*x*z - 2*y*z - 2*z*z))/2;
\n+
597 out[3] = ((x - z)*(2*y + 2*z + 1)*(x - z + 1))/2;
\n+
\n+
599 out[5] = z - z*(2*y + 1) - ((2*z - x*(z - x + 1))*(y + z - 1))/2 - ((2*y - x*(y + 1))*(y + z - 1))/2 + ((y + 1)*(y + z - 1)*(z - 2*x + 1))/2 + x*(y + 1)*(z - x + 1);
\n+
600 out[6] = -((x - z + 1)*(x + z + 3*x*y + x*z + y*z + y*y - 1))/2;
\n+
601 out[7] = -((x - z + 1)*(3*x*y - 4*y - z - x + x*z + y*z + y*y + 1))/2;
\n+
602 out[8] = -((x - z + 1)*(3*x - 2*y + z + 3*x*y + x*z + y*z + y*y - 1))/2;
\n+
603 out[9] = -(z - x + 1)*(y + 3*z - 1);
\n+
604 out[10] = -(x - z + 1)*(y + 3*z - 1);
\n+
605 out[11] = (y + z + 1)*(z - x + 1) - 2*x*z - 6*z + 2*z*z;
\n+
606 out[12] = (x - z + 1)*(y + 3*z + 1);
\n+
607 out[13] = (x - z + 1)*(2*x - 3*y + z + 2*x*y - 2*x*z + 6*y*z + 2*y*y + 4*z*z - 3);
\n+
\n+
\n+
610 DUNE_THROW(RangeError,
"Component out of range.");
\n+
\n+
\n+
\n+
614 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
\n+
\n+
\n+
\n+
\n+
\n+
620 DUNE_THROW(NotImplemented,
"LagrangePyramidLocalBasis::partial for order " << k);
\n+
\n+
\n+
624 static constexpr unsigned int order ()
\n+
\n+
\n+
\n+
\n+
\n+
634 template<
unsigned int k>
\n+
635 class LagrangePyramidLocalCoefficients
\n+
\n+
\n+
639 LagrangePyramidLocalCoefficients ()
\n+
\n+
\n+
\n+
\n+
644 localKeys_[0] = LocalKey(0,0,0);
\n+
\n+
\n+
\n+
\n+
\n+
650 for (std::size_t i=0; i<size(); i++)
\n+
651 localKeys_[i] = LocalKey(i,3,0);
\n+
\n+
\n+
\n+
\n+
\n+
\n+
658 localKeys_[0] = LocalKey(0,3,0);
\n+
659 localKeys_[1] = LocalKey(1,3,0);
\n+
660 localKeys_[2] = LocalKey(2,3,0);
\n+
661 localKeys_[3] = LocalKey(3,3,0);
\n+
662 localKeys_[4] = LocalKey(4,3,0);
\n+
\n+
\n+
665 localKeys_[5] = LocalKey(0,2,0);
\n+
666 localKeys_[6] = LocalKey(1,2,0);
\n+
667 localKeys_[7] = LocalKey(2,2,0);
\n+
668 localKeys_[8] = LocalKey(3,2,0);
\n+
669 localKeys_[9] = LocalKey(4,2,0);
\n+
670 localKeys_[10] = LocalKey(5,2,0);
\n+
671 localKeys_[11] = LocalKey(6,2,0);
\n+
672 localKeys_[12] = LocalKey(7,2,0);
\n+
\n+
\n+
675 localKeys_[13] = LocalKey(0,1,0);
\n+
\n+
\n+
\n+
\n+
\n+
681 DUNE_THROW(NotImplemented,
"LagrangePyramidLocalCoefficients for order " << k);
\n+
\n+
\n+
\n+
686 static constexpr std::size_t size ()
\n+
\n+
688 std::size_t result = 0;
\n+
689 for (
unsigned int i=0; i<=k; i++)
\n+
690 result += power(i+1,2);
\n+
\n+
\n+
\n+
695 const LocalKey& localKey (std::size_t i)
const \n+
\n+
697 return localKeys_[i];
\n+
\n+
\n+
\n+
701 std::vector<LocalKey> localKeys_;
\n+
\n+
\n+
708 template<
class LocalBasis>
\n+
709 class LagrangePyramidLocalInterpolation
\n+
\n+
\n+
\n+
720 template<
typename F,
typename C>
\n+
721 void interpolate (
const F& ff, std::vector<C>& out)
const \n+
\n+
723 constexpr auto k = LocalBasis::order();
\n+
724 using D =
typename LocalBasis::Traits::DomainType;
\n+
725 using DF =
typename LocalBasis::Traits::DomainFieldType;
\n+
\n+
727 auto&& f = Impl::makeFunctionWithCallOperator<D>(ff);
\n+
\n+
729 out.resize(LocalBasis::size());
\n+
\n+
\n+
\n+
\n+
734 auto center = ReferenceElements<DF,3>::general(GeometryTypes::pyramid).position(0,0);
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
742 for (
unsigned int i=0; i<LocalBasis::size(); i++)
\n+
\n+
744 auto vertex = ReferenceElements<DF,3>::general(GeometryTypes::pyramid).position(i,3);
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
753 out[0] = f( D( {0.0, 0.0, 0.0} ) );
\n+
754 out[1] = f( D( {1.0, 0.0, 0.0} ) );
\n+
755 out[2] = f( D( {0.0, 1.0, 0.0} ) );
\n+
756 out[3] = f( D( {1.0, 1.0, 0.0} ) );
\n+
757 out[4] = f( D( {0.0, 0.0, 1.0} ) );
\n+
758 out[5] = f( D( {0.0, 0.5, 0.0} ) );
\n+
759 out[6] = f( D( {1.0, 0.5, 0.0} ) );
\n+
760 out[7] = f( D( {0.5, 0.0, 0.0} ) );
\n+
761 out[8] = f( D( {0.5, 1.0, 0.0} ) );
\n+
762 out[9] = f( D( {0.0, 0.0, 0.5} ) );
\n+
763 out[10] = f( D( {0.5, 0.0, 0.5} ) );
\n+
764 out[11] = f( D( {0.0, 0.5, 0.5} ) );
\n+
765 out[12] = f( D( {0.5, 0.5, 0.5} ) );
\n+
766 out[13] = f( D( {0.5, 0.5, 0.0} ) );
\n+
\n+
\n+
\n+
\n+
771 DUNE_THROW(NotImplemented,
"LagrangePyramidLocalInterpolation not implemented for order " << k);
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
810 template<
class D,
class R,
int k>
\n+
\n+
\n+
\n+
\n+
\n+
817 Impl::LagrangePyramidLocalCoefficients<k>,
\n+
818 Impl::LagrangePyramidLocalInterpolation<Impl::LagrangePyramidLocalBasis<D,R,k> > >;
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
838 return coefficients_;
\n+
\n+
\n+
\n+
\n+
\n+
\n+
845 return interpolation_;
\n+
\n+
\n+
\n+
\n+
849 static constexpr std::size_t
size ()
\n+
\n+
851 return Impl::LagrangePyramidLocalBasis<D,R,k>::size();
\n+
\n+
\n+
\n+
\n+
856 static constexpr GeometryType
type ()
\n+
\n+
858 return GeometryTypes::pyramid;
\n+
\n+
\n+
\n+
\n+
862 Impl::LagrangePyramidLocalBasis<D,R,k> basis_;
\n+
863 Impl::LagrangePyramidLocalCoefficients<k> coefficients_;
\n+
864 Impl::LagrangePyramidLocalInterpolation<Impl::LagrangePyramidLocalBasis<D,R,k> > interpolation_;
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n+
\n
Definition bdfmcube.hh:18
\n-
Brezzi-Douglas-Fortin-Marini finite elements for cubes.
Definition bdfmcube.hh:45
\n-
auto localCoefficients() const -> const LocalCoefficients &
Definition bdfmcube.hh:66
\n-
unsigned int size() const
Number of shape functions in this finite element.
Definition bdfmcube.hh:70
\n-
BDFMCubeLocalFiniteElement()
Standard constructor.
Definition bdfmcube.hh:54
\n-
auto localBasis() const -> const LocalBasis &
Definition bdfmcube.hh:65
\n-
static constexpr auto type() -> GeometryType
Definition bdfmcube.hh:71
\n-
auto localInterpolation() const -> const LocalInterpolation &
Definition bdfmcube.hh:67
\n-
BDFMCubeLocalFiniteElement(std::bitset< 2 *dim > s)
Make set number s, where 0 <= s < 2^(2*dim)
Definition bdfmcube.hh:61
\n-
Brezzi-Douglas-Fortin-Marini shape functions on a reference cube.
Definition brezzidouglasfortinmarini/cube/localbasis.hh:37
\n-
Layout map for Brezzi-Douglas-Fortin-Marini elements on cubes.
Definition localcoefficients.hh:33
\n-
Interpolation for Brezzi-Douglas-Fortin-Marini shape functions on cubes.
Definition brezzidouglasfortinmarini/cube/localinterpolation.hh:38
\n+
D DomainType
domain type
Definition common/localbasis.hh:42
\n
traits helper struct
Definition localfiniteelementtraits.hh:13
\n-
\n-
\n+
LB LocalBasisType
Definition localfiniteelementtraits.hh:16
\n+
LC LocalCoefficientsType
Definition localfiniteelementtraits.hh:20
\n+
LI LocalInterpolationType
Definition localfiniteelementtraits.hh:24
\n+
Lagrange finite element for 3d pyramids with compile-time polynomial order.
Definition lagrangepyramid.hh:812
\n+
const Traits::LocalCoefficientsType & localCoefficients() const
Returns the assignment of the degrees of freedom to the element subentities.
Definition lagrangepyramid.hh:836
\n+
static constexpr std::size_t size()
The number of shape functions.
Definition lagrangepyramid.hh:849
\n+
LagrangePyramidLocalFiniteElement()
Default constructor.
Definition lagrangepyramid.hh:825
\n+
static constexpr GeometryType type()
The reference element that the local finite element is defined on.
Definition lagrangepyramid.hh:856
\n+
const Traits::LocalBasisType & localBasis() const
Returns the local basis, i.e., the set of shape functions.
Definition lagrangepyramid.hh:829
\n+
const Traits::LocalInterpolationType & localInterpolation() const
Returns object that evaluates degrees of freedom.
Definition lagrangepyramid.hh:843
\n+
\n+
\n
![\"doxygen\"/](\"doxygen.svg\")
1.9.8\n \n \n", "details": [{"source1": "html2text {}", "source2": "html2text {}", "unified_diff": "@@ -1,36 +1,34 @@\n dune-localfunctions\u00a02.9.0\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- * _\bo_\br_\bt_\bh_\bo_\bn_\bo_\br_\bm_\ba_\bl\n-_\bC_\bl_\ba_\bs_\bs_\be_\bs | _\bN_\ba_\bm_\be_\bs_\bp_\ba_\bc_\be_\bs | _\bF_\bu_\bn_\bc_\bt_\bi_\bo_\bn_\bs\n-orthonormalcompute.hh File Reference\n-#include