163 |
} |
} |
164 |
} |
} |
165 |
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166 |
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167 |
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168 |
template <typename MeshType> |
template <typename MeshType> |
169 |
const real_t FunctionExpressionFEM:: |
const real_t FunctionExpressionFEM:: |
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__dx(const double& x, |
__dx(const double& x, |
182 |
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183 |
typedef typename MeshType::ElementsGeometry CellType; |
typedef typename MeshType::ElementsGeometry CellType; |
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typedef typename FiniteElementTraits<CellType>::Transformation TransformationType; |
typedef typename FiniteElementTraits<CellType>::Transformation TransformationType; |
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typedef typename FiniteElementTraits<CellType>::JacobianTransformation Jacobian; |
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185 |
typedef typename FiniteElementTraits<CellType>::Type FEMType; |
typedef typename FiniteElementTraits<CellType>::Type FEMType; |
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TransformationType T(*i); |
TransformationType T(*i); |
188 |
Jacobian J(T); |
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189 |
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TinyVector<3,real_t> Xhat; |
190 |
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if (not(T.invertT(x,y,z,Xhat))) { |
191 |
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return 0; |
192 |
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} |
193 |
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194 |
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TinyVector<CellType::NumberOfVertices, real_t> fiValues; |
195 |
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196 |
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TinyMatrix<3, CellType::NumberOfVertices> DwValues; |
197 |
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198 |
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for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
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DwValues(0,k) = FEMType::instance().dxW(k,Xhat); |
200 |
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DwValues(1,k) = FEMType::instance().dyW(k,Xhat); |
201 |
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DwValues(2,k) = FEMType::instance().dzW(k,Xhat); |
202 |
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} |
203 |
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204 |
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Vector<real_t>& f = (*__value); |
205 |
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for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
206 |
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fiValues[k] = f[M.vertexNumber((*i)(k))]; |
207 |
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} |
208 |
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209 |
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TinyVector<3, real_t> gradientPart = DwValues*fiValues; |
210 |
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211 |
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TinyMatrix<3,3, real_t> J; |
212 |
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TinyVector<3, real_t> temp; |
213 |
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214 |
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T.dx(x,y,z,temp); |
215 |
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for(size_t i=0; i<3; ++i) { |
216 |
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J(0,i) = temp[i]; |
217 |
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} |
218 |
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219 |
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T.dy(x,y,z,temp); |
220 |
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for(size_t i=0; i<3; ++i) { |
221 |
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J(1,i) = temp[i]; |
222 |
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} |
223 |
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224 |
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T.dz(x,y,z,temp); |
225 |
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for(size_t i=0; i<3; ++i) { |
226 |
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J(2,i) = temp[i]; |
227 |
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} |
228 |
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229 |
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// now we use |
230 |
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231 |
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TinyVector<3, real_t> result; |
232 |
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233 |
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gaussPivot(J, gradientPart, result); |
234 |
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235 |
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switch (d) { |
236 |
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case FunctionExpressionDx::x: { |
237 |
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return result[0]; |
238 |
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} |
239 |
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case FunctionExpressionDx::y: { |
240 |
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return result[1]; |
241 |
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} |
242 |
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case FunctionExpressionDx::z: { |
243 |
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return result[2]; |
244 |
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} |
245 |
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default: { |
246 |
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fferr(0) << __FILE__ << ':' << __LINE__ << ": " |
247 |
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<< "trying to compute unknown derivative\n"; |
248 |
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std::exit(1); |
249 |
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return 0; |
250 |
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} |
251 |
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} |
252 |
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} |
253 |
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254 |
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template <> |
255 |
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const real_t FunctionExpressionFEM:: |
256 |
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__dx<Structured3DMesh>(const double& x, |
257 |
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const double& y, |
258 |
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const double& z, |
259 |
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const FunctionExpressionDx::Direction& d) const |
260 |
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{ |
261 |
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Structured3DMesh& M = static_cast<Structured3DMesh&>(*(*__mesh).mesh()); |
262 |
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263 |
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Structured3DMesh::iterator i = M.find(x,y,z); |
264 |
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265 |
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if (i == 0) { // outside of the mesh! |
266 |
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return 0; |
267 |
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} |
268 |
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269 |
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typedef Structured3DMesh::ElementsGeometry CellType; |
270 |
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typedef FiniteElementTraits<CellType>::Transformation TransformationType; |
271 |
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typedef FiniteElementTraits<CellType>::Type FEMType; |
272 |
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273 |
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TransformationType T(*i); |
274 |
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275 |
TinyVector<3,real_t> Xhat; |
TinyVector<3,real_t> Xhat; |
276 |
if (not(T.invertT(x,y,z,Xhat))) { |
if (not(T.invertT(x,y,z,Xhat))) { |
285 |
for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
286 |
DwiValues[k] = FEMType::instance().dxW(k,Xhat); |
DwiValues[k] = FEMType::instance().dxW(k,Xhat); |
287 |
} |
} |
288 |
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TinyVector<3, real_t> Dx; |
289 |
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T.dx(x,y,z, Dx); |
290 |
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DwiValues /= Dx[0]; |
291 |
break; |
break; |
292 |
} |
} |
293 |
case FunctionExpressionDx::y: { |
case FunctionExpressionDx::y: { |
294 |
for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
295 |
DwiValues[k] = FEMType::instance().dyW(k,Xhat); |
DwiValues[k] = FEMType::instance().dyW(k,Xhat); |
296 |
} |
} |
297 |
|
TinyVector<3, real_t> Dy; |
298 |
|
T.dy(x,y,z, Dy); |
299 |
|
DwiValues /= Dy[1]; |
300 |
break; |
break; |
301 |
} |
} |
302 |
case FunctionExpressionDx::z: { |
case FunctionExpressionDx::z: { |
303 |
for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
for (size_t k = 0; k<CellType::NumberOfVertices; ++k) { |
304 |
DwiValues[k] = FEMType::instance().dzW(k,Xhat); |
DwiValues[k] = FEMType::instance().dzW(k,Xhat); |
305 |
} |
} |
306 |
|
TinyVector<3, real_t> Dz; |
307 |
|
T.dz(x,y,z, Dz); |
308 |
|
DwiValues /= Dz[2]; |
309 |
break; |
break; |
310 |
} |
} |
311 |
default: { |
default: { |
320 |
fiValues[k] = f[M.vertexNumber((*i)(k))]; |
fiValues[k] = f[M.vertexNumber((*i)(k))]; |
321 |
} |
} |
322 |
|
|
323 |
return (DwiValues*fiValues/J.jacobian(0,0)); |
return (DwiValues*fiValues); |
324 |
} |
} |
325 |
|
|
326 |
const real_t FunctionExpressionFEM::dx(const double& x, |
const real_t FunctionExpressionFEM::dx(const double& x, |
333 |
return __dx<Structured3DMesh>(x,y,z,d); |
return __dx<Structured3DMesh>(x,y,z,d); |
334 |
break; |
break; |
335 |
} |
} |
336 |
|
case Mesh::hexahedraMesh: { |
337 |
|
return __dx<MeshOfHexahedra>(x,y,z,d); |
338 |
|
break; |
339 |
|
} |
340 |
default: { |
default: { |
341 |
fferr(0) << __FILE__ << ':' << __LINE__ |
fferr(0) << __FILE__ << ':' << __LINE__ |
342 |
<< ": not implemented\n"; |
<< ": not implemented\n"; |