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| 1 | // -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- | ||
| 2 | // vi: set et ts=4 sw=4 sts=4: | ||
| 3 | // | ||
| 4 | // SPDX-FileCopyrightInfo: Copyright © DuMux Project contributors, see AUTHORS.md in root folder | ||
| 5 | // SPDX-License-Identifier: GPL-3.0-or-later | ||
| 6 | // | ||
| 7 | /*! | ||
| 8 | * \file | ||
| 9 | * \ingroup PQ1BubbleDiscretization | ||
| 10 | * \brief Evaluate P1/Q1 basis with bubble function | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_DISCRETIZATION_PQ1BUBBLE_LOCAL_FINITE_ELEMENT_HH | ||
| 13 | #define DUMUX_DISCRETIZATION_PQ1BUBBLE_LOCAL_FINITE_ELEMENT_HH | ||
| 14 | |||
| 15 | #include <array> | ||
| 16 | #include <vector> | ||
| 17 | #include <numeric> | ||
| 18 | #include <algorithm> | ||
| 19 | |||
| 20 | #include <dune/common/fmatrix.hh> | ||
| 21 | #include <dune/common/fvector.hh> | ||
| 22 | #include <dune/common/exceptions.hh> | ||
| 23 | |||
| 24 | #include <dune/geometry/type.hh> | ||
| 25 | #include <dune/geometry/referenceelements.hh> | ||
| 26 | |||
| 27 | #include <dune/localfunctions/common/localbasis.hh> | ||
| 28 | #include <dune/localfunctions/common/localfiniteelementtraits.hh> | ||
| 29 | #include <dune/localfunctions/common/localinterpolation.hh> | ||
| 30 | #include <dune/localfunctions/common/localkey.hh> | ||
| 31 | |||
| 32 | #include <dune/localfunctions/lagrange/lagrangesimplex.hh> | ||
| 33 | #include <dune/localfunctions/lagrange/lagrangecube.hh> | ||
| 34 | |||
| 35 | namespace Dumux::Detail { | ||
| 36 | |||
| 37 | /*! | ||
| 38 | * \brief P1/Q1 + Bubble on the reference element | ||
| 39 | * | ||
| 40 | * \tparam D Type to represent the field in the domain | ||
| 41 | * \tparam R Type to represent the field in the range | ||
| 42 | * \tparam dim Dimension of the domain element | ||
| 43 | * \tparam typeId The geometry type | ||
| 44 | */ | ||
| 45 | template<class D, class R, unsigned int dim, Dune::GeometryType::Id typeId> | ||
| 46 | class PQ1BubbleLocalBasis | ||
| 47 | { | ||
| 48 | using PQ1FiniteElement = std::conditional_t< | ||
| 49 | Dune::GeometryType{ typeId } == Dune::GeometryTypes::cube(dim), | ||
| 50 | Dune::LagrangeCubeLocalFiniteElement<D, R, dim, 1>, | ||
| 51 | Dune::LagrangeSimplexLocalFiniteElement<D, R, dim, 1> | ||
| 52 | >; | ||
| 53 | static constexpr std::size_t numDofs | ||
| 54 | = Dune::GeometryType{ typeId } == Dune::GeometryTypes::cube(dim) ? (1<<dim)+1 : (dim+1)+1; | ||
| 55 | public: | ||
| 56 | using Traits = Dune::LocalBasisTraits< | ||
| 57 | D, dim, Dune::FieldVector<D, dim>, | ||
| 58 | R, 1, Dune::FieldVector<R, 1>, | ||
| 59 | Dune::FieldMatrix<R, 1, dim> | ||
| 60 | >; | ||
| 61 | |||
| 62 | 56 | PQ1BubbleLocalBasis() | |
| 63 |
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56 | : pq1FiniteElement_{} |
| 64 | { | ||
| 65 | // precompute center values for normalization | ||
| 66 |
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56 | const auto& p1Basis = pq1FiniteElement_.localBasis(); |
| 67 |
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56 | const auto refElement = Dune::referenceElement<typename Traits::DomainFieldType, dim>(type()); |
| 68 |
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56 | const auto& center = refElement.position(0, 0); |
| 69 |
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56 | p1Basis.evaluateFunction(center, pq1AtCenter_); |
| 70 | 56 | } | |
| 71 | |||
| 72 | /*! | ||
| 73 | * \brief Number of shape functions (one for each vertex and one in the element) | ||
| 74 | */ | ||
| 75 | static constexpr unsigned int size() | ||
| 76 | { return numDofs; } | ||
| 77 | |||
| 78 | /*! | ||
| 79 | * \brief Evaluate all shape functions | ||
| 80 | */ | ||
| 81 | 37431036 | void evaluateFunction(const typename Traits::DomainType& x, | |
| 82 | std::vector<typename Traits::RangeType>& out) const | ||
| 83 | { | ||
| 84 | 37431036 | out.reserve(size()); | |
| 85 | 37431036 | const auto& p1Basis = pq1FiniteElement_.localBasis(); | |
| 86 | 37431036 | p1Basis.evaluateFunction(x, out); | |
| 87 | 74862072 | const auto bubble = evaluateBubble_(x); | |
| 88 | 37431036 | out.resize(size()); | |
| 89 | 37431036 | out.back() = bubble; | |
| 90 |
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166638796 | for (int i = 0; i < numDofs-1; ++i) |
| 91 | 775246560 | out[i] -= pq1AtCenter_[i]*out.back(); | |
| 92 | 37431036 | } | |
| 93 | |||
| 94 | /*! | ||
| 95 | * \brief Evaluate the Jacobians of all shape functions | ||
| 96 | */ | ||
| 97 | 2105276 | void evaluateJacobian(const typename Traits::DomainType& x, | |
| 98 | std::vector<typename Traits::JacobianType>& out) const | ||
| 99 | { | ||
| 100 | 2105276 | out.reserve(size()); | |
| 101 | 2105276 | const auto& p1Basis = pq1FiniteElement_.localBasis(); | |
| 102 | 2105276 | p1Basis.evaluateJacobian(x, out); | |
| 103 | |||
| 104 |
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2105276 | std::vector<typename Traits::RangeType> shapeValues; |
| 105 |
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2105276 | p1Basis.evaluateFunction(x, shapeValues); |
| 106 | |||
| 107 | 2105276 | const auto bubbleJacobian = evaluateBubbleJacobian_(x); | |
| 108 | |||
| 109 |
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9690092 | for (int i = 0; i < numDofs-1; ++i) |
| 110 |
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23167744 | for (int k = 0; k < dim; ++k) |
| 111 | 124663424 | out[i][0][k] -= pq1AtCenter_[i]*bubbleJacobian[0][k]; | |
| 112 | |||
| 113 |
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2105276 | out.resize(size()); |
| 114 |
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4210552 | out.back() = bubbleJacobian; |
| 115 | 2105276 | } | |
| 116 | |||
| 117 | /** \brief Evaluate partial derivatives of any order of all shape functions | ||
| 118 | * | ||
| 119 | * \param order Order of the partial derivatives, in the classic multi-index notation | ||
| 120 | * \param in Position where to evaluate the derivatives | ||
| 121 | * \param[out] out The desired partial derivatives | ||
| 122 | */ | ||
| 123 | ✗ | void partial(const std::array<unsigned int, dim>& order, | |
| 124 | const typename Traits::DomainType& in, | ||
| 125 | std::vector<typename Traits::RangeType>& out) const | ||
| 126 | { | ||
| 127 | ✗ | DUNE_THROW(Dune::NotImplemented, "Partial derivatives"); | |
| 128 | } | ||
| 129 | |||
| 130 | /*! | ||
| 131 | * \brief Evaluate the Jacobians of all shape functions | ||
| 132 | * we are actually cubic/quartic but cannot represent all cubic/quartic polynomials | ||
| 133 | */ | ||
| 134 | static constexpr unsigned int order() | ||
| 135 | { | ||
| 136 | return 1; | ||
| 137 | } | ||
| 138 | |||
| 139 | /*! | ||
| 140 | * \brief The reference element type | ||
| 141 | */ | ||
| 142 | static constexpr Dune::GeometryType type() | ||
| 143 | { | ||
| 144 | return { typeId }; | ||
| 145 | } | ||
| 146 | private: | ||
| 147 | // evaluate bubble function at x | ||
| 148 | ✗ | typename Traits::RangeType evaluateBubble_(const typename Traits::DomainType& x) const | |
| 149 | { | ||
| 150 | if constexpr (type() == Dune::GeometryTypes::simplex(dim)) | ||
| 151 | { | ||
| 152 | if constexpr (dim == 2) | ||
| 153 | 51290960 | return 27*x[0]*x[1]*(1-x[0]-x[1]); | |
| 154 | else if constexpr (dim == 3) | ||
| 155 | 5278434 | return 256*x[0]*x[1]*x[2]*(1-x[0]-x[1]-x[2]); | |
| 156 | } | ||
| 157 | else if constexpr (type() == Dune::GeometryTypes::cube(dim)) | ||
| 158 | { | ||
| 159 | if constexpr (dim == 2) | ||
| 160 | 38516320 | return 16*x[0]*x[1]*(1-x[0])*(1-x[1]); | |
| 161 | else if constexpr (dim == 3) | ||
| 162 | ✗ | return 64*x[0]*x[1]*x[2]*(1-x[0])*(1-x[1])*(1-x[2]); | |
| 163 | } | ||
| 164 | else | ||
| 165 | DUNE_THROW(Dune::NotImplemented, "Bubble function for " << type()); | ||
| 166 | } | ||
| 167 | |||
| 168 | // evaluate bubble function at x | ||
| 169 | 2105276 | typename Traits::JacobianType evaluateBubbleJacobian_(const typename Traits::DomainType& x) const | |
| 170 | { | ||
| 171 | if constexpr (type() == Dune::GeometryTypes::simplex(dim)) | ||
| 172 | { | ||
| 173 | if constexpr (dim == 2) | ||
| 174 | 4181440 | return {{27*(x[1]*(1-x[0]-x[1]) - x[0]*x[1]), | |
| 175 | 5854016 | 27*(x[0]*(1-x[0]-x[1]) - x[0]*x[1])}}; | |
| 176 | else if constexpr (dim == 3) | ||
| 177 | 826592 | return {{256*(x[1]*x[2]*(1-x[0]-x[1]-x[2]) - x[0]*x[1]*x[2]), | |
| 178 | 723268 | 256*(x[0]*x[2]*(1-x[0]-x[1]-x[2]) - x[0]*x[1]*x[2]), | |
| 179 | 1033240 | 256*(x[0]*x[1]*(1-x[0]-x[1]-x[2]) - x[0]*x[1]*x[2])}}; | |
| 180 | } | ||
| 181 | else if constexpr (type() == Dune::GeometryTypes::cube(dim)) | ||
| 182 | { | ||
| 183 | if constexpr (dim == 2) | ||
| 184 | 6993984 | return {{16*(x[1]*(1-x[0])*(1-x[1]) - x[0]*x[1]*(1-x[1])), | |
| 185 | 9325312 | 16*(x[0]*(1-x[0])*(1-x[1]) - x[0]*x[1]*(1-x[0]))}}; | |
| 186 | else if constexpr (dim == 3) | ||
| 187 | ✗ | return {{64*(x[1]*x[2]*(1-x[0])*(1-x[1])*(1-x[2]) - x[0]*x[1]*x[2]*(1-x[1]))*(1-x[2]), | |
| 188 | ✗ | 64*(x[0]*x[2]*(1-x[0])*(1-x[1])*(1-x[2]) - x[0]*x[1]*x[2]*(1-x[0]))*(1-x[2]), | |
| 189 | ✗ | 64*(x[0]*x[1]*(1-x[0])*(1-x[1])*(1-x[2]) - x[0]*x[1]*x[2]*(1-x[0]))*(1-x[1])}}; | |
| 190 | } | ||
| 191 | else | ||
| 192 | DUNE_THROW(Dune::NotImplemented, "Bubble function for " << type() << " dim = " << dim); | ||
| 193 | } | ||
| 194 | |||
| 195 | PQ1FiniteElement pq1FiniteElement_; | ||
| 196 | std::vector<typename Traits::RangeType> pq1AtCenter_; | ||
| 197 | }; | ||
| 198 | |||
| 199 | /*! | ||
| 200 | * \brief Associations of the P1/Q1 + Bubble degrees of freedom to the facets of the reference element | ||
| 201 | * \tparam dim Dimension of the reference element | ||
| 202 | * \tparam typeId The geometry type | ||
| 203 | */ | ||
| 204 | template<int dim, Dune::GeometryType::Id typeId> | ||
| 205 | class PQ1BubbleLocalCoefficients | ||
| 206 | { | ||
| 207 | static constexpr std::size_t numDofs | ||
| 208 | = Dune::GeometryType{ typeId } == Dune::GeometryTypes::cube(dim) ? (1<<dim)+1 : (dim+1)+1; | ||
| 209 | public: | ||
| 210 | |||
| 211 | PQ1BubbleLocalCoefficients() | ||
| 212 | { | ||
| 213 | // Dune::LocalKey is constructed with | ||
| 214 | // - the local index with respect to the subentity type | ||
| 215 | // - the codim of the subentity the dof is attached to | ||
| 216 | // - the local number of the function to evaluate | ||
| 217 | |||
| 218 | // vertex dofs | ||
| 219 | for (std::size_t i=0; i<size()-1; i++) | ||
| 220 | localKeys_[i] = Dune::LocalKey(i, dim, 0); | ||
| 221 | |||
| 222 | // cell dof | ||
| 223 | localKeys_.back() = Dune::LocalKey(0, 0, 0); | ||
| 224 | } | ||
| 225 | |||
| 226 | //! Number of coefficients | ||
| 227 | static constexpr std::size_t size () | ||
| 228 | { return numDofs; } | ||
| 229 | |||
| 230 | //! Get i-th local key | ||
| 231 | const Dune::LocalKey& localKey (std::size_t i) const | ||
| 232 | 9428160 | { return localKeys_[i]; } | |
| 233 | |||
| 234 | private: | ||
| 235 | std::array<Dune::LocalKey, numDofs> localKeys_; | ||
| 236 | }; | ||
| 237 | |||
| 238 | /*! | ||
| 239 | * \brief Evaluate the degrees of freedom of a P1 + Bubble basis | ||
| 240 | * | ||
| 241 | * \tparam LocalBasis The corresponding set of shape functions | ||
| 242 | */ | ||
| 243 | template<class LocalBasis> | ||
| 244 | class PQ1BubbleLocalInterpolation | ||
| 245 | { | ||
| 246 | public: | ||
| 247 | /*! | ||
| 248 | * \brief Evaluate a given function at the vertices and the cell midpoint | ||
| 249 | * | ||
| 250 | * \tparam F Type of function to evaluate | ||
| 251 | * \tparam C Type used for the values of the function | ||
| 252 | * \param[in] f Function to evaluate (call operator that gets a local position) | ||
| 253 | * \param[out] out Array of function values | ||
| 254 | */ | ||
| 255 | template<typename F, typename C> | ||
| 256 | ✗ | void interpolate (const F& f, std::vector<C>& out) const | |
| 257 | { | ||
| 258 | ✗ | constexpr auto dim = LocalBasis::Traits::dimDomain; | |
| 259 | |||
| 260 | ✗ | out.resize(LocalBasis::size()); | |
| 261 | |||
| 262 | ✗ | const auto refElement = Dune::referenceElement<typename LocalBasis::Traits::DomainFieldType,dim>(LocalBasis::type()); | |
| 263 | |||
| 264 | // Evaluate at the vertices and at the center | ||
| 265 | ✗ | for (int i = 0; i < refElement.size(dim); ++i) | |
| 266 | ✗ | out[i] = f(refElement.position(i, dim)); | |
| 267 | ✗ | out.back() = f(refElement.position(0, 0)); | |
| 268 | ✗ | } | |
| 269 | }; | ||
| 270 | |||
| 271 | } // end namespace Dumux::Detail | ||
| 272 | |||
| 273 | namespace Dumux { | ||
| 274 | |||
| 275 | /*! | ||
| 276 | * \brief P1/Q1 + Bubble finite element | ||
| 277 | * | ||
| 278 | * \tparam D type used for domain coordinates | ||
| 279 | * \tparam R type used for function values | ||
| 280 | * \tparam dim dimension of the reference element | ||
| 281 | * \tparam typeId The geometry type | ||
| 282 | */ | ||
| 283 | template<class D, class R, int dim, Dune::GeometryType::Id typeId> | ||
| 284 |
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84 | class PQ1BubbleLocalFiniteElement |
| 285 | { | ||
| 286 | using Basis = Detail::PQ1BubbleLocalBasis<D, R, dim, typeId>; | ||
| 287 | using Coefficients = Detail::PQ1BubbleLocalCoefficients<dim, typeId>; | ||
| 288 | using Interpolation = Detail::PQ1BubbleLocalInterpolation<Basis>; | ||
| 289 | |||
| 290 | static constexpr Dune::GeometryType gt = Dune::GeometryType{ typeId }; | ||
| 291 | static_assert( | ||
| 292 | gt == Dune::GeometryTypes::cube(dim) || gt == Dune::GeometryTypes::simplex(dim), | ||
| 293 | "Only implemented for cubes and simplices" | ||
| 294 | ); | ||
| 295 | |||
| 296 | public: | ||
| 297 | using Traits = Dune::LocalFiniteElementTraits<Basis, Coefficients, Interpolation>; | ||
| 298 | |||
| 299 | /*! | ||
| 300 | * \brief Returns the local basis, i.e., the set of shape functions | ||
| 301 | */ | ||
| 302 | const typename Traits::LocalBasisType& localBasis() const | ||
| 303 | { | ||
| 304 | 28 | return basis_; | |
| 305 | } | ||
| 306 | |||
| 307 | /*! | ||
| 308 | * \brief Returns the assignment of the degrees of freedom to the element subentities | ||
| 309 | */ | ||
| 310 | const typename Traits::LocalCoefficientsType& localCoefficients() const | ||
| 311 | { | ||
| 312 | 28 | return coefficients_; | |
| 313 | } | ||
| 314 | |||
| 315 | /*! | ||
| 316 | * \brief Returns object that evaluates degrees of freedom | ||
| 317 | */ | ||
| 318 | const typename Traits::LocalInterpolationType& localInterpolation() const | ||
| 319 | { | ||
| 320 | 28 | return interpolation_; | |
| 321 | } | ||
| 322 | |||
| 323 | /*! | ||
| 324 | * \brief The number of coefficients in the basis | ||
| 325 | */ | ||
| 326 | static constexpr std::size_t size() | ||
| 327 | { | ||
| 328 | return Basis::size(); | ||
| 329 | } | ||
| 330 | |||
| 331 | /*! | ||
| 332 | * \brief The reference element type that the local finite element is defined on | ||
| 333 | */ | ||
| 334 | static constexpr Dune::GeometryType type() | ||
| 335 | { | ||
| 336 | return Traits::LocalBasisType::type(); | ||
| 337 | } | ||
| 338 | |||
| 339 | private: | ||
| 340 | Basis basis_; | ||
| 341 | Coefficients coefficients_; | ||
| 342 | Interpolation interpolation_; | ||
| 343 | }; | ||
| 344 | |||
| 345 | } // end namespace Dumux | ||
| 346 | |||
| 347 | #endif | ||
| 348 |