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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 Linear | ||
| 10 | * \brief Preconditioned iterative solver for the incompressible Stokes problem | ||
| 11 | */ | ||
| 12 | #ifndef DUMUX_LINEAR_STOKES_SOLVER_HH | ||
| 13 | #define DUMUX_LINEAR_STOKES_SOLVER_HH | ||
| 14 | |||
| 15 | #include <type_traits> | ||
| 16 | #include <memory> | ||
| 17 | #include <tuple> | ||
| 18 | |||
| 19 | #include <dune/common/parametertree.hh> | ||
| 20 | #include <dune/common/hybridutilities.hh> | ||
| 21 | #include <dune/common/exceptions.hh> | ||
| 22 | |||
| 23 | #include <dune/istl/matrixindexset.hh> | ||
| 24 | #include <dune/istl/preconditioner.hh> | ||
| 25 | #include <dune/istl/preconditioners.hh> | ||
| 26 | #include <dune/istl/solvers.hh> | ||
| 27 | #include <dune/istl/paamg/amg.hh> | ||
| 28 | |||
| 29 | #include <dumux/common/math.hh> | ||
| 30 | #include <dumux/linear/solver.hh> | ||
| 31 | #include <dumux/linear/preconditioners.hh> | ||
| 32 | #include <dumux/linear/linearsolverparameters.hh> | ||
| 33 | #include <dumux/linear/parallelhelpers.hh> | ||
| 34 | #include <dumux/linear/linearsolvertraits.hh> | ||
| 35 | #include <dumux/linear/parallelmatrixadapter.hh> | ||
| 36 | #include <dumux/discretization/extrusion.hh> | ||
| 37 | #include <dumux/linear/symmetrize_constraints.hh> | ||
| 38 | |||
| 39 | namespace Dumux::Detail { | ||
| 40 | |||
| 41 | /*! | ||
| 42 | * \ingroup Linear | ||
| 43 | * \brief A Stokes preconditioner (saddle-point problem) for the problem | ||
| 44 | * \f$ | ||
| 45 | \begin{pmatrix} A & B \\ C & 0 \end{pmatrix} | ||
| 46 | \begin{pmatrix} u \\ p \end{pmatrix} = | ||
| 47 | \begin{pmatrix} f \\ g \end{pmatrix}, | ||
| 48 | * \f$ | ||
| 49 | * | ||
| 50 | * where A is the discrete velocity operator and B and C are discrete gradient and divergence operators. | ||
| 51 | * This preconditioner is especially suited for solving the incompressible Stokes equations. | ||
| 52 | * | ||
| 53 | * \tparam M Type of the matrix. | ||
| 54 | * \tparam X Type of the update. | ||
| 55 | * \tparam Y Type of the defect. | ||
| 56 | * \tparam l Preconditioner block level | ||
| 57 | */ | ||
| 58 | template<class M, class X, class Y, int l = 2> | ||
| 59 | class StokesPreconditioner : public Dune::Preconditioner<X,Y> | ||
| 60 | { | ||
| 61 | static_assert(Dumux::isMultiTypeBlockMatrix<M>::value && M::M() == 2 && M::N() == 2, "Expects a 2x2 MultiTypeBlockMatrix."); | ||
| 62 | static_assert(l == 2, "StokesPreconditioner expects a block level of 2 for Matrix type M."); | ||
| 63 | |||
| 64 | using A = std::decay_t<decltype(std::declval<M>()[Dune::Indices::_0][Dune::Indices::_0])>; | ||
| 65 | using U = std::decay_t<decltype(std::declval<X>()[Dune::Indices::_0])>; | ||
| 66 | |||
| 67 | using P = std::decay_t<decltype(std::declval<M>()[Dune::Indices::_1][Dune::Indices::_1])>; | ||
| 68 | using V = std::decay_t<decltype(std::declval<X>()[Dune::Indices::_1])>; | ||
| 69 | |||
| 70 | enum class Mode { symmetric, triangular, diagonal }; | ||
| 71 | |||
| 72 | public: | ||
| 73 | //! \brief The matrix type the preconditioner is for. | ||
| 74 | using matrix_type = M; | ||
| 75 | //! \brief The domain type of the preconditioner. | ||
| 76 | using domain_type = X; | ||
| 77 | //! \brief The range type of the preconditioner. | ||
| 78 | using range_type = Y; | ||
| 79 | //! \brief The field type of the preconditioner. | ||
| 80 | using field_type = typename X::field_type; | ||
| 81 | //! \brief Scalar type underlying the field_type. | ||
| 82 | using scalar_field_type = Dune::Simd::Scalar<field_type>; | ||
| 83 | //! \brief the type of the pressure operator | ||
| 84 | using PressureLinearOperator = Dune::MatrixAdapter<P,V,V>; | ||
| 85 | |||
| 86 | /*! | ||
| 87 | * \brief Constructor | ||
| 88 | * \param fullLinearOperator the Stokes linear operator | ||
| 89 | * \param pressureLinearOperator the linear operator to be used for the pressure space preconditioner | ||
| 90 | * \param params a parameter tree for the preconditioner configuration | ||
| 91 | */ | ||
| 92 | 2 | StokesPreconditioner( | |
| 93 | const std::shared_ptr<const Dune::AssembledLinearOperator<M,X,Y>>& fullLinearOperator, | ||
| 94 | const std::shared_ptr<const PressureLinearOperator>& pressureLinearOperator, | ||
| 95 | const Dune::ParameterTree& params | ||
| 96 | ) | ||
| 97 | 4 | : matrix_(fullLinearOperator->getmat()) | |
| 98 | 4 | , pmatrix_(pressureLinearOperator->getmat()) | |
| 99 |
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4 | , verbosity_(params.get<int>("verbosity")) |
| 100 |
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6 | , paramGroup_(params.get<std::string>("ParameterGroup")) |
| 101 | { | ||
| 102 |
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2 | const auto mode = getParamFromGroup<std::string>( |
| 103 |
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2 | paramGroup_, "LinearSolver.Preconditioner.Mode", "Diagonal" |
| 104 | ); | ||
| 105 | |||
| 106 |
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2 | if (mode == "Symmetric") |
| 107 | ✗ | mode_ = Mode::symmetric; | |
| 108 |
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2 | else if (mode == "Triangular") |
| 109 | 2 | mode_ = Mode::triangular; | |
| 110 | else | ||
| 111 | ✗ | mode_ = Mode::diagonal; | |
| 112 | |||
| 113 |
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2 | initPreconditioner_(params); |
| 114 | 2 | } | |
| 115 | |||
| 116 | /*! | ||
| 117 | * \brief Prepare the preconditioner. | ||
| 118 | */ | ||
| 119 | 2 | void pre(X& update, Y& currentDefect) override {} | |
| 120 | |||
| 121 | /*! | ||
| 122 | * \brief Apply the preconditioner | ||
| 123 | * | ||
| 124 | * \param update The update to be computed. | ||
| 125 | * \param currentDefect The current defect. | ||
| 126 | * | ||
| 127 | * The currentDefect has be be in a consistent representation, | ||
| 128 | * Definition 2.3 Blatt and Bastian (2009) https://doi.org/10.1504/IJCSE.2008.021112 | ||
| 129 | * The update is initially zero. At exit the update has to be | ||
| 130 | * in a consistent representation. This usually requires communication. | ||
| 131 | */ | ||
| 132 | 244 | void apply(X& update, const Y& currentDefect) override | |
| 133 | { | ||
| 134 | using namespace Dune::Indices; | ||
| 135 | |||
| 136 |
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244 | if (mode_ == Mode::symmetric) |
| 137 | { | ||
| 138 | ✗ | update = applyRightBlock_(currentDefect); | |
| 139 | ✗ | update = applyDiagBlock_(update); | |
| 140 | ✗ | update = applyLeftBlock_(update); | |
| 141 | } | ||
| 142 |
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244 | else if (mode_ == Mode::triangular) |
| 143 | { | ||
| 144 | 244 | update = applyRightBlock_(currentDefect); | |
| 145 | 244 | update = applyDiagBlock_(update); | |
| 146 | } | ||
| 147 | else | ||
| 148 | ✗ | update = applyDiagBlock_(currentDefect); | |
| 149 | 244 | } | |
| 150 | |||
| 151 | /*! | ||
| 152 | * \brief Clean up. | ||
| 153 | */ | ||
| 154 | 2 | void post(X& update) override {} | |
| 155 | |||
| 156 | //! Category of the preconditioner (see SolverCategory::Category) | ||
| 157 | 2 | Dune::SolverCategory::Category category() const override | |
| 158 | { | ||
| 159 | 2 | return Dune::SolverCategory::sequential; | |
| 160 | } | ||
| 161 | |||
| 162 | private: | ||
| 163 | 244 | X applyRightBlock_(const Y& d) | |
| 164 | { | ||
| 165 | using namespace Dune::Indices; | ||
| 166 | |||
| 167 | // right bit of LDU decomposition | ||
| 168 | // applied to d | ||
| 169 | // | ||
| 170 | // | I 0 | | ||
| 171 | // | -C*inv(A) I | | ||
| 172 | // | ||
| 173 | |||
| 174 |
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488 | auto dTmp0 = d[_0]; |
| 175 |
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488 | auto vTmp = d; vTmp = 0.0; |
| 176 | |||
| 177 | // invert velocity block (apply to first block of d) | ||
| 178 |
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488 | applyPreconditionerForA_(vTmp[_0], dTmp0); |
| 179 | |||
| 180 | // then multiply with C | ||
| 181 | 1220 | matrix_[_1][_0].mv(vTmp[_0], vTmp[_1]); | |
| 182 | |||
| 183 | // and subtract from d | ||
| 184 |
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244 | auto v = d; |
| 185 |
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732 | v[_0] = vTmp[_0]; // already do A^-1 d of the diagonal block because we already computed it here |
| 186 | 244 | v[_1] -= vTmp[_1]; | |
| 187 | 244 | return v; | |
| 188 | } | ||
| 189 | |||
| 190 | 244 | X applyDiagBlock_(const Y& d) | |
| 191 | { | ||
| 192 | using namespace Dune::Indices; | ||
| 193 | |||
| 194 | // diagonal middle bit of LDU decomposition | ||
| 195 | 488 | auto dTmp = d; | |
| 196 |
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244 | auto v = d; v = 0.0; |
| 197 | |||
| 198 | // invert velocity block | ||
| 199 |
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244 | if (mode_ == Mode::diagonal) |
| 200 | ✗ | applyPreconditionerForA_(v[_0], dTmp[_0]); | |
| 201 | |||
| 202 | // reuse the already computed A^-1 d (see applyRightBlock_) | ||
| 203 | else | ||
| 204 |
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732 | v[_0] = dTmp[_0]; |
| 205 | |||
| 206 | // invert pressure block | ||
| 207 |
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732 | applyPreconditionerForP_(v[_1], dTmp[_1]); |
| 208 | |||
| 209 | 244 | return v; | |
| 210 | } | ||
| 211 | |||
| 212 | ✗ | X applyLeftBlock_(const Y& d) | |
| 213 | { | ||
| 214 | using namespace Dune::Indices; | ||
| 215 | |||
| 216 | // left bit of LDU decomposition | ||
| 217 | // applied to d | ||
| 218 | // | ||
| 219 | // | I -inv(A)*B | | ||
| 220 | // | 0 I | | ||
| 221 | // | ||
| 222 | |||
| 223 | ✗ | auto dTmp = d; | |
| 224 | ✗ | auto vTmp = d; vTmp = 0.0; | |
| 225 | |||
| 226 | // multiply with B | ||
| 227 | ✗ | matrix_[_0][_1].umv(dTmp[_1], vTmp[_0]); | |
| 228 | |||
| 229 | // invert velocity block (apply to first block of d) | ||
| 230 | ✗ | auto vTmp0 = vTmp[_0]; vTmp0 = 0.0; | |
| 231 | ✗ | applyPreconditionerForA_(vTmp0, vTmp[_0]); | |
| 232 | |||
| 233 | // and subtract from d | ||
| 234 | ✗ | auto v = d; | |
| 235 | ✗ | v[_0] -= vTmp0; | |
| 236 | |||
| 237 | ✗ | return v; | |
| 238 | } | ||
| 239 | |||
| 240 | 2 | void initPreconditioner_(const Dune::ParameterTree& params) | |
| 241 | { | ||
| 242 | using namespace Dune::Indices; | ||
| 243 | |||
| 244 |
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2 | if (getParamFromGroup<bool>(paramGroup_, "LinearSolver.DirectSolverForVelocity", false)) |
| 245 | { | ||
| 246 | #if HAVE_UMFPACK | ||
| 247 | ✗ | directSolver_ = std::make_shared<Dune::UMFPack<A>>(matrix_[_0][_0], verbosity_); | |
| 248 | using Wrap = Dune::InverseOperator2Preconditioner<Dune::InverseOperator<U, U>>; | ||
| 249 | ✗ | preconditionerForA_ = std::make_shared<Wrap>(*directSolver_); | |
| 250 | #else | ||
| 251 | DUNE_THROW(Dune::InvalidStateException, "Selected direct solver but UMFPack is not available."); | ||
| 252 | #endif | ||
| 253 | } | ||
| 254 | else | ||
| 255 | { | ||
| 256 | using VelLinearOperator = Dune::MatrixAdapter<A, U, U>; | ||
| 257 |
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8 | auto lopV = std::make_shared<VelLinearOperator>(matrix_[_0][_0]); |
| 258 |
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2 | preconditionerForA_ = std::make_shared< |
| 259 | Dune::Amg::AMG<VelLinearOperator, U, Dumux::ParMTSSOR<A,U,U>> | ||
| 260 | >(lopV, params); | ||
| 261 | } | ||
| 262 | |||
| 263 | using PressJacobi = Dumux::ParMTJac<P, V, V>; | ||
| 264 |
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2 | preconditionerForP_ = std::make_shared<PressJacobi>(pmatrix_, 1, 1.0); |
| 265 | 2 | } | |
| 266 | |||
| 267 | template<class Sol, class Rhs> | ||
| 268 | 244 | void applyPreconditionerForA_(Sol& sol, Rhs& rhs) const | |
| 269 | { | ||
| 270 | 488 | preconditionerForA_->pre(sol, rhs); | |
| 271 | 488 | preconditionerForA_->apply(sol, rhs); | |
| 272 | 488 | preconditionerForA_->post(sol); | |
| 273 | 244 | } | |
| 274 | |||
| 275 | template<class Sol, class Rhs> | ||
| 276 | 244 | void applyPreconditionerForP_(Sol& sol, Rhs& rhs) const | |
| 277 | { | ||
| 278 | 488 | preconditionerForP_->pre(sol, rhs); | |
| 279 | 488 | preconditionerForP_->apply(sol, rhs); | |
| 280 | 488 | preconditionerForP_->post(sol); | |
| 281 | 244 | } | |
| 282 | |||
| 283 | //! \brief The matrix we operate on. | ||
| 284 | const M& matrix_; | ||
| 285 | //! \brief The matrix we operate on. | ||
| 286 | const P& pmatrix_; | ||
| 287 | //! \brief The verbosity level | ||
| 288 | const int verbosity_; | ||
| 289 | |||
| 290 | std::shared_ptr<Dune::Preconditioner<U, U>> preconditionerForA_; | ||
| 291 | std::shared_ptr<Dune::Preconditioner<V, V>> preconditionerForP_; | ||
| 292 | std::shared_ptr<Dune::InverseOperator<U, U>> directSolver_; | ||
| 293 | |||
| 294 | const std::string paramGroup_; | ||
| 295 | Mode mode_; | ||
| 296 | }; | ||
| 297 | |||
| 298 | } // end namespace Detail | ||
| 299 | |||
| 300 | namespace Dumux { | ||
| 301 | |||
| 302 | /*! | ||
| 303 | * \ingroup Linear | ||
| 304 | * \brief Preconditioned iterative solver for the incompressible Stokes problem | ||
| 305 | * \note Uses StokesPreconditioner as preconditioner (tailored to the incompressible Stokes problem) | ||
| 306 | * \note No MPI parallelization implemented, some shared-memory parallelism is enabled | ||
| 307 | */ | ||
| 308 | template<class Matrix, class Vector, class VelocityGG, class PressureGG> | ||
| 309 | class StokesSolver | ||
| 310 | : public LinearSolver | ||
| 311 | { | ||
| 312 | using Preconditioner = Detail::StokesPreconditioner<Matrix, Vector, Vector>; | ||
| 313 | public: | ||
| 314 | /*! | ||
| 315 | * \brief Constructor | ||
| 316 | * \param vGridGeometry grid geometry of the velocity discretization | ||
| 317 | * \param pGridGeometry grid geometry of the pressure discretization | ||
| 318 | * \param dirichletDofs a vector (same size and shape as right hand side) where the dirichlet dofs are marked with 1.0 | ||
| 319 | * and all other entries are 0.0. | ||
| 320 | * \param paramGroup group prefix when looking up keys in the parameter tree | ||
| 321 | */ | ||
| 322 | 2 | StokesSolver(std::shared_ptr<const VelocityGG> vGridGeometry, | |
| 323 | std::shared_ptr<const PressureGG> pGridGeometry, | ||
| 324 | const Vector& dirichletDofs, | ||
| 325 | const std::string& paramGroup = "") | ||
| 326 | : LinearSolver(paramGroup) | ||
| 327 | 2 | , vGridGeometry_(std::move(vGridGeometry)) | |
| 328 | 2 | , pGridGeometry_(std::move(pGridGeometry)) | |
| 329 |
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2 | , dirichletDofs_(dirichletDofs) |
| 330 | { | ||
| 331 |
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4 | params_ = LinearSolverParameters<LinearSolverTraits<VelocityGG>>::createParameterTree(this->paramGroup()); |
| 332 |
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4 | density_ = getParamFromGroup<double>(this->paramGroup(), "Component.LiquidDensity"); |
| 333 |
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4 | viscosity_ = getParamFromGroup<double>(this->paramGroup(), "Component.LiquidDynamicViscosity"); |
| 334 |
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4 | weight_ = getParamFromGroup<double>(this->paramGroup(), "LinearSolver.Preconditioner.MassMatrixWeight", 1.0); |
| 335 |
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4 | solverType_ = getParamFromGroup<std::string>(this->paramGroup(), "LinearSolver.Type", "gmres"); |
| 336 |
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2 | scalarProduct_ = std::make_shared<Dune::ScalarProduct<Vector>>(); |
| 337 | 2 | } | |
| 338 | |||
| 339 | 2 | bool solve(const Matrix& A, Vector& x, const Vector& b) | |
| 340 | { | ||
| 341 | 2 | auto bTmp = b; | |
| 342 |
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4 | auto ATmp = A; |
| 343 | |||
| 344 |
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4 | return applyIterativeSolver_(ATmp, x, bTmp); |
| 345 | } | ||
| 346 | |||
| 347 | Scalar norm(const Vector& b) const | ||
| 348 | { | ||
| 349 |
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8 | return scalarProduct_->norm(b); |
| 350 | } | ||
| 351 | |||
| 352 | std::string name() const | ||
| 353 | { | ||
| 354 | return "Block-preconditioned Stokes solver"; | ||
| 355 | } | ||
| 356 | |||
| 357 | const Dune::InverseOperatorResult& result() const | ||
| 358 | { | ||
| 359 | return result_; | ||
| 360 | } | ||
| 361 | |||
| 362 | private: | ||
| 363 | 2 | bool applyIterativeSolver_(Matrix& A, Vector& x, Vector& b) | |
| 364 | { | ||
| 365 | // make Dirichlet boundary conditions symmetric | ||
| 366 |
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4 | if (getParamFromGroup<bool>(this->paramGroup(), "LinearSolver.SymmetrizeDirichlet", true)) |
| 367 | 2 | symmetrizeConstraints(A, b, dirichletDofs_); | |
| 368 | |||
| 369 | // make Matrix symmetric on the block-scale | ||
| 370 | using namespace Dune::Indices; | ||
| 371 | 4 | A[_1] *= -1.0/density_; | |
| 372 | 4 | b[_1] *= -1.0/density_; | |
| 373 | |||
| 374 |
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2 | auto op = std::make_shared<Dumux::ParallelMultiTypeMatrixAdapter<Matrix, Vector, Vector>>(A); |
| 375 |
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4 | auto pop = makePressureLinearOperator_<typename Preconditioner::PressureLinearOperator>(); |
| 376 |
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6 | auto preconditioner = std::make_shared<Preconditioner>(op, pop, params_.sub("preconditioner")); |
| 377 |
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6 | params_["verbose"] = pGridGeometry_->gridView().comm().rank() == 0 ? params_["verbose"] : "0"; |
| 378 | |||
| 379 | // defaults to restarted GMRes | ||
| 380 |
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2 | std::unique_ptr<Dune::InverseOperator<Vector, Vector>> solver; |
| 381 |
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2 | if (solverType_ == "minres") |
| 382 | ✗ | solver = std::make_unique<Dune::MINRESSolver<Vector>>(op, scalarProduct_, preconditioner, params_); | |
| 383 |
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2 | else if (solverType_ == "bicgstab") |
| 384 | ✗ | solver = std::make_unique<Dune::BiCGSTABSolver<Vector>>(op, scalarProduct_, preconditioner, params_); | |
| 385 |
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2 | else if (solverType_ == "gmres") |
| 386 |
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2 | solver = std::make_unique<Dune::RestartedGMResSolver<Vector>>(op, scalarProduct_, preconditioner, params_); |
| 387 | else | ||
| 388 | ✗ | DUNE_THROW(Dune::NotImplemented, "Solver choice " << solverType_ << " is not implemented"); | |
| 389 | |||
| 390 |
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4 | solver->apply(x, b, result_); |
| 391 | |||
| 392 | 4 | return result_.converged; | |
| 393 | } | ||
| 394 | |||
| 395 | template<class LinearOperator> | ||
| 396 | 2 | std::shared_ptr<LinearOperator> makePressureLinearOperator_() | |
| 397 | { | ||
| 398 | using M = typename LinearOperator::matrix_type; | ||
| 399 |
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2 | auto massMatrix = createMassMatrix_<M>(); |
| 400 |
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4 | return std::make_shared<LinearOperator>(massMatrix); |
| 401 | } | ||
| 402 | |||
| 403 | template<class M> | ||
| 404 | 2 | std::shared_ptr<M> createMassMatrix_() | |
| 405 | { | ||
| 406 | 2 | auto massMatrix = std::make_shared<M>(); | |
| 407 |
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4 | massMatrix->setBuildMode(M::random); |
| 408 |
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4 | const auto numDofs = pGridGeometry_->numDofs(); |
| 409 | |||
| 410 |
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4 | Dune::MatrixIndexSet pattern; |
| 411 |
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2 | pattern.resize(numDofs, numDofs); |
| 412 |
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43765 | for (unsigned int globalI = 0; globalI < numDofs; ++globalI) |
| 413 |
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43763 | pattern.add(globalI, globalI); |
| 414 |
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4 | pattern.exportIdx(*massMatrix); |
| 415 | |||
| 416 |
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4 | const auto& gv = pGridGeometry_->gridView(); |
| 417 |
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4 | auto fvGeometry = localView(*pGridGeometry_); |
| 418 |
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115794 | for (const auto& element : elements(gv)) |
| 419 | { | ||
| 420 |
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57896 | fvGeometry.bindElement(element); |
| 421 |
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231584 | for (const auto& scv : scvs(fvGeometry)) |
| 422 | { | ||
| 423 | using Extrusion = Extrusion_t<PressureGG>; | ||
| 424 |
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115792 | const auto dofIndex = scv.dofIndex(); |
| 425 |
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115792 | if (element.partitionType() == Dune::GhostEntity) // do not modify ghosts |
| 426 | ✗ | (*massMatrix)[dofIndex][dofIndex] = 1.0; | |
| 427 | else | ||
| 428 |
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463168 | (*massMatrix)[dofIndex][dofIndex] += weight_*Extrusion::volume(fvGeometry, scv)/(2.0*viscosity_); |
| 429 | } | ||
| 430 | } | ||
| 431 | |||
| 432 | 2 | return massMatrix; | |
| 433 | } | ||
| 434 | |||
| 435 | double density_, viscosity_, weight_; | ||
| 436 | Dune::InverseOperatorResult result_; | ||
| 437 | Dune::ParameterTree params_; | ||
| 438 | std::shared_ptr<const VelocityGG> vGridGeometry_; | ||
| 439 | std::shared_ptr<const PressureGG> pGridGeometry_; | ||
| 440 | const Vector& dirichletDofs_; | ||
| 441 | std::string solverType_; | ||
| 442 | |||
| 443 | std::shared_ptr<Dune::ScalarProduct<Vector>> scalarProduct_; | ||
| 444 | }; | ||
| 445 | |||
| 446 | } // end namespace Dumux | ||
| 447 | |||
| 448 | #endif | ||
| 449 |