iterativeblockjacobipreconditioner.hh

// -*- tab-width: 2; indent-tabs-mode: nil -*-
// vi: set et ts=2 sw=2 sts=2:
#ifndef DUNE_PDELAB_BACKEND_ISTL_MATRIXFREE_ITERATIVEBLOCKJACOBIPRECONDITIONER_HH
#define DUNE_PDELAB_BACKEND_ISTL_MATRIXFREE_ITERATIVEBLOCKJACOBIPRECONDITIONER_HH
 
#include<dune/grid/common/scsgmapper.hh>
#include<dune/istl/solvers.hh>
#include<dune/istl/operators.hh>
 
#include <dune/pdelab/localoperator/pointdiagonalwrapper.hh>
#include <dune/pdelab/localoperator/blockdiagonalwrapper.hh>
 
#include<dune/pdelab/backend/istl/matrixfree/solverstatistics.hh>
#include<dune/pdelab/backend/istl/matrixfree/assembledblockjacobipreconditioner.hh>
 
namespace Dune {
  namespace PDELab {
 
    namespace impl{
 
      /* \brief Point Jacobi preconditioner for local diagonal block systems
       *
       * This class will do the Jacobi preconditioning for a diagonal
       * block. The values of the inverse of the diagonal need to be provided
       * during construction.
       */
      template<typename X>
      class LocalPointJacobiPreconditioner : public Dune::Preconditioner<X,X>
      {
      public :
        typedef X domain_type;
        typedef X range_type;
        typedef typename X::BaseContainer InvDiagonal;
        typedef typename X::value_type value_type;
 
        Dune::SolverCategory::Category category() const override
        {
          return Dune::SolverCategory::sequential;
        }
 
        LocalPointJacobiPreconditioner(const InvDiagonal& invDiagonal,
                                       const value_type diagonalWeight,
                                       const bool precondition=true)
          : _precondition(precondition)
          , _invDiagonal(invDiagonal)
          , _diagonalWeight(diagonalWeight)
        {}
 
        void pre (domain_type& x, range_type& b) override {}
 
        void apply (domain_type& v, const range_type& d) override
        {
          if(_precondition){
            std::transform(d.data(),
                           d.data()+d.size(),
                           _invDiagonal.begin(),
                           v.data(),
                           [this](const value_type& a,
                                  const value_type& b){
                             return _diagonalWeight*a*b;
                           });
          }
          else{
            std::copy(d.data(),d.data()+d.size(),v.data());
          }
        }
 
        void post (domain_type& x) override {}
 
      private :
        const bool _precondition;
        const InvDiagonal& _invDiagonal;
        const value_type _diagonalWeight;
      };
 
 
      template<typename BlockDiagonalLocalOperator, typename W, typename XView, typename EG, typename LFSU, typename LFSV>
      struct BlockDiagonalOperator
        : public Dune::LinearOperator<W,W>
      {
        using Base = Dune::LinearOperator<W,W>;
        using field_type = typename Base::field_type;
        using weight_type = typename W::WeightedAccumulationView::weight_type;
        static constexpr bool isLinear = BlockDiagonalLocalOperator::isLinear;
 
        Dune::SolverCategory::Category category() const override
        {
          return Dune::SolverCategory::sequential;
        }
 
        BlockDiagonalOperator(const BlockDiagonalLocalOperator& blockDiagonalLocalOperator,
                              const EG& eg,
                              const LFSU& lfsu,
                              const LFSV& lfsv)
          : _blockDiagonalLocalOperator(blockDiagonalLocalOperator)
          , _eg(eg)
          , _lfsu(lfsu)
          , _lfsv(lfsv)
          , _tmp(lfsu.size(),0.0)
          , _u(nullptr)
        {}
 
        void apply(const W& z, W& y) const override
        {
          y = 0.0;
          typename W::WeightedAccumulationView y_view(y, _weight);
          if (isLinear)
            applyLocalDiagonalBlock(_blockDiagonalLocalOperator, _eg, _lfsu, z, z, _lfsv, y_view);
          else
            applyLocalDiagonalBlock(_blockDiagonalLocalOperator, _eg, _lfsu, *_u, z, _lfsv, y_view);
        }
 
        void applyscaleadd(field_type alpha, const W& z, W& y) const override
        {
          apply(z, _tmp);
          y.axpy(alpha, _tmp);
        }
 
        void setLinearizationPoint(const XView& u)
        {
          _u = &u;
        }
 
        void setWeight(const weight_type& weight)
        {
          _weight = weight;
        }
 
      private :
        const BlockDiagonalLocalOperator& _blockDiagonalLocalOperator;
        const EG& _eg;
        const LFSU& _lfsu;
        const LFSV& _lfsv;
        mutable W _tmp;
        const XView* _u;
        weight_type _weight;
      };
 
      template<typename C>
      class WeightedPointDiagonalAccumulationView
      {
      public :
        using Container = C;
 
        using value_type = typename Container::value_type;
        using size_type = typename Container::size_type;
        using weight_type = value_type;
 
        const weight_type& weight()
        {
          return _weight;
        }
 
        auto data()
        {
          return _container.data();
        }
 
        auto data() const
        {
          return _container.data();
        }
 
        template<typename LFSV>
        void accumulate(const LFSV& lfsv, size_type i, value_type value)
        {
          _container.data()[lfsv.localIndex(i)] += _weight * value;
        }
 
        WeightedPointDiagonalAccumulationView(Container& container, weight_type weight)
          : _container(container)
          , _weight(weight)
        {}
 
      private :
        Container& _container;
        weight_type _weight;
      };
 
    } // namespace impl
 
 
    struct BlockSolverOptions
    {
      BlockSolverOptions(const double resreduction=1e-5,
                         const size_t maxiter=100,
                         const bool precondition=true,
                         const double weight=1.0,
                         const int verbose=0)
        : _resreduction(resreduction)
        , _maxiter(maxiter)
        , _precondition(precondition)
        , _weight(weight)
        , _verbose(verbose)
      {}
      double _resreduction;
      size_t _maxiter;
      bool _precondition;
      double _weight;
      int _verbose;
    }; // end struct BlockSolverOptions
 
 
    template<typename BlockDiagonalLocalOperator,
             typename PointDiagonalLocalOperator,
             typename GridFunctionSpace,
             typename DomainField,
             template<typename> class IterativeSolver>
    class IterativeBlockJacobiPreconditionerLocalOperator
      : public Dune::PDELab::FullVolumePattern
      , public Dune::PDELab::LocalOperatorDefaultFlags
    {
      // Extract some types
      using GridView = typename GridFunctionSpace::Traits::GridViewType;
      using Grid = typename GridView::Traits::Grid;
      using EntityType = typename Grid::template Codim<0>::Entity;
      using value_type = DomainField;
      using LocalVector = Dune::PDELab::LocalVector<value_type>;
      using InvDiagonal = typename LocalVector::BaseContainer;
 
    public:
      // Since this class implements something like D^{-1}v for a diagonal
      // block matrix D we will only have volume methods. The underlying local
      // operator that describes the block diagonal might of course have
      // skeleton or boundary parts.
      static constexpr bool doPatternVolume = true;
      static constexpr bool doAlphaVolume = true;
      static constexpr bool isLinear = BlockDiagonalLocalOperator::isLinear;
 
      IterativeBlockJacobiPreconditionerLocalOperator(const BlockDiagonalLocalOperator& blockDiagonalLocalOperator,
                                                      const PointDiagonalLocalOperator& pointDiagonalLocalOperator,
                                                      const GridFunctionSpace& gridFunctionSpace,
                                                      SolverStatistics<int>& solverStatiscits,
                                                      BlockSolverOptions solveroptions,
                                                      const bool verbose=0)
        : _blockDiagonalLocalOperator(blockDiagonalLocalOperator)
        , _pointDiagonalLocalOperator(pointDiagonalLocalOperator)
        , _gridFunctionSpace(gridFunctionSpace)
        , _solverStatistics(solverStatiscits)
        , _mapper(gridFunctionSpace.gridView())
        , _invDiagonalCache(_mapper.size())
        , _solveroptions(solveroptions)
        , _verbose(verbose)
        , _requireSetup(true)
      {}
 
      // Before we can call the jacobian_apply methods we need to assemble the
      // point diagonal of the diagonal block. This will be used as a preconditioner
      // for the iterative matrix free solver on the diagonal block.
      bool requireSetup()
      {
        return _requireSetup;
      }
      void setRequireSetup(bool v)
      {
        _requireSetup = v;
      }
 
      template<typename EG, typename LFSU, typename X, typename LFSV, typename Y>
      void alpha_volume(const EG& eg, const LFSU& lfsu, const X& x, const LFSV& lfsv, Y& y) const
      {
        const std::size_t size = lfsu.size();
        assert(lfsv.size() == size);
 
        // Assemble point diagonal
        std::size_t cache_idx = _mapper.index(eg.entity());
        _invDiagonalCache[cache_idx].resize(lfsu.size());
        using TmpView = impl::WeightedPointDiagonalAccumulationView<InvDiagonal>;
        TmpView view(_invDiagonalCache[cache_idx], y.weight());
        assembleLocalPointDiagonal(_pointDiagonalLocalOperator, eg, lfsu, x, lfsv, view);
 
        // Invert this and store it (will later be used as a preconditioner)
        for(auto& val : _invDiagonalCache[cache_idx]){
          val = 1. / val;
        }
      }
 
 
      template<typename EG, typename LFSU, typename Z, typename LFSV, typename Y>
      void jacobian_apply_volume(const EG& eg, const LFSU& lfsu, const Z& z, const LFSV& lfsv, Y& y) const
      {
        assert(not _requireSetup);
 
        // Get correct point diagonal from the cache
        std::size_t cache_idx = _mapper.index(eg.entity());
        const auto& invDiagonal = _invDiagonalCache[cache_idx];
 
        // Create iterative solver with point Jacobi preconditioner for solving
        // the local block diagonal system
        impl::LocalPointJacobiPreconditioner<LocalVector> pointJacobi(invDiagonal,
                                                                      _solveroptions._weight,
                                                                      _solveroptions._precondition);
        impl::BlockDiagonalOperator<BlockDiagonalLocalOperator, LocalVector, Z, EG, LFSU, LFSV>
          op(_blockDiagonalLocalOperator, eg, lfsu, lfsv);
        op.setWeight(y.weight());
        IterativeSolver<LocalVector> solver(op,
                                            pointJacobi,
                                            _solveroptions._resreduction,
                                            _solveroptions._maxiter,
                                            _solveroptions._verbose);
        Dune::InverseOperatorResult stat;
 
        // Set up local right hand side
        LocalVector z_tmp(lfsu.size(), 0.0);
        std::copy(z.data(), z.data()+z.size(), z_tmp.data());
 
        // Solve local blocks iteratively
        LocalVector y_tmp(lfsv.size(), 0.0);
        solver.apply(y_tmp, z_tmp, stat);
        _solverStatistics.append(stat.iterations);
        std::transform(y.data(),
                       y.data()+y.size(),
                       y_tmp.data(),
                       y.data(),
                       std::plus<value_type>{});
      } // end jacobian_apply_volume
 
 
      template<typename EG, typename LFSU, typename X, typename Z, typename LFSV, typename Y>
      void jacobian_apply_volume(const EG& eg, const LFSU& lfsu, const X& x, const Z& z, const LFSV& lfsv, Y& y) const
      {
        assert(not _requireSetup);
 
        // Get correct point diagonal from the cache
        std::size_t cache_idx = _mapper.index(eg.entity());
        const auto& invDiagonal = _invDiagonalCache[cache_idx];
 
        // Create iterative solver with point Jacobi preconditioner for solving
        // the local block diagonal system
        impl::LocalPointJacobiPreconditioner<LocalVector> pointJacobi(invDiagonal,
                                                                      _solveroptions._weight,
                                                                      _solveroptions._precondition);
        impl::BlockDiagonalOperator<BlockDiagonalLocalOperator, LocalVector, X, EG, LFSU, LFSV>
          op(_blockDiagonalLocalOperator, eg, lfsu, lfsv);
        op.setLinearizationPoint(x);
        op.setWeight(y.weight());
        IterativeSolver<LocalVector> solver(op,
                                            pointJacobi,
                                            _solveroptions._resreduction,
                                            _solveroptions._maxiter,
                                            _solveroptions._verbose);
        Dune::InverseOperatorResult stat;
 
        // Set up local right hand side
        LocalVector z_tmp(lfsu.size(), 0.0);
        std::copy(z.data(), z.data()+z.size(), z_tmp.data());
 
        // Solve local blocks iteratively
        LocalVector y_tmp(lfsv.size(), 0.0);
        solver.apply(y_tmp, z_tmp, stat);
        _solverStatistics.append(stat.iterations);
        std::transform(y.data(),
                       y.data()+y.size(),
                       y_tmp.data(),
                       y.data(),
                       std::plus<value_type>{});
      } // end jacobian_apply_volume
 
    private :
      BlockDiagonalLocalOperator _blockDiagonalLocalOperator;
      PointDiagonalLocalOperator _pointDiagonalLocalOperator;
      const GridFunctionSpace& _gridFunctionSpace;
      SolverStatistics<int>& _solverStatistics;
      typename Dune::SingleCodimSingleGeomTypeMapper<GridView, 0> _mapper;
      mutable std::vector<InvDiagonal> _invDiagonalCache;
      mutable BlockSolverOptions _solveroptions;
      const int _verbose;
      bool _requireSetup;
    }; // end class IterativeBlockJacobiPreconditionerLocalOperator
 
  } // namespace PDELab
} // namespace Dune
#endif