parallelhelpers.hh

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// -*- mode: C++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
// vi: set et ts=4 sw=4 sts=4:
//
// SPDX-FileCopyrightText: Copyright © DuMux Project contributors, see AUTHORS.md in root folder
// SPDX-License-Identifier: GPL-3.0-or-later
//
#ifndef DUMUX_LINEAR_PARALLELHELPERS_HH
#define DUMUX_LINEAR_PARALLELHELPERS_HH
 
#include <dune/common/exceptions.hh>
#include <dune/geometry/dimension.hh>
#include <dune/grid/common/datahandleif.hh>
#include <dune/grid/common/partitionset.hh>
#include <dune/istl/owneroverlapcopy.hh>
#include <dune/istl/paamg/pinfo.hh>
#include <dune/istl/bvector.hh>
#include <dune/istl/multitypeblockvector.hh>
#include <dumux/parallel/vectorcommdatahandle.hh>
#include <dumux/common/gridcapabilities.hh>
 
namespace Dumux::Detail {
 
template<class LinearSolverTraits, bool canCommunicate = false>
class ParallelISTLHelperImpl {};
 
template<class LinearSolverTraits>
class ParallelISTLHelperImpl<LinearSolverTraits, true>
{
    using GridView = typename LinearSolverTraits::GridView;
    using DofMapper = typename LinearSolverTraits::DofMapper;
    static constexpr int dofCodim = LinearSolverTraits::dofCodim;
 
    // TODO: this is some large number (replace by limits?)
    static constexpr std::size_t ghostMarker_ = 1<<24;
 
    class BaseGatherScatter
    {
    public:
        BaseGatherScatter(const DofMapper& mapper)
        : mapper_(mapper) {}
 
        template<class EntityType>
        int index(const EntityType& e) const
        { return mapper_.index(e); }
 
        bool contains(int dim, int codim) const
        { return dofCodim == codim; }
 
        bool fixedSize(int dim, int codim) const
        { return true; }
 
        template<class EntityType>
        std::size_t size(EntityType& e) const
        { return 1; }
 
        template<class EntityType>
        bool isNeitherInteriorNorBorderEntity(EntityType& e) const
        { return e.partitionType() != Dune::InteriorEntity && e.partitionType() != Dune::BorderEntity; }
 
    private:
        const DofMapper& mapper_;
    };
 
    class GhostGatherScatter
    : public BaseGatherScatter
    , public Dune::CommDataHandleIF<GhostGatherScatter, std::size_t>
    {
    public:
        using DataType = std::size_t;
        using BaseGatherScatter::contains;
        using BaseGatherScatter::fixedSize;
        using BaseGatherScatter::size;
 
        GhostGatherScatter(std::vector<std::size_t>& ranks, const DofMapper& mapper)
        : BaseGatherScatter(mapper)
        , ranks_(ranks)
        {}
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, const EntityType& e) const
        {
            auto& data = ranks_[this->index(e)];
            if (this->isNeitherInteriorNorBorderEntity(e))
                data = ghostMarker_;
            buff.write(data);
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType& e, std::size_t n)
        {
            std::size_t x;
            buff.read(x);
            auto& data = ranks_[this->index(e)];
            if (this->isNeitherInteriorNorBorderEntity(e))
                data = ghostMarker_;
        }
    private:
        std::vector<std::size_t>& ranks_;
    };
 
    class InteriorBorderGatherScatter
    : public BaseGatherScatter
    , public Dune::CommDataHandleIF<InteriorBorderGatherScatter, std::size_t>
    {
    public:
        using DataType = std::size_t;
        using BaseGatherScatter::contains;
        using BaseGatherScatter::fixedSize;
        using BaseGatherScatter::size;
 
        InteriorBorderGatherScatter(std::vector<std::size_t>& ranks, const DofMapper& mapper)
        : BaseGatherScatter(mapper)
        , ranks_(ranks)
        {}
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, const EntityType& e) const
        {
            auto& data = ranks_[this->index(e)];
            if (this->isNeitherInteriorNorBorderEntity(e))
                data = ghostMarker_;
            buff.write(data);
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType& e, std::size_t n)
        {
            std::size_t x;
            buff.read(x);
            auto& data = ranks_[this->index(e)];
 
            // we leave ghost unchanged
            // for other dofs, the process with the lowest rank
            // is assigned to be the (unique) owner
            using std::min;
            data = this->isNeitherInteriorNorBorderEntity(e) ? x : min(data, x);
        }
    private:
        std::vector<std::size_t>& ranks_;
    };
 
    struct NeighbourGatherScatter
    : public BaseGatherScatter
    , public Dune::CommDataHandleIF<NeighbourGatherScatter, int>
    {
        using DataType = int;
        using BaseGatherScatter::contains;
        using BaseGatherScatter::fixedSize;
        using BaseGatherScatter::size;
 
        NeighbourGatherScatter(const DofMapper& mapper, int rank, std::set<int>& neighbours)
        : BaseGatherScatter(mapper)
        , rank_(rank)
        , neighbours_(neighbours)
        {}
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, const EntityType& e) const
        {
            buff.write(rank_);
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType& e, std::size_t n)
        {
            int x;
            buff.read(x);
            neighbours_.insert(x);
        }
    private:
        int rank_;
        std::set<int>& neighbours_;
    };
 
 
    struct SharedGatherScatter
    : public BaseGatherScatter
    , public Dune::CommDataHandleIF<SharedGatherScatter, int>
    {
        using DataType = int;
        using BaseGatherScatter::contains;
        using BaseGatherScatter::fixedSize;
        using BaseGatherScatter::size;
 
        SharedGatherScatter(std::vector<int>& shared, const DofMapper& mapper)
        : BaseGatherScatter(mapper)
        , shared_(shared)
        {}
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, EntityType& e) const
        {
            int data = true;
            buff.write(data);
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType &e, std::size_t n)
        {
            int x;
            buff.read(x);
            auto& data = shared_[this->index(e)];
            data = data || x;
        }
    private:
        std::vector<int>& shared_;
    };
 
    template<typename GlobalIndex>
    struct GlobalIndexGatherScatter
    : public BaseGatherScatter
    , public Dune::CommDataHandleIF<GlobalIndexGatherScatter<GlobalIndex>, GlobalIndex>
    {
        using DataType = GlobalIndex;
        using BaseGatherScatter::contains;
        using BaseGatherScatter::fixedSize;
        using BaseGatherScatter::size;
 
        GlobalIndexGatherScatter(std::vector<GlobalIndex>& globalIndices, const DofMapper& mapper)
        : BaseGatherScatter(mapper)
        , globalIndices_(globalIndices)
        {}
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, const EntityType& e) const
        {
            buff.write(globalIndices_[this->index(e)]);
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType& e, std::size_t n)
        {
            DataType x;
            buff.read(x);
            using std::min;
            DataType& data = globalIndices_[this->index(e)];
            data = min(data, x);
        }
    private:
        std::vector<GlobalIndex>& globalIndices_;
    };
 
public:
 
    ParallelISTLHelperImpl(const GridView& gridView, const DofMapper& mapper)
    : gridView_(gridView), mapper_(mapper)
    {
        if constexpr (Dune::Capabilities::canCommunicate<typename GridView::Traits::Grid, dofCodim>::v)
            initGhostsAndOwners_();
        else
            DUNE_THROW(Dune::InvalidStateException,
                "Cannot initialize parallel helper for a grid that cannot communicate codim-" << dofCodim << "-entities."
            );
    }
 
    bool isGhost(std::size_t i) const
    { return isGhost_[i] == ghostMarker_; }
 
    bool isOwned(std::size_t i) const
    { return isOwned_[i] == 1; }
 
    template<class Comm>
    void createParallelIndexSet(Comm& comm) const
    {
        if constexpr (Dune::Capabilities::canCommunicate<typename GridView::Traits::Grid, dofCodim>::v)
        {
            if (gridView_.comm().size() <= 1)
            {
                comm.remoteIndices().template rebuild<false>();
                return;
            }
 
            // First find out which dofs we share with other processors
            std::vector<int> isShared(mapper_.size(), false);
            SharedGatherScatter sgs(isShared, mapper_);
            gridView_.communicate(sgs, Dune::All_All_Interface, Dune::ForwardCommunication);
 
            // Count shared dofs that we own
            using GlobalIndex = typename Comm::ParallelIndexSet::GlobalIndex;
            GlobalIndex count = 0;
            for (std::size_t i = 0; i < isShared.size(); ++i)
                if (isShared[i] && isOwned_[i] == 1)
                    ++count;
 
            std::vector<GlobalIndex> counts(gridView_.comm().size());
            gridView_.comm().allgather(&count, 1, counts.data());
 
            // Compute start index start_p = \sum_{i=0}^{i<p} counts_i
            const int rank = gridView_.comm().rank();
            auto start = std::accumulate(counts.begin(), counts.begin() + rank, GlobalIndex(0));
 
            // starting from start (offset), number global indices owned by this process consecutively
            std::vector<GlobalIndex> globalIndices(mapper_.size(), std::numeric_limits<GlobalIndex>::max());
            for (std::size_t i = 0; i < globalIndices.size(); ++i)
            {
                if (isOwned_[i] == 1 && isShared[i])
                {
                    globalIndices[i] = start;
                    ++start;
                }
            }
 
            // publish global indices for the shared DOFS to other processors.
            GlobalIndexGatherScatter<GlobalIndex> gigs(globalIndices, mapper_);
            gridView_.communicate(gigs, Dune::All_All_Interface, Dune::ForwardCommunication);
 
            // put the information into the parallel index set
            resizeAndFillIndexSet_(comm, globalIndices);
 
            // Compute neighbours using communication
            std::set<int> neighbours;
            NeighbourGatherScatter ngs(mapper_, gridView_.comm().rank(), neighbours);
            gridView_.communicate(ngs, Dune::All_All_Interface, Dune::ForwardCommunication);
            comm.remoteIndices().setNeighbours(neighbours);
 
            comm.remoteIndices().template rebuild<false>();
        }
        else
            DUNE_THROW(Dune::InvalidStateException,
                "Cannot build parallel index set for a grid that cannot communicate codim-" << dofCodim << "-entities."
            );
    }
 
    const DofMapper& dofMapper() const
    { return mapper_; }
 
    const GridView& gridView() const
    { return gridView_; }
 
private:
    void initGhostsAndOwners_()
    {
        const auto rank = gridView_.comm().rank();
        isOwned_.assign(mapper_.size(), rank);
 
        // find out about ghosts
        GhostGatherScatter ggs(isOwned_, mapper_);
 
        if (gridView_.comm().size() > 1)
            gridView_.communicate(ggs, Dune::InteriorBorder_All_Interface, Dune::ForwardCommunication);
 
        // isGhost_ contains rank when the dof is not on a ghost entity (interior or border)
        // and ghostMarker_ when the dof is on a ghost
        isGhost_ = isOwned_;
 
        // partition interior/border uniquely
        // after the communication each dof is assigned to one unique owner process rank
        InteriorBorderGatherScatter dh(isOwned_, mapper_);
 
        if (gridView_.comm().size() > 1)
            gridView_.communicate(dh, Dune::InteriorBorder_InteriorBorder_Interface, Dune::ForwardCommunication);
 
        // convert vector into mask vector
        for (auto& v : isOwned_)
            v = (v == rank) ? 1 : 0;
    }
 
    template<class Comm, class GlobalIndices>
    void resizeAndFillIndexSet_(Comm& comm, const GlobalIndices& globalIndices) const
    {
        comm.indexSet().beginResize();
 
        // add triplets characterizing each dof in the parallel index set
        // (globalIndex, (localIndex, attribute)) where attribute is owner, overlap or copy
        for (std::size_t localIndex = 0; localIndex < globalIndices.size(); ++localIndex)
        {
            const auto globalIndex = globalIndices[localIndex];
            if (globalIndex != std::numeric_limits<typename GlobalIndices::value_type>::max())
            {
                const bool isOwned = isOwned_[localIndex] > 0;
                const auto attr = getAttribute_(comm, isOwned, isGhost(localIndex));
                using LocalIndex = typename Comm::ParallelIndexSet::LocalIndex;
                comm.indexSet().add(globalIndex, LocalIndex{localIndex, attr});
            }
        }
 
        comm.indexSet().endResize();
    }
 
    template<class Comm>
    Dune::OwnerOverlapCopyAttributeSet::AttributeSet
    getAttribute_(const Comm& comm, const bool isOwned, const bool isGhost) const
    {
        if (isOwned) // this process owns the dof (uniquely)
            return Dune::OwnerOverlapCopyAttributeSet::owner;
        else if (isGhost && (comm.category() == Dune::SolverCategory::nonoverlapping) )
            return Dune::OwnerOverlapCopyAttributeSet::overlap;
        else
            return Dune::OwnerOverlapCopyAttributeSet::copy;
    }
 
    const GridView gridView_; 
    const DofMapper& mapper_; 
    std::vector<std::size_t> isOwned_;
    std::vector<std::size_t> isGhost_;
 
};
 
} // end namespace Dumux::Detail
 
namespace Dumux {
 
template<class LinearSolverTraits>
using ParallelISTLHelper =
    Detail::ParallelISTLHelperImpl<
        LinearSolverTraits, LinearSolverTraits::canCommunicate
    >;
 
 
template<class GridView, class DofMapper, int dofCodim>
class ParallelVectorHelper
{
public:
    ParallelVectorHelper(const GridView& gridView, const DofMapper& mapper)
    : gridView_(gridView), mapper_(mapper)
    {}
 
    template<class Block, class Alloc>
    void makeNonOverlappingConsistent(Dune::BlockVector<Block, Alloc>& v) const
    {
        if constexpr (Dune::Capabilities::canCommunicate<typename GridView::Traits::Grid, dofCodim>::v)
        {
            VectorCommDataHandleSum<DofMapper, Dune::BlockVector<Block, Alloc>, dofCodim, Block> gs(mapper_, v);
            if (gridView_.comm().size() > 1)
                gridView_.communicate(gs, Dune::InteriorBorder_InteriorBorder_Interface,
                                    Dune::ForwardCommunication);
        }
        else
            DUNE_THROW(Dune::InvalidStateException, "Cannot call makeNonOverlappingConsistent for a grid that cannot communicate codim-" << dofCodim << "-entities.");
    }
 
    template<class Block, class Alloc>
    void makeOverlappingConsistent(Dune::BlockVector<Block, Alloc>& v) const
    {
        if constexpr (Dune::Capabilities::canCommunicate<typename GridView::Traits::Grid, dofCodim>::v)
        {
            // Iterate over the gridView_ to make overlap entries 0. This is necessary to make
            // `VectorCommDataHandleSum` work properly.
            for (const auto& element : elements(gridView_))
                if (element.partitionType() == Dune::OverlapEntity)
                    v[gridView_.indexSet().index(element)] = 0;
 
            if (gridView_.comm().size() > 1)
            {
                VectorCommDataHandleSum<DofMapper, Dune::BlockVector<Block, Alloc>, dofCodim, Block> gs(mapper_, v);
                gridView_.communicate(gs, Dune::Overlap_All_Interface,
                                    Dune::ForwardCommunication);
            }
        }
        else
            DUNE_THROW(Dune::InvalidStateException, "Cannot call makeNonOverlappingConsistent for a grid that cannot communicate codim-" << dofCodim << "-entities.");
    }
 
    template<class... Blocks>
    void makeNonOverlappingConsistent(Dune::MultiTypeBlockVector<Blocks...>& v) const
    {
        DUNE_THROW(Dune::NotImplemented, "makeNonOverlappingConsistent for Dune::MultiTypeBlockVector");
    }
 
private:
    const GridView gridView_; 
    const DofMapper& mapper_; 
};
 
template<class Matrix, class GridView,
         class RowDofMapper, int rowDofCodim>
class ParallelMatrixHelper
{
    using IdType = typename GridView::Traits::Grid::Traits::GlobalIdSet::IdType;
 
    template<class ColIsGhostFunc>
    struct MatrixPatternExchange
    : public Dune::CommDataHandleIF<MatrixPatternExchange<ColIsGhostFunc>, IdType>
    {
        using DataType = IdType;
 
        MatrixPatternExchange(const RowDofMapper& rowEntityMapper,
                              const std::map<IdType,int>& globalToLocal,
                              const std::map<int,IdType>& localToGlobal,
                              Matrix& A,
                              std::vector<std::set<int>>& sparsityPattern,
                              const ColIsGhostFunc& isGhostColumDof)
        : rowEntityMapper_(rowEntityMapper), idToIndex_(globalToLocal), indexToID_(localToGlobal)
        , sparsityPattern_(sparsityPattern), A_(A), isGhostColumDof_(isGhostColumDof)
        {
            sparsityPattern_.resize(A.N());
        }
 
        bool contains (int dim, int codim) const
        { return (codim == rowDofCodim); }
 
        bool fixedSize(int dim, int codim) const
        { return false; }
 
        template<class EntityType>
        std::size_t size(EntityType& e) const
        {
            const auto rowIdx = rowEntityMapper_.index(e);
 
            // all column entity indices of this row that are in the index set
            std::size_t n = 0;
            for (auto colIt = A_[rowIdx].begin(); colIt != A_[rowIdx].end(); ++colIt)
                if (indexToID_.count(colIt.index()))
                    n++;
 
            return n;
        }
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, const EntityType& e) const
        {
            const auto rowIdx = rowEntityMapper_.index(e);
 
            // send all column entity ids of this row that are in the index set
            for (auto colIt = A_[rowIdx].begin(); colIt != A_[rowIdx].end(); ++colIt)
                if (auto it = indexToID_.find(colIt.index()); it != indexToID_.end())
                    buff.write(it->second);
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType& e, std::size_t n)
        {
            const auto rowIdx = rowEntityMapper_.index(e);
            for (std::size_t k = 0; k < n; k++)
            {
                // receive n column entity IDs
                IdType id;
                buff.read(id);
 
                // only add entries that are contained in the index set
                if (const auto it = idToIndex_.find(id); it != idToIndex_.end())
                {
                    const auto colIdx = it->second; // get local column index
                    // add this entry (if it doesn't exist yet)
                    // (and only if the column dof is not associated with a ghost entity)
                    if (!isGhostColumDof_(colIdx))
                        // std::set takes care that each index only is inserted once
                        sparsityPattern_[rowIdx].insert(colIdx);
                }
            }
        }
 
    private:
        const RowDofMapper& rowEntityMapper_;
        const std::map<IdType, int>& idToIndex_;
        const std::map<int, IdType>& indexToID_;
        std::vector<std::set<int>>& sparsityPattern_;
        Matrix& A_;
        const ColIsGhostFunc& isGhostColumDof_;
 
    }; // class MatrixPatternExchange
 
    struct MatrixEntry
    {
        IdType first;
        typename Matrix::block_type second;
    };
 
    struct MatrixEntryExchange
    : public Dune::CommDataHandleIF<MatrixEntryExchange, MatrixEntry>
    {
        using DataType = MatrixEntry;
 
        MatrixEntryExchange(const RowDofMapper& rowEntityMapper,
                            const std::map<IdType, int>& globalToLocal,
                            const std::map<int, IdType>& localToGlobal,
                            Matrix& A)
        : rowEntityMapper_(rowEntityMapper), idToIndex_(globalToLocal), indexToID_(localToGlobal), A_(A)
        {}
 
        bool contains(int dim, int codim) const
        { return (codim == rowDofCodim); }
 
        bool fixedSize(int dim, int codim) const
        { return false; }
 
        template<class EntityType>
        std::size_t size(EntityType& e) const
        {
            const auto rowIdx = rowEntityMapper_.index(e);
            std::size_t n = 0;
            for (auto colIt = A_[rowIdx].begin(); colIt != A_[rowIdx].end(); ++colIt)
                if (indexToID_.count(colIt.index()))
                    n++;
 
            return n;
        }
 
        template<class MessageBuffer, class EntityType>
        void gather(MessageBuffer& buff, const EntityType& e) const
        {
            const auto rowIdx = rowEntityMapper_.index(e);
            // send all matrix entries for which the column index is in the index set
            for (auto colIt = A_[rowIdx].begin(); colIt != A_[rowIdx].end(); ++colIt)
                if (auto it = indexToID_.find(colIt.index()); it != indexToID_.end())
                    buff.write(MatrixEntry{ it->second, *colIt });
        }
 
        template<class MessageBuffer, class EntityType>
        void scatter(MessageBuffer& buff, const EntityType& e, std::size_t n)
        {
            const auto rowIdx = rowEntityMapper_.index(e);
            for (std::size_t k = 0; k < n; k++)
            {
                MatrixEntry m;
                buff.read(m);
                const auto& [colDofID, matrixBlock] = m; // unpack
 
                // only add entries in the index set and for which A has allocated memory
                if (auto it = idToIndex_.find(colDofID); it != idToIndex_.end())
                    if (A_[rowIdx].find(it->second) != A_[rowIdx].end())
                        A_[rowIdx][it->second] += matrixBlock;
            }
        }
 
    private:
        const RowDofMapper& rowEntityMapper_;
        const std::map<IdType, int>& idToIndex_;
        const std::map<int, IdType>& indexToID_;
        Matrix& A_;
 
    }; // class MatrixEntryExchange
 
public:
 
    ParallelMatrixHelper(const GridView& gridView, const RowDofMapper& mapper)
    : gridView_(gridView), mapper_(mapper)
    {
        idToIndex_.clear();
        indexToID_.clear();
 
        std::vector<bool> handledDof(gridView_.size(rowDofCodim), false);
        for (const auto& element : elements(gridView_))
        {
            for (int i = 0; i < element.subEntities(rowDofCodim); ++i)
            {
                const auto entity = element.template subEntity<rowDofCodim>(i);
                if (entity.partitionType() == Dune::BorderEntity)
                {
                    const auto localRowIdx = mapper_.index(entity);
                    if (!handledDof[localRowIdx])
                    {
                        IdType dofIdxGlobal = gridView_.grid().globalIdSet().id(entity);
                        idToIndex_.emplace(dofIdxGlobal, localRowIdx);
                        indexToID_.emplace(localRowIdx, dofIdxGlobal);
                    }
                }
            }
        }
    }
 
    template<class IsGhostFunc>
    void extendMatrix(Matrix& A, const IsGhostFunc& isGhost)
    {
        if constexpr (Dune::Capabilities::canCommunicate<typename GridView::Grid, rowDofCodim>::v)
        {
            if (gridView_.comm().size() <= 1)
                return;
 
            // make a copy of the matrix as originally assembled
            Matrix matrixAsAssembled(A);
 
            // first get entries in sparsity pattern from other processes
            std::size_t numNonZeroEntries = 0;
            std::vector<std::set<int>> sparsityPattern; // column indices for every row
            MatrixPatternExchange<IsGhostFunc> dataHandle(mapper_, idToIndex_, indexToID_, A, sparsityPattern, isGhost);
            gridView_.communicate(
                dataHandle, Dune::InteriorBorder_InteriorBorder_Interface, Dune::ForwardCommunication
            );
 
            // add own entries to the sparsity pattern and count number of non-zeros
            for (auto rowIt = A.begin(); rowIt != A.end(); ++rowIt)
            {
                const auto colEndIt = A[rowIt.index()].end();
                for (auto colIt = rowIt->begin(); colIt != colEndIt; ++colIt)
                    if (!sparsityPattern[rowIt.index()].count(colIt.index()))
                        sparsityPattern[rowIt.index()].insert(colIt.index());
 
                numNonZeroEntries += sparsityPattern[rowIt.index()].size();
            }
 
            // insert any additional entries into the matrix
            A.setSize(matrixAsAssembled.N(), matrixAsAssembled.M(), numNonZeroEntries);
            A.setBuildMode(Matrix::row_wise);
            auto citer = A.createbegin();
            for (auto i = sparsityPattern.begin(), end = sparsityPattern.end(); i!=end; ++i, ++citer)
                for (auto si = i->begin(), send = i->end(); si!=send; ++si)
                    citer.insert(*si);
 
            // reset matrix to contain original values
            A = 0;
            const auto rowEndIt = matrixAsAssembled.end();
            for (auto rowIt = matrixAsAssembled.begin(); rowIt != rowEndIt; ++rowIt)
                for (auto colIt = matrixAsAssembled[rowIt.index()].begin(); colIt != matrixAsAssembled[rowIt.index()].end(); ++colIt)
                    A[rowIt.index()][colIt.index()] = *colIt;
 
            // The matrix A has now a possible extended sparsity pattern but any additional entries are
            // initialized to zero and have to be filled by the sumEntries function
        }
        else
            DUNE_THROW(Dune::InvalidStateException, "Cannot call extendMatrix for a grid that cannot communicate codim-" << rowDofCodim << "-entities.");
    }
 
    void sumEntries(Matrix& A)
    {
        if constexpr (Dune::Capabilities::canCommunicate<typename GridView::Grid, rowDofCodim>::v)
        {
            if (gridView_.comm().size() <= 1)
                return;
 
            MatrixEntryExchange dataHandle(mapper_, idToIndex_, indexToID_, A);
            gridView_.communicate(
                dataHandle, Dune::InteriorBorder_InteriorBorder_Interface, Dune::ForwardCommunication
            );
        }
        else
            DUNE_THROW(Dune::InvalidStateException,
                "Cannot call sumEntries for a grid that cannot communicate codim-" << rowDofCodim << "-entities."
            );
    }
 
private:
    const GridView gridView_;
    const RowDofMapper& mapper_;
    std::map<IdType, int> idToIndex_;
    std::map<int, IdType> indexToID_;
 
};
 
template<class LinearSolverTraits, class ParallelTraits,
         class Matrix, class ParallelHelper>
void prepareMatrixParallel(Matrix& A, ParallelHelper& pHelper)
{
    if constexpr (ParallelTraits::isNonOverlapping)
    {
        // extend the matrix pattern such that it is usable for a parallel solver
        // and make right-hand side consistent
        using GridView = typename LinearSolverTraits::GridView;
        using DofMapper = typename LinearSolverTraits::DofMapper;
        static constexpr int dofCodim = LinearSolverTraits::dofCodim;
        ParallelMatrixHelper<Matrix, GridView, DofMapper, dofCodim> matrixHelper(pHelper.gridView(), pHelper.dofMapper());
        matrixHelper.extendMatrix(A, [&pHelper](auto idx){ return pHelper.isGhost(idx); });
        matrixHelper.sumEntries(A);
    }
}
 
template<class LinearSolverTraits, class ParallelTraits,
         class Vector, class ParallelHelper>
void prepareVectorParallel(Vector& b, ParallelHelper& pHelper)
{
    if constexpr (ParallelTraits::isNonOverlapping)
    {
        // extend the matrix pattern such that it is usable for a parallel solver
        // and make right-hand side consistent
        using GridView = typename LinearSolverTraits::GridView;
        using DofMapper = typename LinearSolverTraits::DofMapper;
        static constexpr int dofCodim = LinearSolverTraits::dofCodim;
        ParallelVectorHelper<GridView, DofMapper, dofCodim> vectorHelper(pHelper.gridView(), pHelper.dofMapper());
        vectorHelper.makeNonOverlappingConsistent(b);
    }
}
 
template<class LinearSolverTraits, class ParallelTraits,
         class Matrix, class Vector, class ParallelHelper>
void prepareLinearAlgebraParallel(Matrix& A, Vector& b, ParallelHelper& pHelper)
{
    prepareMatrixParallel<LinearSolverTraits, ParallelTraits>(A, pHelper);
    prepareVectorParallel<LinearSolverTraits, ParallelTraits>(b, pHelper);
}
 
template<class LinearSolverTraits, class ParallelTraits,
         class Matrix, class Vector, class ParallelHelper>
void prepareLinearAlgebraParallel(Matrix& A, Vector& b,
                                  std::shared_ptr<typename ParallelTraits::Comm>& comm,
                                  std::shared_ptr<typename ParallelTraits::LinearOperator>& fop,
                                  std::shared_ptr<typename ParallelTraits::ScalarProduct>& sp,
                                  ParallelHelper& pHelper)
{
    prepareLinearAlgebraParallel<LinearSolverTraits, ParallelTraits>(A, b, pHelper);
    const auto category = ParallelTraits::isNonOverlapping ?
        Dune::SolverCategory::nonoverlapping : Dune::SolverCategory::overlapping;
 
    comm = std::make_shared<typename ParallelTraits::Comm>(pHelper.gridView().comm(), category);
    pHelper.createParallelIndexSet(*comm);
    fop = std::make_shared<typename ParallelTraits::LinearOperator>(A, *comm);
    sp = std::make_shared<typename ParallelTraits::ScalarProduct>(*comm);
}
 
} // end namespace Dumux
 
#endif