galerkin.hh

Go to the documentation of this file.

// SPDX-FileCopyrightText: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_GALERKIN_HH
#define DUNE_GALERKIN_HH
 
#include "aggregates.hh"
#include "pinfo.hh"
#include <dune/common/poolallocator.hh>
#include <dune/common/enumset.hh>
#include <set>
#include <limits>
#include <algorithm>
 
namespace Dune
{
  namespace Amg
  {
    template<class T>
    struct OverlapVertex
    {
      typedef T Aggregate;
 
      typedef T Vertex;
 
      Aggregate* aggregate;
 
      Vertex vertex;
    };
 
 
 
    template<class M>
    class SparsityBuilder
    {
    public:
      SparsityBuilder(M& matrix);
 
      void insert(const typename M::size_type& index);
 
      void operator++();
 
      std::size_t minRowSize();
 
      std::size_t maxRowSize();
 
      std::size_t sumRowSize();
      std::size_t index()
      {
        return row_.index();
      }
    private:
      typename M::CreateIterator row_;
      std::size_t minRowSize_;
      std::size_t maxRowSize_;
      std::size_t sumRowSize_;
#ifdef DUNE_ISTL_WITH_CHECKING
      bool diagonalInserted;
#endif
    };
 
    class BaseGalerkinProduct
    {
    public:
      template<class M, class V, class I, class O>
      void calculate(const M& fine, const AggregatesMap<V>& aggregates, M& coarse,
                     const I& pinfo, const O& copy);
 
    };
 
    template<class T>
    class GalerkinProduct
      : public BaseGalerkinProduct
    {
    public:
      typedef T ParallelInformation;
 
      template<class G, class V, class Set>
      typename G::MutableMatrix* build(G& fineGraph, V& visitedMap,
                                       const ParallelInformation& pinfo,
                                       AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                       const typename G::Matrix::size_type& size,
                                       const Set& copy);
    private:
 
      template<class G, class I, class Set>
      const OverlapVertex<typename G::VertexDescriptor>*
      buildOverlapVertices(const G& graph,  const I& pinfo,
                           AggregatesMap<typename G::VertexDescriptor>& aggregates,
                           const Set& overlap,
                           std::size_t& overlapCount);
 
      template<class A>
      struct OVLess
      {
        bool operator()(const OverlapVertex<A>& o1, const OverlapVertex<A>& o2)
        {
          return *o1.aggregate < *o2.aggregate;
        }
      };
    };
 
    template<>
    class GalerkinProduct<SequentialInformation>
      : public BaseGalerkinProduct
    {
    public:
      template<class G, class V, class Set>
      typename G::MutableMatrix* build(G& fineGraph, V& visitedMap,
                                       const SequentialInformation& pinfo,
                                       const AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                       const typename G::Matrix::size_type& size,
                                       const Set& copy);
    };
 
    struct BaseConnectivityConstructor
    {
      template<class R, class G, class V>
      static void constructOverlapConnectivity(R& row, G& graph, V& visitedMap,
                                               const AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                               const OverlapVertex<typename G::VertexDescriptor>*& seed,
                                               const OverlapVertex<typename G::VertexDescriptor>* overlapEnd);
 
      template<class R, class G, class V>
      static void constructNonOverlapConnectivity(R& row, G& graph, V& visitedMap,
                                                  const AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                                  const typename G::VertexDescriptor& seed);
 
 
      template<class G, class S, class V>
      class ConnectedBuilder
      {
      public:
        typedef G Graph;
        typedef typename Graph::ConstEdgeIterator ConstEdgeIterator;
 
        typedef S Set;
 
        typedef V VisitedMap;
 
        typedef typename Graph::VertexDescriptor Vertex;
 
        ConnectedBuilder(const AggregatesMap<Vertex>& aggregates, Graph& graph,
                         VisitedMap& visitedMap, Set& connected);
 
        void operator()(const ConstEdgeIterator& edge);
 
      private:
        const AggregatesMap<Vertex>& aggregates_;
 
        Graph& graph_;
 
        VisitedMap& visitedMap_;
 
        Set& connected_;
      };
 
    };
 
    template<class G, class T>
    struct ConnectivityConstructor : public BaseConnectivityConstructor
    {
      typedef typename G::VertexDescriptor Vertex;
 
      template<class V, class O, class R>
      static void examine(G& graph,
                          V& visitedMap,
                          const T& pinfo,
                          const AggregatesMap<Vertex>& aggregates,
                          const O& overlap,
                          const OverlapVertex<Vertex>* overlapVertices,
                          const OverlapVertex<Vertex>* overlapEnd,
                          R& row);
    };
 
    template<class G>
    struct ConnectivityConstructor<G,SequentialInformation> : public BaseConnectivityConstructor
    {
      typedef typename G::VertexDescriptor Vertex;
 
      template<class V, class R>
      static void examine(G& graph,
                          V& visitedMap,
                          const SequentialInformation& pinfo,
                          const AggregatesMap<Vertex>& aggregates,
                          R& row);
    };
 
    template<class T>
    struct DirichletBoundarySetter
    {
      template<class M, class O>
      static void set(M& coarse, const T& pinfo, const O& copy);
    };
 
    template<>
    struct DirichletBoundarySetter<SequentialInformation>
    {
      template<class M, class O>
      static void set(M& coarse, const SequentialInformation& pinfo, const O& copy);
    };
 
    template<class R, class G, class V>
    void BaseConnectivityConstructor::constructNonOverlapConnectivity(R& row, G& graph, V& visitedMap,
                                                                      const AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                                                      const typename G::VertexDescriptor& seed)
    {
      assert(row.index()==aggregates[seed]);
      row.insert(aggregates[seed]);
      ConnectedBuilder<G,R,V> conBuilder(aggregates, graph, visitedMap, row);
      typedef typename G::VertexDescriptor Vertex;
      typedef std::allocator<Vertex> Allocator;
      typedef SLList<Vertex,Allocator> VertexList;
      typedef typename AggregatesMap<Vertex>::DummyEdgeVisitor DummyVisitor;
      VertexList vlist;
      DummyVisitor dummy;
      aggregates.template breadthFirstSearch<true,false>(seed,aggregates[seed], graph, vlist, dummy,
                                                         conBuilder, visitedMap);
    }
 
    template<class R, class G, class V>
    void BaseConnectivityConstructor::constructOverlapConnectivity(R& row, G& graph, V& visitedMap,
                                                                   const AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                                                   const OverlapVertex<typename G::VertexDescriptor>*& seed,
                                                                   const OverlapVertex<typename G::VertexDescriptor>* overlapEnd)
    {
      ConnectedBuilder<G,R,V> conBuilder(aggregates, graph, visitedMap, row);
      const typename G::VertexDescriptor aggregate=*seed->aggregate;
 
      if (row.index()==*seed->aggregate) {
        while(seed != overlapEnd && aggregate == *seed->aggregate) {
          row.insert(*seed->aggregate);
          // Walk over all neighbours and add them to the connected array.
          visitNeighbours(graph, seed->vertex, conBuilder);
          // Mark vertex as visited
          put(visitedMap, seed->vertex, true);
          ++seed;
        }
      }
    }
 
    template<class G, class S, class V>
    BaseConnectivityConstructor::ConnectedBuilder<G,S,V>::ConnectedBuilder(const AggregatesMap<Vertex>& aggregates,
                                                                           Graph& graph, VisitedMap& visitedMap,
                                                                           Set& connected)
      : aggregates_(aggregates), graph_(graph), visitedMap_(visitedMap), connected_(connected)
    {}
 
    template<class G, class S, class V>
    void BaseConnectivityConstructor::ConnectedBuilder<G,S,V>::operator()(const ConstEdgeIterator& edge)
    {
      const Vertex& vertex = aggregates_[edge.target()];
      assert(vertex!= AggregatesMap<Vertex>::UNAGGREGATED);
      if(vertex!= AggregatesMap<Vertex>::ISOLATED)
        connected_.insert(vertex);
    }
 
    template<class T>
    template<class G, class I, class Set>
    const OverlapVertex<typename G::VertexDescriptor>*
    GalerkinProduct<T>::buildOverlapVertices(const G& graph, const I& pinfo,
                                             AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                             const Set& overlap,
                                             std::size_t& overlapCount)
    {
      // count the overlap vertices.
      typedef typename G::ConstVertexIterator ConstIterator;
      typedef typename I::GlobalLookupIndexSet GlobalLookup;
      typedef typename GlobalLookup::IndexPair IndexPair;
 
      const ConstIterator end = graph.end();
      overlapCount = 0;
 
      const GlobalLookup& lookup=pinfo.globalLookup();
 
      for(ConstIterator vertex=graph.begin(); vertex != end; ++vertex) {
        const IndexPair* pair = lookup.pair(*vertex);
 
        if(pair!=0 && overlap.contains(pair->local().attribute()))
          ++overlapCount;
      }
      // Allocate space
      typedef typename G::VertexDescriptor Vertex;
 
      OverlapVertex<Vertex>* overlapVertices = new OverlapVertex<Vertex>[overlapCount=0 ? 1 : overlapCount];
      if(overlapCount==0)
        return overlapVertices;
 
      // Initialize them
      overlapCount=0;
      for(ConstIterator vertex=graph.begin(); vertex != end; ++vertex) {
        const IndexPair* pair = lookup.pair(*vertex);
 
        if(pair!=0 && overlap.contains(pair->local().attribute())) {
          overlapVertices[overlapCount].aggregate = &aggregates[pair->local()];
          overlapVertices[overlapCount].vertex = pair->local();
          ++overlapCount;
        }
      }
 
      dverb << overlapCount<<" overlap vertices"<<std::endl;
 
      std::sort(overlapVertices, overlapVertices+overlapCount, OVLess<Vertex>());
      // due to the sorting the isolated aggregates (to be skipped) are at the end.
 
      return overlapVertices;
    }
 
    template<class G, class T>
    template<class V, class O, class R>
    void ConnectivityConstructor<G,T>::examine(G& graph,
                                               V& visitedMap,
                                               const T& pinfo,
                                               const AggregatesMap<Vertex>& aggregates,
                                               const O& overlap,
                                               const OverlapVertex<Vertex>* overlapVertices,
                                               const OverlapVertex<Vertex>* overlapEnd,
                                               R& row)
    {
      typedef typename T::GlobalLookupIndexSet GlobalLookup;
      const GlobalLookup& lookup = pinfo.globalLookup();
 
      typedef typename G::VertexIterator VertexIterator;
 
      VertexIterator vend=graph.end();
 
#ifdef DUNE_ISTL_WITH_CHECKING
      std::set<Vertex> examined;
#endif
 
      // The aggregates owned by the process have lower local indices
      // then those not owned. We process them in the first pass.
      // They represent the rows 0, 1, ..., n of the coarse matrix
      for(VertexIterator vertex = graph.begin(); vertex != vend; ++vertex)
        if(!get(visitedMap, *vertex)) {
          // In the first pass we only process owner nodes
          typedef typename GlobalLookup::IndexPair IndexPair;
          const IndexPair* pair = lookup.pair(*vertex);
          if(pair==0 || !overlap.contains(pair->local().attribute())) {
#ifdef DUNE_ISTL_WITH_CHECKING
            assert(examined.find(aggregates[*vertex])==examined.end());
            examined.insert(aggregates[*vertex]);
#endif
            constructNonOverlapConnectivity(row, graph, visitedMap, aggregates, *vertex);
 
            // only needed for ALU
            // (ghosts with same global id as owners on the same process)
            if (SolverCategory::category(pinfo) == static_cast<int>(SolverCategory::nonoverlapping)) {
              if(overlapVertices != overlapEnd) {
                if(*overlapVertices->aggregate!=AggregatesMap<Vertex>::ISOLATED) {
                  constructOverlapConnectivity(row, graph, visitedMap, aggregates, overlapVertices, overlapEnd);
                }
                else{
                  ++overlapVertices;
                }
              }
            }
            ++row;
          }
        }
 
      dvverb<<"constructed "<<row.index()<<" non-overlapping rows"<<std::endl;
 
      // Now come the aggregates not owned by use.
      // They represent the rows n+1, ..., N
      while(overlapVertices != overlapEnd)
        if(*overlapVertices->aggregate!=AggregatesMap<Vertex>::ISOLATED) {
 
#ifdef DUNE_ISTL_WITH_CHECKING
          typedef typename GlobalLookup::IndexPair IndexPair;
          const IndexPair* pair = lookup.pair(overlapVertices->vertex);
          assert(pair!=0 && overlap.contains(pair->local().attribute()));
          assert(examined.find(aggregates[overlapVertices->vertex])==examined.end());
          examined.insert(aggregates[overlapVertices->vertex]);
#endif
          constructOverlapConnectivity(row, graph, visitedMap, aggregates, overlapVertices, overlapEnd);
          ++row;
        }else{
          ++overlapVertices;
        }
    }
 
    template<class G>
    template<class V, class R>
    void ConnectivityConstructor<G,SequentialInformation>::examine(G& graph,
                                                                   V& visitedMap,
                                                                   [[maybe_unused]] const SequentialInformation& pinfo,
                                                                   const AggregatesMap<Vertex>& aggregates,
                                                                   R& row)
    {
      typedef typename G::VertexIterator VertexIterator;
 
      VertexIterator vend=graph.end();
      for(VertexIterator vertex = graph.begin(); vertex != vend; ++vertex) {
        if(!get(visitedMap, *vertex)) {
          constructNonOverlapConnectivity(row, graph, visitedMap, aggregates, *vertex);
          ++row;
        }
      }
 
    }
 
    template<class M>
    SparsityBuilder<M>::SparsityBuilder(M& matrix)
      : row_(matrix.createbegin()),
        minRowSize_(std::numeric_limits<std::size_t>::max()),
        maxRowSize_(0), sumRowSize_(0)
    {
#ifdef DUNE_ISTL_WITH_CHECKING
      diagonalInserted = false;
#endif
    }
    template<class M>
    std::size_t SparsityBuilder<M>::maxRowSize()
    {
      return maxRowSize_;
    }
    template<class M>
    std::size_t SparsityBuilder<M>::minRowSize()
    {
      return minRowSize_;
    }
 
    template<class M>
    std::size_t SparsityBuilder<M>::sumRowSize()
    {
      return sumRowSize_;
    }
    template<class M>
    void SparsityBuilder<M>::operator++()
    {
      sumRowSize_ += row_.size();
      minRowSize_=std::min(minRowSize_, row_.size());
      maxRowSize_=std::max(maxRowSize_, row_.size());
      ++row_;
#ifdef DUNE_ISTL_WITH_CHECKING
      assert(diagonalInserted);
      diagonalInserted = false;
#endif
    }
 
    template<class M>
    void SparsityBuilder<M>::insert(const typename M::size_type& index)
    {
      row_.insert(index);
#ifdef DUNE_ISTL_WITH_CHECKING
      diagonalInserted = diagonalInserted || row_.index()==index;
#endif
    }
 
    template<class T>
    template<class G, class V, class Set>
    typename G::MutableMatrix*
    GalerkinProduct<T>::build(G& fineGraph, V& visitedMap,
                              const ParallelInformation& pinfo,
                              AggregatesMap<typename G::VertexDescriptor>& aggregates,
                              const typename G::Matrix::size_type& size,
                              const Set& overlap)
    {
      typedef OverlapVertex<typename G::VertexDescriptor> OverlapVertex;
 
      std::size_t count;
 
      const OverlapVertex* overlapVertices = buildOverlapVertices(fineGraph,
                                                                  pinfo,
                                                                  aggregates,
                                                                  overlap,
                                                                  count);
      typedef typename G::MutableMatrix M;
      M* coarseMatrix = new M(size, size, M::row_wise);
 
      // Reset the visited flags of all vertices.
      // As the isolated nodes will be skipped we simply mark them as visited
 
      typedef typename G::VertexIterator Vertex;
      Vertex vend = fineGraph.end();
      for(Vertex vertex = fineGraph.begin(); vertex != vend; ++vertex) {
        assert(aggregates[*vertex] != AggregatesMap<typename G::VertexDescriptor>::UNAGGREGATED);
        put(visitedMap, *vertex, aggregates[*vertex]==AggregatesMap<typename G::VertexDescriptor>::ISOLATED);
      }
 
      typedef typename G::MutableMatrix M;
      SparsityBuilder<M> sparsityBuilder(*coarseMatrix);
 
      ConnectivityConstructor<G,T>::examine(fineGraph, visitedMap, pinfo,
                                            aggregates, overlap,
                                            overlapVertices,
                                            overlapVertices+count,
                                            sparsityBuilder);
 
      dinfo<<pinfo.communicator().rank()<<": Matrix ("<<coarseMatrix->N()<<"x"<<coarseMatrix->M()<<" row: min="<<sparsityBuilder.minRowSize()<<" max="
           <<sparsityBuilder.maxRowSize()<<" avg="
           <<static_cast<double>(sparsityBuilder.sumRowSize())/coarseMatrix->N()
           <<std::endl;
 
      delete[] overlapVertices;
 
      return coarseMatrix;
    }
 
    template<class G, class V, class Set>
    typename G::MutableMatrix*
    GalerkinProduct<SequentialInformation>::build(G& fineGraph, V& visitedMap,
                                                  const SequentialInformation& pinfo,
                                                  const AggregatesMap<typename G::VertexDescriptor>& aggregates,
                                                  const typename G::Matrix::size_type& size,
                                                  [[maybe_unused]] const Set& overlap)
    {
      typedef typename G::MutableMatrix M;
      M* coarseMatrix = new M(size, size, M::row_wise);
 
      // Reset the visited flags of all vertices.
      // As the isolated nodes will be skipped we simply mark them as visited
 
      typedef typename G::VertexIterator Vertex;
      Vertex vend = fineGraph.end();
      for(Vertex vertex = fineGraph.begin(); vertex != vend; ++vertex) {
        assert(aggregates[*vertex] != AggregatesMap<typename G::VertexDescriptor>::UNAGGREGATED);
        put(visitedMap, *vertex, aggregates[*vertex]==AggregatesMap<typename G::VertexDescriptor>::ISOLATED);
      }
 
      SparsityBuilder<M> sparsityBuilder(*coarseMatrix);
 
      ConnectivityConstructor<G,SequentialInformation>::examine(fineGraph, visitedMap, pinfo,
                                                                aggregates, sparsityBuilder);
      dinfo<<"Matrix row: min="<<sparsityBuilder.minRowSize()<<" max="
           <<sparsityBuilder.maxRowSize()<<" average="
           <<static_cast<double>(sparsityBuilder.sumRowSize())/coarseMatrix->N()<<std::endl;
      return coarseMatrix;
    }
 
    template<class M, class V, class P, class O>
    void BaseGalerkinProduct::calculate(const M& fine, const AggregatesMap<V>& aggregates, M& coarse,
                                        const P& pinfo, [[maybe_unused]] const O& copy)
    {
      coarse = static_cast<typename M::field_type>(0);
 
      typedef typename M::ConstIterator RowIterator;
      RowIterator endRow = fine.end();
 
      for(RowIterator row = fine.begin(); row != endRow; ++row)
        if(aggregates[row.index()] != AggregatesMap<V>::ISOLATED) {
          assert(aggregates[row.index()]!=AggregatesMap<V>::UNAGGREGATED);
          typedef typename M::ConstColIterator ColIterator;
          ColIterator endCol = row->end();
 
          for(ColIterator col = row->begin(); col != endCol; ++col)
            if(aggregates[col.index()] != AggregatesMap<V>::ISOLATED) {
              assert(aggregates[row.index()]!=AggregatesMap<V>::UNAGGREGATED);
              coarse[aggregates[row.index()]][aggregates[col.index()]]+=*col;
            }
        }
 
      // get the right diagonal matrix values on copy lines from owner processes
      typedef typename M::block_type BlockType;
      std::vector<BlockType> rowsize(coarse.N(),BlockType(0));
      for (RowIterator row = coarse.begin(); row != coarse.end(); ++row)
        rowsize[row.index()]=coarse[row.index()][row.index()];
      pinfo.copyOwnerToAll(rowsize,rowsize);
      for (RowIterator row = coarse.begin(); row != coarse.end(); ++row)
        coarse[row.index()][row.index()] = rowsize[row.index()];
 
      // don't set dirichlet boundaries for copy lines to make novlp case work,
      // the preconditioner yields slightly different results now.
 
      // Set the dirichlet border
      //DirichletBoundarySetter<P>::template set<M>(coarse, pinfo, copy);
 
    }
 
    template<class T>
    template<class M, class O>
    void DirichletBoundarySetter<T>::set(M& coarse, const T& pinfo, const O& copy)
    {
      typedef typename T::ParallelIndexSet::const_iterator ConstIterator;
      ConstIterator end = pinfo.indexSet().end();
      typedef typename M::block_type Block;
      Block identity=Block(0.0);
      for(typename Block::RowIterator b=identity.begin(); b !=  identity.end(); ++b)
        b->operator[](b.index())=1.0;
 
      for(ConstIterator index = pinfo.indexSet().begin();
          index != end; ++index) {
        if(copy.contains(index->local().attribute())) {
          typedef typename M::ColIterator ColIterator;
          typedef typename M::row_type Row;
          Row row = coarse[index->local()];
          ColIterator cend = row.find(index->local());
          ColIterator col  = row.begin();
          for(; col != cend; ++col)
            *col = 0;
 
          cend = row.end();
 
          assert(col != cend); // There should be a diagonal entry
          *col = identity;
 
          for(++col; col != cend; ++col)
            *col = 0;
        }
      }
    }
 
    template<class M, class O>
    void DirichletBoundarySetter<SequentialInformation>::set(M& coarse,
                                                             const SequentialInformation& pinfo,
                                                             const O& overlap)
    {}
 
  } // namespace Amg
} // namespace Dune
#endif