seq_amg_dg_backend.hh

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#ifndef DUNE_PDELAB_BACKEND_ISTL_SEQ_AMG_DG_BACKEND_HH
#define DUNE_PDELAB_BACKEND_ISTL_SEQ_AMG_DG_BACKEND_HH
 
#include <dune/common/math.hh>
#include <dune/common/parametertree.hh>
 
#include <dune/istl/matrixmatrix.hh>
 
#include <dune/grid/common/datahandleif.hh>
 
#include <dune/pdelab/backend/istl/vector.hh>
#include <dune/pdelab/backend/istl/bcrsmatrix.hh>
#include <dune/pdelab/backend/istl/bcrsmatrixbackend.hh>
#include <dune/pdelab/backend/istl/ovlpistlsolverbackend.hh>
#include <dune/pdelab/gridoperator/gridoperator.hh>
 
namespace Dune {
  namespace PDELab {
 
    template<class DGMatrix, class DGPrec, class CGPrec, class P>
    class SeqDGAMGPrec : public Dune::Preconditioner<typename DGPrec::domain_type,typename DGPrec::range_type>
    {
      DGMatrix& dgmatrix;
      DGPrec& dgprec;
      CGPrec& cgprec;
      P& p;
      int n1,n2;
      bool firstapply;
 
    public:
      typedef typename DGPrec::domain_type X;
      typedef typename DGPrec::range_type Y;
      typedef typename CGPrec::domain_type CGX;
      typedef typename CGPrec::range_type CGY;
 
      SolverCategory::Category category() const override
      {
        return SolverCategory::sequential;
      }
 
      SeqDGAMGPrec (DGMatrix& dgmatrix_, DGPrec& dgprec_, CGPrec& cgprec_, P& p_, int n1_, int n2_)
        : dgmatrix(dgmatrix_), dgprec(dgprec_), cgprec(cgprec_), p(p_), n1(n1_), n2(n2_),
          firstapply(true)
      {
      }
 
      virtual void pre (X& x, Y& b) override
      {
        dgprec.pre(x,b);
        CGY cgd(p.M());
        cgd = 0.0;
        CGX cgv(p.M());
        cgv = 0.0;
        cgprec.pre(cgv,cgd);
      }
 
      virtual void apply (X& x, const Y& b) override
      {
        // need local copies to store defect and solution
        Y d(b);
        X v(x);
 
        // pre-smoothing on DG matrix
        for (int i=0; i<n1; i++)
          {
            v = 0.0;
            dgprec.apply(v,d);
            dgmatrix.mmv(v,d);
            x += v;
          }
 
        // restrict defect to CG subspace
        CGY cgd(p.M());
        p.mtv(d,cgd);
        CGX cgv(p.M());
        cgv = 0.0;
 
        // apply AMG
        cgprec.apply(cgv,cgd);
 
        // prolongate correction
        p.mv(cgv,v);
        dgmatrix.mmv(v,d);
        x += v;
 
        // pre-smoothing on DG matrix
        for (int i=0; i<n2; i++)
          {
            v = 0.0;
            dgprec.apply(v,d);
            dgmatrix.mmv(v,d);
            x += v;
          }
      }
 
      virtual void post (X& x) override
      {
        dgprec.post(x);
        CGX cgv(p.M());
        cgv = 0.0;
        cgprec.post(cgv);
      }
    };
 
 
    template<class DGGO, class CGGFS, class TransferLOP, template<class,class,class,int> class DGPrec, template<class> class Solver>
    class ISTLBackend_SEQ_AMG_4_DG : public Dune::PDELab::LinearResultStorage
    {
      // DG grid function space
      typedef typename DGGO::Traits::TrialGridFunctionSpace GFS;
 
      // vectors and matrices on DG level
      typedef typename DGGO::Traits::Jacobian M; // wrapped istl DG matrix
      typedef typename DGGO::Traits::Domain V;   // wrapped istl DG vector
      typedef Backend::Native<M> Matrix;         // istl DG matrix
      typedef Backend::Native<V> Vector;         // istl DG vector
      typedef typename Vector::field_type field_type;
 
      // vectors and matrices on CG level
      using CGV = Dune::PDELab::Backend::Vector<CGGFS,field_type>; // wrapped istl CG vector
      typedef Backend::Native<CGV> CGVector;                       // istl CG vector
 
      // prolongation matrix
      typedef Dune::PDELab::ISTL::BCRSMatrixBackend<> MBE;
      typedef Dune::PDELab::EmptyTransformation CC;
      typedef TransferLOP CGTODGLOP; // local operator
      typedef Dune::PDELab::GridOperator<CGGFS,GFS,CGTODGLOP,MBE,field_type,field_type,field_type,CC,CC> PGO;
      typedef typename PGO::Jacobian PMatrix; // wrapped ISTL prolongation matrix
      typedef Backend::Native<PMatrix> P;     // ISTL prolongation matrix
 
      // CG subspace matrix
      typedef typename Dune::TransposedMatMultMatResult<P,Matrix>::type PTADG;
      typedef typename Dune::MatMultMatResult<PTADG,P>::type ACG; // istl coarse space matrix
      typedef ACG CGMatrix; // another name
 
      // AMG in CG-subspace
      typedef Dune::MatrixAdapter<CGMatrix,CGVector,CGVector> CGOperator;
      typedef Dune::SeqSSOR<CGMatrix,CGVector,CGVector,1> Smoother;
      typedef Dune::Amg::AMG<CGOperator,CGVector,Smoother> AMG;
      typedef Dune::Amg::Parameters Parameters;
 
      DGGO& dggo;
      CGGFS& cggfs;
      std::shared_ptr<CGOperator> cgop;
      std::shared_ptr<AMG> amg;
      Parameters amg_parameters;
      unsigned maxiter;
      int verbose;
      bool reuse;
      bool firstapply;
      bool usesuperlu;
      std::size_t low_order_space_entries_per_row;
 
      // Parameters for DG smoother
      int smoother_relaxation = 1.0; // Relaxation parameter of DG smoother
      int n1=2; // Number of DG pre-smoothing steps
      int n2=2; // Number of DG post-smoothing steps
 
      CGTODGLOP cgtodglop;  // local operator to assemble prolongation matrix
      PGO pgo;              // grid operator to assemble prolongation matrix
      PMatrix pmatrix;      // wrapped prolongation matrix
      ACG acg;              // CG-subspace matrix
 
    public:
      ISTLBackend_SEQ_AMG_4_DG(DGGO& dggo_, CGGFS& cggfs_, unsigned maxiter_=5000, int verbose_=1, bool reuse_=false, bool usesuperlu_=true)
        : dggo(dggo_)
        , cggfs(cggfs_)
        , amg_parameters(15,2000)
        , maxiter(maxiter_)
        , verbose(verbose_)
        , reuse(reuse_)
        , firstapply(true)
        , usesuperlu(usesuperlu_)
        , low_order_space_entries_per_row(Dune::power(3,GFS::Traits::GridView::dimension))
        , cgtodglop()
        , pgo(cggfs,dggo.trialGridFunctionSpace(),cgtodglop,MBE(low_order_space_entries_per_row))
        , pmatrix(pgo)
        , acg()
      {
        amg_parameters.setDefaultValuesIsotropic(GFS::Traits::GridViewType::Traits::Grid::dimension);
        amg_parameters.setDebugLevel(verbose_);
#if !HAVE_SUPERLU
        if (usesuperlu == true)
          {
            std::cout << "WARNING: You are using AMG without SuperLU!"
                      << " Please consider installing SuperLU,"
                      << " or set the usesuperlu flag to false"
                      << " to suppress this warning." << std::endl;
          }
#endif
 
        // assemble prolongation matrix; this will not change from one apply to the next
        pmatrix = 0.0;
        if (verbose>0) std::cout << "allocated prolongation matrix of size " << pmatrix.N() << " x " << pmatrix.M() << std::endl;
        CGV cgx(cggfs,0.0);         // need vector to call jacobian
        pgo.jacobian(cgx,pmatrix);
      }
 
      ISTLBackend_SEQ_AMG_4_DG(DGGO& dggo_, CGGFS& cggfs_, const ParameterTree& params)//unsigned maxiter_=5000, int verbose_=1, bool usesuperlu_=true)
        : dggo(dggo_)
        , cggfs(cggfs_)
        , amg_parameters(15,2000)
        , maxiter(params.get<int>("max_iterations",5000))
        , verbose(params.get<int>("verbose",1))
        , reuse(params.get<bool>("reuse", false))
        , firstapply(true)
        , usesuperlu(params.get<bool>("use_superlu",true))
        , low_order_space_entries_per_row(params.get<std::size_t>("low_order_space.entries_per_row",Dune::power(3,GFS::Traits::GridView::dimension)))
        , cgtodglop()
        , pgo(cggfs,dggo.trialGridFunctionSpace(),cgtodglop,MBE(low_order_space_entries_per_row))
        , pmatrix(pgo)
      {
        amg_parameters.setDefaultValuesIsotropic(GFS::Traits::GridViewType::Traits::Grid::dimension);
        amg_parameters.setDebugLevel(params.get<int>("verbose",1));
#if !HAVE_SUPERLU
        if (usesuperlu == true)
          {
            std::cout << "WARNING: You are using AMG without SuperLU!"
                      << " Please consider installing SuperLU,"
                      << " or set the usesuperlu flag to false"
                      << " to suppress this warning." << std::endl;
          }
#endif
 
 
        // assemble prolongation matrix; this will not change from one apply to the next
        pmatrix = 0.0;
        if (verbose>0) std::cout << "allocated prolongation matrix of size " << pmatrix.N() << " x " << pmatrix.M() << std::endl;
        CGV cgx(cggfs,0.0);         // need vector to call jacobian
        pgo.jacobian(cgx,pmatrix);
      }
 
      typename V::ElementType norm (const V& v) const
      {
        return Backend::native(v).two_norm();
      }
 
      void setParameters(const Parameters& amg_parameters_)
      {
        amg_parameters = amg_parameters_;
      }
 
      const Parameters& parameters() const
      {
        return amg_parameters;
      }
 
      void setReuse(bool reuse_)
      {
        reuse = reuse_;
      }
 
      bool getReuse() const
      {
        return reuse;
      }
 
      void setDGSmootherRelaxation(double relaxation_)
      {
        smoother_relaxation = relaxation_;
      }
 
      void setNoDGPreSmoothSteps(int n1_)
      {
        n1 = n1_;
      }
 
      void setNoDGPostSmoothSteps(int n2_)
      {
        n2 = n2_;
      }
 
      void apply (M& A, V& z, V& r, typename Dune::template FieldTraits<typename V::ElementType >::real_type reduction)
      {
        using Backend::native;
        // do triple matrix product ACG = P^T ADG P
        Dune::Timer watch;
        watch.reset();
        // only do triple matrix product if the matrix changes
        double triple_product_time = 0.0;
        // no need to set acg here back to zero, this is done in matMultmat
        if(reuse == false || firstapply == true) {
          PTADG ptadg;
          Dune::transposeMatMultMat(ptadg,native(pmatrix),native(A));
          Dune::matMultMat(acg,ptadg,native(pmatrix));
          triple_product_time = watch.elapsed();
          if (verbose>0)
            std::cout << "=== triple matrix product " << triple_product_time << " s" << std::endl;
          //Dune::printmatrix(std::cout,acg,"triple product matrix","row",10,2);
        }
        else if (verbose>0)
          std::cout << "=== reuse CG matrix, SKIPPING triple matrix product " << std::endl;
 
        // set up AMG solver for the CG subspace
        typedef typename Dune::Amg::SmootherTraits<Smoother>::Arguments SmootherArgs;
        SmootherArgs smootherArgs;
        smootherArgs.iterations = 1;
        smootherArgs.relaxationFactor = 1.0;
        typedef Dune::Amg::CoarsenCriterion<Dune::Amg::SymmetricCriterion<CGMatrix,Dune::Amg::FirstDiagonal> > Criterion;
        Criterion criterion(amg_parameters);
        watch.reset();
 
        // only construct a new AMG for the CG-subspace if the matrix changes
        double amg_setup_time = 0.0;
        if(reuse == false || firstapply == true) {
          cgop.reset(new CGOperator(acg));
          amg.reset(new AMG(*cgop,criterion,smootherArgs));
          firstapply = false;
          amg_setup_time = watch.elapsed();
          if (verbose>0)
            std::cout << "=== AMG setup " <<amg_setup_time << " s" << std::endl;
        }
        else if (verbose>0)
          std::cout << "=== reuse CG matrix, SKIPPING AMG setup " << std::endl;
 
        // set up hybrid DG/CG preconditioner
        Dune::MatrixAdapter<Matrix,Vector,Vector> op(native(A));
        DGPrec<Matrix,Vector,Vector,1> dgprec(native(A),1,smoother_relaxation);
        typedef SeqDGAMGPrec<Matrix,DGPrec<Matrix,Vector,Vector,1>,AMG,P> HybridPrec;
        HybridPrec hybridprec(native(A),dgprec,*amg,native(pmatrix),n1,n2);
 
        // set up solver
        Solver<Vector> solver(op,hybridprec,reduction,maxiter,verbose);
 
        // solve
        Dune::InverseOperatorResult stat;
        watch.reset();
        solver.apply(native(z),native(r),stat);
        double amg_solve_time = watch.elapsed();
        if (verbose>0) std::cout << "=== Hybrid total solve time " << amg_solve_time+amg_setup_time+triple_product_time << " s" << std::endl;
        res.converged  = stat.converged;
        res.iterations = stat.iterations;
        res.elapsed    = amg_solve_time+amg_setup_time+triple_product_time;
        res.reduction  = stat.reduction;
        res.conv_rate  = stat.conv_rate;
      }
 
    };
  }
}
#endif // DUNE_PDELAB_BACKEND_ISTL_SEQ_AMG_DG_BACKEND_HH