basicrow.hh

#ifndef DUNE_FEM_SOLVER_RUNGEKUTTA_BASICROW_HH
#define DUNE_FEM_SOLVER_RUNGEKUTTA_BASICROW_HH
 
//- system includes
#include <algorithm>
#include <cmath>
#include <cassert>
#include <limits>
#include <sstream>
#include <string>
#include <vector>
 
//- dune-common includes
#include <dune/common/dynmatrix.hh>
#include <dune/common/dynvector.hh>
 
//- dune-fem includes
#include <dune/fem/solver/odesolver.hh>
#include <dune/fem/solver/parameter.hh>
 
namespace DuneODE
{
 
  // NoROWRungeKuttaSourceTerm
  // ------------------------------
 
  struct NoROWRungeKuttaSourceTerm
  {
    template< class T >
    bool operator() ( double time, double timeStepSize, int stage, const T &u, const std::vector< T * > &update, T &source )
    {
      return false;
    }
 
    template< class T >
    void limit( T& update, const double time ) {}
 
    template< class T >
    double initialTimeStepEstimate ( double time, const T &u ) const
    {
      // return negative value to indicate that implicit time step should be used
      return -1.0;
    }
 
    double timeStepEstimate () const
    {
      return std::numeric_limits< double >::max();
    }
 
  };
 
  template< class HelmholtzOperator, class NonlinearSolver, class TimeStepControl, class SourceTerm = NoROWRungeKuttaSourceTerm >
  class BasicROWRungeKuttaSolver
  : public OdeSolverInterface< typename HelmholtzOperator::DomainFunctionType >
  {
    typedef BasicROWRungeKuttaSolver< HelmholtzOperator, NonlinearSolver, TimeStepControl, SourceTerm > ThisType;
    typedef OdeSolverInterface< typename HelmholtzOperator::DomainFunctionType > BaseType;
 
  public:
    typedef typename BaseType::MonitorType MonitorType;
    typedef typename BaseType::DestinationType DestinationType;
 
    typedef HelmholtzOperator HelmholtzOperatorType;
    typedef NonlinearSolver NonlinearSolverType;
    typedef TimeStepControl TimeStepControlType;
    typedef SourceTerm SourceTermType;
 
    typedef typename NonlinearSolver::ParameterType                    NonlinearSolverParameterType;
    typedef typename NonlinearSolverType::LinearInverseOperatorType    LinearInverseOperatorType;
 
    typedef typename HelmholtzOperator::SpaceOperatorType::PreconditionOperatorType PreconditionOperatorType;
 
    typedef Dune::Fem::TimeProviderBase TimeProviderType;
 
    template< class ButcherTable >
    BasicROWRungeKuttaSolver ( HelmholtzOperatorType &helmholtzOp,
                               TimeProviderType& timeProvider,
                               const ButcherTable &butcherTable,
                               const TimeStepControlType &timeStepControl,
                               const SourceTermType &sourceTerm,
                               const NonlinearSolverParameterType& parameter )
    : helmholtzOp_( helmholtzOp ),
      linearSolver_( parameter.linear() ),
      timeStepControl_( timeStepControl ),
      sourceTerm_( sourceTerm ),
      stages_( butcherTable.stages() ),
      ord_( butcherTable.order() ),
      alpha_( butcherTable.A() ),
      alpha2_( butcherTable.B() ),
      gamma_( stages() ),
      beta_( stages() ),
      c_( butcherTable.c() ),
      rhs_( "RK rhs", helmholtzOp_.space() ),
      temp_( "RK temp", helmholtzOp_.space() ),
      update_( stages(), nullptr ),
      maxLinearIterations_( parameter.linear().maxIterations() ),
      preconditioner_(helmholtzOp.spaceOperator().preconditioner())
    {
      setup( butcherTable );
    }
 
    template< class ButcherTable >
    BasicROWRungeKuttaSolver ( HelmholtzOperatorType &helmholtzOp,
                               TimeProviderType& timeProvider,
                               const ButcherTable &butcherTable,
                               const TimeStepControlType &timeStepControl,
                               const SourceTermType &sourceTerm,
                               const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : BasicROWRungeKuttaSolver( helmholtzOp, timeProvider, butcherTable, timeStepControl, sourceTerm, NonlinearSolverParameterType( parameter ) )
    {}
 
    template< class ButcherTable >
    BasicROWRungeKuttaSolver ( HelmholtzOperatorType &helmholtzOp,
                               TimeProviderType& timeProvider,
                               const ButcherTable &butcherTable,
                               const TimeStepControlType &timeStepControl,
                               const NonlinearSolverParameterType& parameter )
    : BasicROWRungeKuttaSolver( helmholtzOp, timeProvider, butcherTable, timeStepControl, SourceTermType(), parameter )
    {}
 
    template< class ButcherTable >
    BasicROWRungeKuttaSolver ( HelmholtzOperatorType &helmholtzOp,
                               TimeProviderType& timeProvider,
                               const ButcherTable &butcherTable,
                               const TimeStepControlType &timeStepControl,
                               const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : BasicROWRungeKuttaSolver( helmholtzOp, timeProvider, butcherTable, timeStepControl, SourceTermType(), NonlinearSolverParameterType( parameter ) )
    {}
 
    template< class ButcherTable >
    BasicROWRungeKuttaSolver ( HelmholtzOperatorType &helmholtzOp,
                               TimeProviderType& timeProvider,
                               const ButcherTable &butcherTable,
                               const NonlinearSolverParameterType& parameter )
    : BasicROWRungeKuttaSolver( helmholtzOp, timeProvider, butcherTable, TimeStepControlType(), SourceTermType(), parameter )
    {}
 
    template< class ButcherTable >
    BasicROWRungeKuttaSolver ( HelmholtzOperatorType &helmholtzOp,
                               TimeProviderType& timeProvider,
                               const ButcherTable &butcherTable,
                               const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : BasicROWRungeKuttaSolver( helmholtzOp, timeProvider, butcherTable, TimeStepControlType(), SourceTermType(), NonlinearSolverParameterType( parameter ) )
    {}
 
    template< class ButcherTable >
    void setup( const ButcherTable& butcherTable )
    {
      if( Dune::Fem::Parameter::verbose() )
      {
        std::cout << "ROW method of order=" << butcherTable.order() << " with " << stages_ << " stages" << std::endl;
      }
 
      // create intermediate functions
      for( int i = 0; i < stages(); ++i )
      {
        std::ostringstream name;
        name << "RK stage " << i;
        update_[ i ] = new DestinationType( name.str(), helmholtzOp_.space() );
      }
 
      // compute coefficients
      for( int i = 0; i < stages(); ++i )
        gamma_[ i ] = alpha_[ i ][ i ];
 
      alpha_.invert();
      alpha_.mtv( butcherTable.b(), beta_ );
      alpha2_.rightmultiply( alpha_ );
    }
 
    ~BasicROWRungeKuttaSolver ()
    {
      for( int i = 0; i < stages(); ++i )
        delete update_[ i ];
    }
 
    void initialize ( const DestinationType &U0 )
    {
      const double time = timeStepControl_.time();
 
      helmholtzOp_.setTime( time );
      helmholtzOp_.initializeTimeStepSize( U0 );
      const double helmholtzEstimate = helmholtzOp_.timeStepEstimate();
 
      double sourceTermEstimate = sourceTerm_.initialTimeStepEstimate( time, U0 );
      // negative time step is given by the empty source term
      if( sourceTermEstimate < 0.0 ) sourceTermEstimate = helmholtzEstimate ;
 
      timeStepControl_.initialTimeStepSize( helmholtzEstimate, sourceTermEstimate );
    }
 
    using BaseType::solve;
 
    void solve ( DestinationType &U, MonitorType &monitor )
    {
      monitor.reset();
 
      typename HelmholtzOperatorType::JacobianOperatorType jOp( "jacobianOperator", U.space(), U.space() );
 
      const double time = timeStepControl_.time();
      const double timeStepSize = timeStepControl_.timeStepSize();
      assert( timeStepSize > 0.0 );
      // std::cout << "solving... " << time << "    :     " << U << std::endl;
      for( int s = 0; s < stages(); ++s )
      {
        // update for stage s
        DestinationType& updateStage = *update_[ s ];
 
        rhs_.assign( U );
        for( int k = 0; k < s; ++k )
          rhs_.axpy( alpha2_[ s ][ k ], *update_[ k ] );
        helmholtzOp_.spaceOperator()(rhs_,updateStage);
        updateStage *= (gamma_[s]*timeStepSize);
        for( int k = 0; k < s; ++k )
          updateStage.axpy( -gamma_[s]*alpha_[ s ][ k ], *update_[ k ] );
 
        rhs_.assign( updateStage );
 
        // solve the system
        const double stageTime = time + c_[ s ]*timeStepSize;
        helmholtzOp_.setTime( stageTime );
        // compute jacobian if the diagonal entry in the butcher tableau changes
        // if ( s==0 || (gamma_[s-1] != gamma_[s]) )
        {
          // std::cout << "lambda=" << gamma_[ s ]*timeStepSize << std::endl;
          helmholtzOp_.setLambda( gamma_[ s ]*timeStepSize );
          helmholtzOp_.jacobian( U, jOp );
        }
        const int remLinearIts = maxLinearIterations_;
 
        linearSolver_.parameter().setMaxIterations( remLinearIts );
 
        if (preconditioner_)
          linearSolver_.bind( jOp, *preconditioner_ );
        else
          linearSolver_.bind( jOp );
 
        linearSolver_( rhs_, updateStage );
        monitor.linearSolverIterations_ += linearSolver_.iterations();
 
        linearSolver_.unbind();
      }
 
      double error = 0.0;
      if(0 && timeStepControl_.computeError() )
      {
        // store U (to be revised)
        DestinationType Uerr( U );
 
        // update solution
        U *= delta_;
        for( int s = 0; s < stages(); ++s )
          U.axpy( beta_[ s ], *update_[ s ] );
 
        //error = infNorm( U, Uerr );
        Uerr.axpy( -1.0, U );
        const double errorU = Uerr.scalarProductDofs( Uerr );
        const double normU = U.scalarProductDofs( U );
 
        if( normU > 0 && errorU > 0 )
        {
          error = std::sqrt( errorU / normU );
        }
        std::cout << std::scientific << "Error in RK = " << error << " norm " << errorU << " " << normU << std::endl;
        //std::cout << std::scientific << "Error in RK = " << error << std::endl;
      }
      else
      {
        // update solution
        for( int s = 0; s < stages(); ++s )
          U.axpy( beta_[ s ], *update_[ s ] );
      }
      // set error to monitor
      monitor.error_ = error;
 
      // update time step size
      timeStepControl_.timeStepEstimate( helmholtzOp_.timeStepEstimate(), sourceTerm_.timeStepEstimate(), monitor );
    }
 
    int stages () const { return stages_; }
 
    int order () const { return ord_; }
 
    void description ( std::ostream &out ) const
    {
      out << "Generic " << stages() << "-stage implicit Runge-Kutta solver.\\\\" << std::endl;
    }
 
  protected:
 
    double infNorm(const DestinationType& U, const DestinationType& Uerr ) const
    {
      typedef typename DestinationType :: ConstDofIteratorType ConstDofIteratorType ;
      const ConstDofIteratorType uend = U.dend();
      double res = 0;
      for( ConstDofIteratorType u = U.dbegin(), uerr = Uerr.dbegin(); u != uend; ++u, ++uerr )
      {
        double uval = *u;
        double uerrval = *uerr ;
        double div = std::abs( std::max( uval, uerrval ) );
 
        double norm = std::abs( uval - uerrval );
        if( std::abs(div) > 1e-12 )
          norm /= div;
        res = std::max( res, norm );
      }
      return res;
    }
 
    HelmholtzOperatorType&     helmholtzOp_;
    LinearInverseOperatorType  linearSolver_;
 
    TimeStepControl timeStepControl_;
    SourceTerm sourceTerm_;
 
    int stages_;
    int ord_;
 
    double delta_;
    Dune::DynamicMatrix< double > alpha_, alpha2_;
    Dune::DynamicVector< double > gamma_, beta_, c_;
 
    DestinationType rhs_,temp_;
    std::vector< DestinationType * > update_;
 
    const int maxLinearIterations_;
 
    const PreconditionOperatorType *preconditioner_;
  };
 
} // namespace DuneODE
 
#endif // #ifndef DUNE_FEM_SOLVER_RUNGEKUTTA_BASICROW_HH