timestepcontrol.hh

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#ifndef DUNE_FEM_SOLVER_RUNGEKUTTA_TIMESTEPCONTROL_HH
#define DUNE_FEM_SOLVER_RUNGEKUTTA_TIMESTEPCONTROL_HH
 
//- system includes
#include <cassert>
#include <memory>
 
//- dune-common includes
#include <dune/common/exceptions.hh>
 
//- dune-fem includes
#include <dune/fem/io/parameter.hh>
#include <dune/fem/solver/timeprovider.hh>
 
namespace DuneODE
{
 
  // ImplicitRungeKuttaSolverParameters
  // ----------------------------------
 
  struct ImplicitRungeKuttaSolverParameters
  : public Dune::Fem::LocalParameter< ImplicitRungeKuttaSolverParameters, ImplicitRungeKuttaSolverParameters >
  {
    enum { noVerbosity = 0,  noConvergenceVerbosity = 1,
           cflVerbosity = 2, fullVerbosity = 3 };
 
  protected:
    // key prefix, default is fem.ode (can be overloaded by user)
    const std::string keyPrefix_;
 
    // number of minimal iterations that the linear solver should do
    // if the number of iterations done is smaller then the cfl number is increased
    const int minIter_;
    // number of maximal iterations that the linear solver should do
    // if the number of iterations larger then the cfl number is decreased
    const int maxIter_;
    // factor for cfl number on increase (decrease is 0.5)
    const double sigma_;
 
    Dune::Fem::ParameterReader parameter_;
 
  public:
    ImplicitRungeKuttaSolverParameters ( const std::string keyPrefix, const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
      : keyPrefix_( keyPrefix ),
        minIter_( parameter.getValue< int >( keyPrefix_ + "miniterations", 14 ) ),
        maxIter_( parameter.getValue< int >( keyPrefix_ + "maxiterations" , 16 ) ),
        sigma_( parameter.getValue< double >( keyPrefix_ + "cflincrease" , 1.1 ) ),
        parameter_( parameter )
    {}
 
    ImplicitRungeKuttaSolverParameters ( const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
      : ImplicitRungeKuttaSolverParameters( "fem.ode.", parameter )
    {}
 
    // destructor (virtual)
    virtual ~ImplicitRungeKuttaSolverParameters() {}
 
    const Dune::Fem::ParameterReader &parameter () const { return parameter_; }
 
    virtual double tolerance () const
    {
      return parameter().getValue< double >( keyPrefix_ + "tolerance" , 1e-6 );
    }
 
    virtual int iterations() const
    {
      return parameter().getValue< int >( keyPrefix_ + "iterations" , 1000 );
    }
 
    virtual int verbose () const
    {
      static const std::string verboseTypeTable[] = { "none", "noconv", "cfl", "full" };
      return parameter().getEnum( keyPrefix_ + "verbose", verboseTypeTable, 0 );
    }
 
    virtual double cflStart () const
    {
      return parameter().getValue< double >( keyPrefix_ + "cflStart", 1 );
    }
 
    virtual double cflMax () const
    {
      return parameter().getValue< double >( keyPrefix_ + "cflMax" , std::numeric_limits< double >::max() );
    }
 
    double initialDeltaT ( double dt ) const
    {
      return std::min( parameter().getValue< double >( keyPrefix_ + "initialdt", 987654321 ), dt );
    }
 
    virtual bool cflFactor( const double imOpTimeStepEstimate,
                            const double exOpTimeStepEstimate,
                            const int numberOfLinearIterations,
                            bool converged,
                            double &factor) const
    {
      const int iter = numberOfLinearIterations;
      factor = 1.;
      bool changed = false;
      if (converged)
      {
        if (iter < minIter_)
        {
          if( imOpTimeStepEstimate <= exOpTimeStepEstimate )
          {
            factor = sigma_;
            changed = true;
          }
        }
        else if (iter > maxIter_)
        {
          factor = (double)maxIter_/(sigma_*(double)iter);
          changed = true;
        }
      }
      else
      {
        factor = 0.5;
        changed = true;
      }
      return changed;
    }
 
    virtual void initTimeStepEstimate ( const double dtEstExpl, const double dtEstImpl, double &dtEst, double &cfl ) const
    {
      // initial time step already set to explicit time step
      dtEst = dtEstExpl;
 
      // heuristics for initial CFL number
      cfl = 1.0;
      if( (dtEstImpl > 0) && (dtEstExpl > dtEstImpl) )
        cfl = dtEstExpl / dtEstImpl;
    }
 
    // return number of max linear iterations per newton step
    virtual int maxLinearIterations () const { return maxIter_; }
 
    virtual int selectedSolver( const int order ) const
    {
      const std::string names [] = { "ImplicitEuler", "CrankNicolson", "DIRK23", "DIRK34", "SDIRK22" };
      // by default select according to order
      return parameter().getEnum( keyPrefix_ + "solvername", names, order-1 ) + 1;
    }
  };
 
 
 
  // ImplicitRungeKuttaTimeStepControl
  // ---------------------------------
 
  class ImplicitRungeKuttaTimeStepControl
  {
    typedef ImplicitRungeKuttaTimeStepControl ThisType;
 
  public:
    typedef Dune::Fem::TimeProviderBase TimeProviderType;
    typedef ImplicitRungeKuttaSolverParameters ParameterType;
 
    ImplicitRungeKuttaTimeStepControl ( TimeProviderType &timeProvider, const ParameterType &parameters )
    : timeProvider_( timeProvider ),
      parameters_( parameters.clone() ),
      cfl_( parameters_->cflStart() ),
      cflMax_( parameters_->cflMax() ),
      verbose_( parameters_->verbose() ),
      initialized_( false )
    {}
 
    explicit ImplicitRungeKuttaTimeStepControl ( TimeProviderType &timeProvider, const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : timeProvider_( timeProvider ),
      parameters_( std::make_shared<ParameterType>( parameter ) ),
      cfl_( parameters_->cflStart() ),
      cflMax_( parameters_->cflMax() ),
      verbose_( parameters_->verbose() ),
      initialized_( false )
    {}
 
    double time () const { return timeProvider_.time(); }
    double timeStepSize () const { return timeProvider_.deltaT(); }
 
    void initialTimeStepSize ( double helmholtzEstimate, double sourceTermEstimate )
    {
      double estimate = std::numeric_limits< double >::max();
      parameters().initTimeStepEstimate( sourceTermEstimate, helmholtzEstimate, estimate, cfl_ );
      timeProvider_.provideTimeStepEstimate( estimate );
      initialized_ = true;
    }
 
    template< class Monitor >
    void reduceTimeStep ( double helmholtzEstimate, double sourceTermEstimate, const Monitor &monitor )
    {
      if( !initialized_ )
        DUNE_THROW( Dune::InvalidStateException, "ImplicitRungeKuttaSolver must be initialized before first solve." );
 
      double factor( 1 );
      parameters().cflFactor( helmholtzEstimate, sourceTermEstimate, monitor.linearSolverIterations_, false, factor );
 
      if( !((factor >= std::numeric_limits< double >::min()) && (factor < 1.0)) )
        DUNE_THROW( Dune::InvalidStateException, "invalid cfl factor: " << factor );
 
      cfl_ *= factor;
 
      if( (verbose_ >= ImplicitRungeKuttaSolverParameters::noConvergenceVerbosity) && (Dune::Fem::MPIManager::rank() == 0) )
      {
        Dune::derr << "Implicit Runge-Kutta step failed to converge." << std::endl;
        Dune::derr << "New cfl number: " << cfl_
                   << ", iterations per time step: ILS = " << monitor.linearSolverIterations_
                   << ", INLS = " << monitor.newtonIterations_
                   << std::endl;
      }
 
      timeProvider_.provideTimeStepEstimate( factor * timeStepSize() );
      timeProvider_.invalidateTimeStep();
    }
 
    template< class Monitor >
    void timeStepEstimate ( double helmholtzEstimate, double sourceTermEstimate, const Monitor &monitor )
    {
      if( !initialized_ )
        DUNE_THROW( Dune::InvalidStateException, "ImplicitRungeKuttaSolver must be initialized before first solve." );
 
      double factor( 1 );
      // true means converged, which is always true since this function is only called
      // when the implicit solver did converge
      parameters().cflFactor( helmholtzEstimate, sourceTermEstimate, monitor.linearSolverIterations_, true, factor );
      if( !((factor >= std::numeric_limits< double >::min()) && (factor <= std::numeric_limits< double >::max())) )
        DUNE_THROW( Dune::InvalidStateException, "invalid cfl factor: " << factor );
 
      const double oldCfl = cfl_;
      cfl_ = std::min( cflMax_, factor * cfl_ );
 
      timeProvider_.provideTimeStepEstimate( std::min( sourceTermEstimate, cfl_ * helmholtzEstimate ) );
 
      if( (cfl_ != oldCfl) && (verbose_ >= ImplicitRungeKuttaSolverParameters::cflVerbosity) && (Dune::Fem::MPIManager::rank() == 0) )
      {
        Dune::derr << "New cfl number: " << cfl_
                   << ", iterations per time step: ILS = " << monitor.linearSolverIterations_
                   << ", INLS = " << monitor.newtonIterations_
                   << std::endl;
      }
    }
 
    bool computeError () const { return false; }
 
  protected:
    const ParameterType &parameters () const
    {
      assert( parameters_ );
      return *parameters_;
    }
 
    TimeProviderType &timeProvider_;
    std::shared_ptr< const ParameterType > parameters_;
    double cfl_, cflMax_;
    int verbose_;
    bool initialized_;
  };
 
 
 
  // PIDTimeStepControl
  // ------------------
 
  class PIDTimeStepControl : public ImplicitRungeKuttaTimeStepControl
  {
    typedef PIDTimeStepControl ThisType;
    typedef ImplicitRungeKuttaTimeStepControl BaseType;
 
  protected:
    using BaseType :: initialized_;
    using BaseType :: cfl_;
    using BaseType :: parameters ;
  public:
    typedef Dune::Fem::TimeProviderBase TimeProviderType;
    typedef typename BaseType::ParameterType ParameterType;
 
    PIDTimeStepControl ( TimeProviderType &timeProvider, const ParameterType &parameters )
    : BaseType( timeProvider, parameters ),
      errors_(),
      tol_( 1e-3 )
    {
      if( parameters.parameter().getValue("fem.ode.pidcontrol", bool(false) ) )
      {
        tol_ = parameters.parameter().getValue("fem.ode.pidtolerance", tol_ );
        errors_.resize( 3, tol_ );
      }
    }
 
    PIDTimeStepControl ( TimeProviderType &timeProvider, const Dune::Fem::ParameterReader &parameter = Dune::Fem::Parameter::container() )
    : BaseType( timeProvider, parameter ),
      errors_(),
      tol_( 1e-3 )
    {
      if( parameter.getValue("fem.ode.pidcontrol", bool(false) ) )
      {
        tol_ = parameter.getValue("fem.ode.pidtolerance", tol_ );
        errors_.resize( 3, tol_ );
      }
    }
 
    bool computeError () const { return ! errors_.empty() ; }
 
    template< class Monitor >
    void timeStepEstimate ( double helmholtzEstimate, double sourceTermEstimate, const Monitor &monitor )
    {
      if( !initialized_ )
        DUNE_THROW( Dune::InvalidStateException, "ImplicitRungeKuttaSolver must be initialized before first solve." );
 
      if( computeError() ) // use pid control
      {
        cfl_ = 1.0; // reset cfl for next reduceTimeStep
        double dtEst = pidTimeStepControl( std::min( sourceTermEstimate, helmholtzEstimate ), monitor );
        /*
        const int targetIterations = parameters().maxLinearIterations();
        if( monitor.linearSolverIterations_ > targetIterations &&
            targetIterations > 0 )
        {
          dtEst *= double( targetIterations ) / double(monitor.linearSolverIterations_);
        }
        */
        std::cout << "Set dt = " << dtEst << std::endl;
        timeProvider_.provideTimeStepEstimate( dtEst );
 
        if( (verbose_ >= ImplicitRungeKuttaSolverParameters::cflVerbosity) && (Dune::Fem::MPIManager::rank() == 0) )
        {
          Dune::derr << "New dt: " << dtEst
                     << ", iterations per time step: ILS = " << monitor.linearSolverIterations_
                     << ", INLS = " << monitor.newtonIterations_
                     << std::endl;
        }
      }
      else
      {
        BaseType::timeStepEstimate( helmholtzEstimate, sourceTermEstimate, monitor );
      }
    }
 
    template < class Monitor >
    double pidTimeStepControl( const double dt, const Monitor& monitor )
    {
      // get error || u^n - u^n+1 || / || u^n+1 || from monitor
      const double error = monitor.error_;
      std::cout << error << " error " << std::endl;
      if( std::abs( error ) < 1e-12 ) return 10. * dt;
 
      // shift errors
      for( int i=0; i<2; ++i )
      {
        errors_[ i ] = errors_[i+1];
      }
 
      // store new error
      errors_[ 2 ] = error ;
 
      if( error > tol_ )
      {
        // adjust dt by given tolerance
        const double newDt = dt * tol_ / error;
        return newDt;
      }
      else if( error > 1e-12 )
      {
        // values taking from turek time stepping paper
        const double kP = 0.075 ;
        const double kI = 0.175 ;
        const double kD = 0.01 ;
        const double newDt = (dt * std::pow( errors_[ 1 ] / errors_[ 2 ], kP ) *
                             std::pow( tol_         / errors_[ 2 ], kI ) *
                             std::pow( errors_[0]*errors_[0]/errors_[ 1 ]/errors_[ 2 ], kD ));
        std::cout << "newDt = " << newDt << std::endl;
        return newDt;
      }
 
      return dt ;
    }
 
  protected:
    std::vector< double > errors_;
    double tol_;
  };
 
} // namespace DuneODE
 
#endif // #ifndef DUNE_FEM_SOLVER_RUNGEKUTTA_TIMESTEPCONTROL_HH