explicit_timesteppers.h

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//Header functions for classes that represent explicit time-stepping schemes

//Include guards to prevent multiple inclusion of this header
#ifndef OOMPH_EXPLICIT_TIMESTEPPERS
#define OOMPH_EXPLICIT_TIMESTEPPERS

// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
  #include <oomph-lib-config.h>
#endif


#ifdef OOMPH_HAS_MPI
#include "mpi.h"
#endif

#include "Vector.h"
#include "double_vector.h"
#include "oomph_utilities.h"

namespace oomph
{

 class Time;

//===============================================================
/// Class for objects than can be advanced in time by an Explicit
/// Timestepper.
/// WARNING: For explicit time stepping to work the object's residual
/// function (as used by get_inverse_mass_matrix_times_residuals(..)) MUST
/// be in the form r = f(t, u) - [timestepper approximation to dudt]!
/// Standard implicit time stepping will work with plenty of residuals that
/// don't fit into this form. Some examples where implicit time stepping
/// will work fine but explicit will fail:
/// 1) The negation of the above formula, this implementation will end up
/// using dudt = - f(u,t).
/// 2) A residual which is implicit or non-linear in dudt, such as r = dudt
/// - u x dudt.
//===============================================================
class ExplicitTimeSteppableObject
{
 //Dummy double value for time
 static double Dummy_time_value;
public:

 ///Empty constructor
 ExplicitTimeSteppableObject() { }

 /// Broken copy constructor
 ExplicitTimeSteppableObject(const ExplicitTimeSteppableObject&) 
  { 
   BrokenCopy::broken_copy("ExplicitTimeSteppableObject");
  } 
 
 /// Broken assignment operator
 void operator=(const ExplicitTimeSteppableObject&) 
  {
   BrokenCopy::broken_assign("ExplicitTimeSteppableObject");
  } 

 ///Empty destructor
 virtual ~ExplicitTimeSteppableObject() { }

 ///\short A single virtual function that returns the residuals
 ///vector multiplied by the inverse mass matrix
 virtual void get_dvaluesdt(DoubleVector &minv_res);
  
 /// Function that gets the values of the dofs in the object
 virtual void get_dofs(DoubleVector &dofs) const;

 /// Function that gets the history values of the dofs in the object
 virtual void get_dofs(const unsigned &t, DoubleVector &dofs) const;

 /// Function that sets the values of the dofs in the object
 virtual void set_dofs(const DoubleVector &dofs);

 ///Function that adds the values to the dofs
 virtual void add_to_dofs(const double &lambda,
                          const DoubleVector &increment_dofs);

 /// \short Empty virtual function to do anything needed before a stage of
 /// an explicit time step (Runge-Kutta steps contain multiple stages per
 /// time step, most others only contain one).
 virtual void actions_before_explicit_stage() {}

 /// \short Empty virtual function that should be overloaded to update and
 /// slaved data or boundary conditions that should be advanced after each
 /// stage of an explicit time step (Runge-Kutta steps contain multiple
 /// stages per time step, most others only contain one).
 virtual void actions_after_explicit_stage() {}

 /// \short Empty virtual function that can be overloaded to do anything
 /// needed before an explicit step.
 virtual void actions_before_explicit_timestep() {}

 /// \short Empty virtual function that can be overloaded to do anything
 /// needed after an explicit step.
 virtual void actions_after_explicit_timestep() {}

 ///\short Broken virtual function that should be overloaded to
 ///return access to the local time in the object
 virtual double &time();

 /// \short Virtual function that should be overloaded to return a pointer to a
 /// Time object.
 virtual Time* time_pt() const;
};


//=====================================================================
/// A Base class for explicit timesteppers
//=====================================================================
class ExplicitTimeStepper
{
 protected:

 /// \short String that indicates the type of the timestepper 
 ///(e.g. "RungeKutta", etc.)
 std::string Type;

public:
 
 /// \short Empty Constructor. 
 ExplicitTimeStepper()  {}

 /// Broken copy constructor
 ExplicitTimeStepper(const ExplicitTimeStepper&) 
  { 
   BrokenCopy::broken_copy("ExplicitTimeStepper");
  } 
 
 /// Broken assignment operator
 void operator=(const ExplicitTimeStepper&) 
  {
   BrokenCopy::broken_assign("ExplicitTimeStepper");
  } 

 /// Empty virtual destructor --- no memory is allocated in this class
 virtual ~ExplicitTimeStepper(){}

 /// Pure virtual function that is used to advance time in the object
 // referenced by object_pt by an amount dt
 virtual void timestep(ExplicitTimeSteppableObject* const &object_pt,
                       const double &dt)=0;
 
};


///===========================================================
///Simple first-order Euler Timestepping
//============================================================
class Euler : public ExplicitTimeStepper
{
public:
 
 ///Constructor, set the type
 Euler() {Type="Euler";}

 /// Broken copy constructor
 Euler(const Euler&) 
  { 
   BrokenCopy::broken_copy("Euler");
  } 
 
 /// Broken assignment operator
 void operator=(const Euler&) 
  {
   BrokenCopy::broken_assign("Euler");
  } 

 /// \short Overload function that is used to advance time in the object
 /// reference by object_pt by an amount dt
 void timestep(ExplicitTimeSteppableObject* const &object_pt,
               const double &dt);
};

///===========================================================
///Standard Runge Kutta Timestepping
//============================================================
template<unsigned ORDER>
class RungeKutta : public ExplicitTimeStepper
{
public:
 
 ///Constructor, set the type
 RungeKutta()
  {
   Type="RungeKutta";
  }

 /// Broken copy constructor
 RungeKutta(const RungeKutta&) 
  { 
   BrokenCopy::broken_copy("RungeKutta");
  } 
 
 /// Broken assignment operator
 void operator=(const RungeKutta&) 
  {
   BrokenCopy::broken_assign("RungeKutta");
  } 

 /// Function that is used to advance time in the object
 // reference by object_pt by an amount dt
 void timestep(ExplicitTimeSteppableObject* const &object_pt,
               const double &dt);
};


///===========================================================
///Runge Kutta Timestepping that uses low storage
//============================================================
template<unsigned ORDER>
class LowStorageRungeKutta : public ExplicitTimeStepper
{
 //Storage for the coefficients
 Vector<double> A, B, C;

public:
 
 ///Constructor, set the type
 LowStorageRungeKutta();

 /// Broken copy constructor
 LowStorageRungeKutta(const LowStorageRungeKutta&) 
  { 
   BrokenCopy::broken_copy("LowStorageRungeKutta");
  } 
 
 /// Broken assignment operator
 void operator=(const LowStorageRungeKutta&) 
  {
   BrokenCopy::broken_assign("LowStorageRungeKutta");
  } 

 /// Function that is used to advance the solution by time dt
 void timestep(ExplicitTimeSteppableObject* const &object_pt,
               const double &dt);

};


 ///===========================================================
 /// An explicit version of BDF3 (i.e. uses derivative evaluation at y_n
 /// instead of y_{n+1}). Useful as a predictor because it is third order
 /// accurate but requires only one function evaluation (i.e. only one mass
 /// matrix inversion + residual calculation).
 //============================================================
 class EBDF3 : public ExplicitTimeStepper
 {
  double Yn_weight;
  double Ynm1_weight;
  double Ynm2_weight;
  double Fn_weight;

 public:
 
  ///Constructor, set the type
  EBDF3() {}

  /// Broken copy constructor
  EBDF3(const EBDF3&) 
  { 
   BrokenCopy::broken_copy("EBDF3");
  } 
 
  /// Broken assignment operator
  void operator=(const EBDF3&) 
  {
   BrokenCopy::broken_assign("EBDF3");
  }

  void set_weights(const double &dtn, const double &dtnm1, const double &dtnm2);

  /// Function that is used to advance the solution by time dt
  void timestep(ExplicitTimeSteppableObject* const &object_pt,
                const double &dt);

 };

}

#endif