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animal::integration::Solver< DerivativeF, StepF, TraitsT > Struct Template Reference

#include <solver.h>

Inheritance diagram for animal::integration::Solver< DerivativeF, StepF, TraitsT >:

List of all members.

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Detailed Description

template<class DerivativeF, class StepF, class TraitsT>
struct animal::integration::Solver< DerivativeF, StepF, TraitsT >

Base class for all explicit Ordinary Differential Equation solvers.

A Solver integrates a function of time over a given time step. Contrary with a Stepper, a Solver can NOT decide to subdivide the given time step for purposes of accuracy.

State and derivative variables are seen as stl-like containers of elementary variables. Iterators begin() and end() are used, and methods * (dereferencing) and ++ (next element) are applied to iterators. Auxiliary state and derivative containers are internally used by the different integration schemes.

The base class is pure virtual. Derived classes implement Euler's method (the simplest), Runge_Kutta with order 2 or 4, and the "modified midpoint method".

Three auxiliary types are used to instanciate the template class:

• DerivativeF provides the solver with a method which computes the time-derivative of a given state at a given time;

• StepF provides the solver with a method which increments a given state by a given derivative and a given time step. When performing second-oder simulations, StepF may implement modified Euler step (also known as Newton-Cotes method) or Stoermer's method.

• TraitsT includes the type definitions needed by the other methods. It also defines how containers are resized, and how to perform linear combinations of derivative variables for Rung-Kutta_4.

Author:

David Bourguignon, March 2000, file animal/integration/solver.h

See also:

Solver_Traits

Solver_Traits_M

Euler

Runge_Kutta_2

Runge_Kutta_4

Modified_Midpoint

Definition at line 71 of file solver.h.

Public Types
typedef TraitsT	Traits
	Traits class: includes all type definitions.
typedef Traits::Real	Real
	Floating-point value for time.
typedef Traits::State	State
	Container of state variables.
typedef Traits::CopyState	CopyState
	Container of copies of state variables.
typedef Traits::Derivative	Derivative
	Container of derivative variables.
typedef Traits::SizeType	SizeType
	Natural number to define container size, typically unsigned int.
Public Member Functions
Constructor
Default constructor is typically used, unless the lower-level objects include special data.
	Solver (const DerivativeF &df=DerivativeF(), const StepF &sf=StepF(), const Traits &tr=Traits())
	Just calls the base class constructor.
virtual	~Solver ()
	Destructor does nothing.
Integration scheme
Implementation of the numerical integration method.
virtual void	doStep (const State &initial_S, State &final_S, const Derivative &initial_D, const Real t, const Real h)=0
	This method implements the integration scheme to be applied (Euler, Runge-Kutta, ...) Given a state initial_S and a derivative initial_D at time t, integrate over a time step h and write the result in final_S.
Call operators
These methods apply time integration. They internally call the doStep method. However, the doStep method may be called directly if the derivative at the beginning of the time step is known.
template<class S> void	operator() (const State &initial_S, S &final_S, const Real t, const Real h)
	Starting from state initial_S at time t, integrate time to t+h and write the result in final_S.
template<class S> void	operator() (S &s, const Real t, const Real h)
	Similar with the other call operator, except that the final state overwrites the initial state.
Resize
Resize the auxiliary container(s).
void	resize (const SizeType size)
	Resize the auxiliary container(s) when the number of elements in the state grows.
Public Attributes
Lower-level objects and algorithms
Traits	traits
	An instance of Traits is defined in order to allow data storage within the Traits.
DerivativeF	writeDerivative
	Computation of the derivative.
StepF	applyStep
	Increment state by a given derivative over a given time step.
Protected Member Functions
virtual void	setSize (const SizeType size)=0
	Pure virtual method used to resize all the additional auxiliary containers used by the derived classes.
Protected Attributes
Derivative	D1
	An auxiliary derivative container used by all integration schemes.

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Member Typedef Documentation

template<class DerivativeF, class StepF, class TraitsT> typedef Traits::CopyState animal::integration::Solver< DerivativeF, StepF, TraitsT >::CopyState

Container of copies of state variables. Reimplemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Definition at line 84 of file solver.h.

template<class DerivativeF, class StepF, class TraitsT> typedef Traits::Derivative animal::integration::Solver< DerivativeF, StepF, TraitsT >::Derivative

Container of derivative variables. Reimplemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Definition at line 87 of file solver.h.

template<class DerivativeF, class StepF, class TraitsT> typedef Traits::Real animal::integration::Solver< DerivativeF, StepF, TraitsT >::Real

Floating-point value for time. Reimplemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Definition at line 78 of file solver.h.

template<class DerivativeF, class StepF, class TraitsT> typedef Traits::SizeType animal::integration::Solver< DerivativeF, StepF, TraitsT >::SizeType

Natural number to define container size, typically unsigned int. Reimplemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Definition at line 90 of file solver.h.

template<class DerivativeF, class StepF, class TraitsT> typedef Traits::State animal::integration::Solver< DerivativeF, StepF, TraitsT >::State

Container of state variables. Reimplemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Definition at line 81 of file solver.h.

template<class DerivativeF, class StepF, class TraitsT> typedef TraitsT animal::integration::Solver< DerivativeF, StepF, TraitsT >::Traits

Traits class: includes all type definitions. Reimplemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Definition at line 75 of file solver.h.

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Constructor & Destructor Documentation

template<class DerivativeF, class StepF, class TraitsT> animal::integration::Solver< DerivativeF, StepF, TraitsT >::Solver (  const DerivativeF &  df = DerivativeF(), const StepF &  sf = StepF(), const Traits &  tr = Traits() )  [inline]

Just calls the base class constructor. Definition at line 124 of file solver.h.

template<class DerivativeF, class StepF, class TraitsT> virtual animal::integration::Solver< DerivativeF, StepF, TraitsT >::~Solver (   )  [inline, virtual]

Destructor does nothing. Definition at line 135 of file solver.h.

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Member Function Documentation

template<class DerivativeF, class StepF, class TraitsT> virtual void animal::integration::Solver< DerivativeF, StepF, TraitsT >::doStep (  const State &  initial_S, State &  final_S, const Derivative &  initial_D, const Real  t, const Real  h )  [pure virtual]

This method implements the integration scheme to be applied (Euler, Runge-Kutta, ...) Given a state initial_S and a derivative initial_D at time t, integrate over a time step h and write the result in final_S. This method is typically called indirectly by the operator () of the solver, but it may be called directly if the derivative at the beginning of the time step is known. Implemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Referenced by animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator()().

template<class DerivativeF, class StepF, class TraitsT> template<class S> void animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator() (  S &  s, const Real  t, const Real  h )  [inline]

Similar with the other call operator, except that the final state overwrites the initial state. Definition at line 188 of file solver.h. References animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator()().

template<class DerivativeF, class StepF, class TraitsT> template<class S> void animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator() (  const State &  initial_S, S &  final_S, const Real  t, const Real  h )  [inline]

Starting from state initial_S at time t, integrate time to t+h and write the result in final_S. Definition at line 171 of file solver.h. References animal::integration::Solver< DerivativeF, StepF, TraitsT >::D1, animal::integration::Solver< DerivativeF, StepF, TraitsT >::doStep(), and animal::integration::Solver< DerivativeF, StepF, TraitsT >::writeDerivative. Referenced by animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator()().

template<class DerivativeF, class StepF, class TraitsT> void animal::integration::Solver< DerivativeF, StepF, TraitsT >::resize (  const SizeType  size  )  [inline]

Resize the auxiliary container(s) when the number of elements in the state grows. Must be called at initialization. Automatically called when the Solver is included within a Driver. Calls method setSize to resize the auxiliary containers included in the derived classes. Definition at line 206 of file solver.h. References animal::integration::Solver< DerivativeF, StepF, TraitsT >::D1, animal::integration::Solver< DerivativeF, StepF, TraitsT >::setSize(), and animal::integration::Solver< DerivativeF, StepF, TraitsT >::traits.

template<class DerivativeF, class StepF, class TraitsT> virtual void animal::integration::Solver< DerivativeF, StepF, TraitsT >::setSize (  const SizeType  size  )  [protected, pure virtual]

Pure virtual method used to resize all the additional auxiliary containers used by the derived classes. Implemented in animal::integration::Euler< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >, animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >, animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >, and animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >. Referenced by animal::integration::Solver< DerivativeF, StepF, TraitsT >::resize().

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Member Data Documentation

template<class DerivativeF, class StepF, class TraitsT> StepF animal::integration::Solver< DerivativeF, StepF, TraitsT >::applyStep

Increment state by a given derivative over a given time step. Computation is performed by applying the call operator () to this object. Definition at line 110 of file solver.h. Referenced by animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >::doStep(), animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >::doStep(), animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >::doStep(), animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >::doStep(), and animal::integration::Euler< DerivativeF, StepF, TraitsT >::doStep().

template<class DerivativeF, class StepF, class TraitsT> Derivative animal::integration::Solver< DerivativeF, StepF, TraitsT >::D1 [protected]

An auxiliary derivative container used by all integration schemes. Definition at line 217 of file solver.h. Referenced by animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator()(), and animal::integration::Solver< DerivativeF, StepF, TraitsT >::resize().

template<class DerivativeF, class StepF, class TraitsT> Traits animal::integration::Solver< DerivativeF, StepF, TraitsT >::traits

An instance of Traits is defined in order to allow data storage within the Traits. The basic solvers (Euler, Runge-Kutta, modified midpoint) do not use this feature. Definition at line 101 of file solver.h. Referenced by animal::integration::Solver< DerivativeF, StepF, TraitsT >::resize().

template<class DerivativeF, class StepF, class TraitsT> DerivativeF animal::integration::Solver< DerivativeF, StepF, TraitsT >::writeDerivative

Computation of the derivative. A functor (function object) is used to represent the computation of the derivative. Computation is performed by applying the call operator () to this object. Definition at line 106 of file solver.h. Referenced by animal::integration::Modified_Midpoint_V< NStepF, DerivativeF, StepF, TraitsT >::doStep(), animal::integration::Modified_Midpoint< N, DerivativeF, StepF, TraitsT >::doStep(), animal::integration::Runge_Kutta_4< DerivativeF, StepF, TraitsT >::doStep(), animal::integration::Runge_Kutta_2< DerivativeF, StepF, TraitsT >::doStep(), and animal::integration::Solver< DerivativeF, StepF, TraitsT >::operator()().

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The documentation for this struct was generated from the following file:

• solver.h

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