#include <bdf.hpp>

Detailed Description

template<typename SpaceType>
class Feel::Bdf< SpaceType >

Backward differencing formula time discretization.

A differential equation of the form

$ M u' = A u + f $

is discretized in time as

$M p'(t_{k+1}) = A u_{k+1} + f_{k+1}$

where p denotes the polynomial of order n in t that interpolates (t_i,u_i) for i = k-n+1,...,k+1.

The approximative time derivative $p'(t_{k+1})$ is a linear combination of state vectors u_i:

$p'(t_{k+1}) = \frac{1}{\Delta t} (\alpha_0 u_{k+1} - \sum_{i=0}^n \alpha_i u_{k+1-i} )$

Thus we have

$\frac{\alpha_0}{\Delta t} M u_{k+1} = A u_{k+1} + f + M \bar{p}$

with

$\bar{p} = \frac{1}{\Delta t} \sum_{i=1}^n \alpha_i u_{k+1-i}$

This class stores the n last state vectors in order to be able to calculate $\bar{p}$ . It also provides alpha_i and can extrapolate the the new state from the n last states with a polynomial of order n-1:

$u_{k+1} \approx \sum_{i=0}^{n-1} \beta_i u_{k-i}$

Inherits Feel::BdfBase.

Public Types
typedef boost::shared_ptr < bdf_type >	bdf_ptrtype

typedef Bdf< SpaceType >	bdf_type

typedef space_type::element_type	element_type

typedef space_type::element_type	element_type

typedef node< value_type >::type	node_type

typedef node< value_type >::type	node_type

typedef space_type::return_type	return_type

typedef space_type::return_type	return_type

typedef boost::shared_ptr < space_type >	space_ptrtype

typedef boost::shared_ptr < space_type >	space_ptrtype

typedef SpaceType	space_type

typedef SpaceType	space_type

typedef super::time_iterator	time_iterator

typedef boost::shared_ptr < element_type >	unknown_type

typedef boost::shared_ptr < element_type >	unknown_type

typedef std::vector< unknown_type >	unknowns_type

typedef std::vector< unknown_type >	unknowns_type

typedef element_type::value_type	value_type

typedef element_type::value_type	value_type

Public Types inherited from Feel::BdfBase
typedef std::vector< double > ::const_iterator	time_const_iterator

typedef std::vector< double > ::iterator	time_iterator

typedef std::vector< double >	time_values_map_type

Public Member Functions
	Bdf (space_ptrtype const &space)

	Bdf (po::variables_map const &vm, space_ptrtype const &space, std::string const &name, std::string const &prefix="")

	Bdf (space_ptrtype const &space, std::string const &name)

	Bdf (Bdf const &b)
	copy operator

bdf_ptrtype	deepCopy () const
	return a deep copy of the bdf object

element_type	derivate (int, scalar_type dt) const

element_type	derivate (int n) const

double	derivateCoefficient (int n, size_type i, double dt=1.0) const
	Return the i-th coefficient of the time derivative alpha_i.

element_type	extrapolate (int n) const

double	extrapolateCoefficient (int n, size_type i, double dt=1.0) const
	Return the i-th coefficient of the time extrapolation beta_i.

void	initialize (element_type const &u0)

void	initialize (unknowns_type const &uv0)

void	initialize (element_type const &u0)

void	initialize (unknowns_type const &uv0)

void	loadCurrent ()

BDFTimeScheme	order () const

element_type	poly () const

element_type	polyDeriv () const

double	restart ()

template<typename container_type >
void	setUnknown (int i, typename space_type::template Element< value_type, container_type > const &e)

template<typename container_type >
void	setUnknown (int i, typename space_type::template Element< value_type, container_type > const &e)

template<typename container_type >
void	shiftRight (typename space_type::template Element< value_type, container_type > const &u_curr)

template<typename container_type >
void	shiftRight (typename space_type::template Element< value_type, container_type > const &u_curr)

void	showMe (std::ostream &__out=std::cout) const

void	showMe (std::ostream &__out=std::cout) const

double	start ()

double	start (element_type const &u0)

double	start (unknowns_type const &uv0)

element_type &	unknown (int i)
	Return a vector with the last n state vectors.

element_type &	unknown (int i)
	Return a vector with the last n state vectors.

unknowns_type const &	unknowns () const
	Return a vector with the last n state vectors.

unknowns_type const &	unknowns () const
	Return a vector with the last n state vectors.

Public Member Functions inherited from Feel::BdfBase
	BdfBase (po::variables_map const &vm, std::string name, std::string const &prefix, WorldComm const &worldComm)

	BdfBase (std::string name, WorldComm const &worldComm)

	BdfBase (BdfBase const &b)

bool	doRestartAtLastSave () const
	return value of do restart at last save

bool	isFinished () const
	return true if Bdf is finished, false otherwise

bool	isRestart () const
	return the value of the bool restart

int	iteration () const
	return the iteration number

double	next () const

int	nRestart () const
	return the number of restarts

int	numberOfIterationsBetweenOrderChange () const
	return the number of iterations between order change

int	numberOfIterationsSinceOrderChange () const
	return the number of iterations since last order change

BdfBase &	operator= (BdfBase const &b)

fs::path	path ()
	return the relative path where the bdf data is stored

double	polyCoefficient (int i) const

double	polyDerivCoefficient (int i) const

void	print () const

bool	rankProcInNameOfFiles () const

double	realTimePerIteration () const
	return the real time in seconds spent in the iteration

double	restart ()
	restart the bdf

fs::path	restartPath ()

int	saveFreq () const

bool	saveInFile () const

template<class Archive >
void	serialize (Archive &ar, const unsigned int version)
	save/load Bdf metadata

void	setOrder (int order)

void	setRankProcInNameOfFiles (bool b)

void	setRestart (bool doRestart)

void	setRestartAtLastSave (bool b)

void	setRestartPath (std::string s)

void	setSaveFreq (int v)

void	setSaveInFile (bool b)

void	setSteady (bool steady=true)

void	setStrategy (int strategy)

void	setTimeFinal (double T)

void	setTimeInitial (double ti)

void	setTimeStep (double dt)

virtual void	shiftRight ()

double	start ()
	start the bdf

BDFState	state () const
	return the state of the BDF

BDFStragegy	strategy () const
	return the BDF strategy

double	time () const
	return the current time

double	timeFinal () const
	return the final time

double	timeInitial () const
	return the initial time

int	timeOrder () const
	return the order in time

double	timeStep () const
	return the final step

time_values_map_type	timeValues () const
	return vector of time

virtual void	update ()

WorldComm const &	worldComm () const

Friends
class	boost::serialization::access

Additional Inherited Members
Protected Member Functions inherited from Feel::BdfBase
void	init ()

Protected Attributes inherited from Feel::BdfBase
std::vector< ublas::vector < double > >	M_alpha
	Coefficients $\alpha_i$ of the time bdf discretization.

std::vector< ublas::vector < double > >	M_beta
	Coefficients $\beta_i$ of the extrapolation.

double	M_dt
	timestep

int	M_iteration

int	M_iterations_between_order_change

int	M_last_iteration_since_order_change

int	M_n_restart

std::string	M_name
	name of the file holding the bdf data

int	M_order
	time order

int	M_order_cur

fs::path	M_path_save
	path to the directory to store the functions

bool	M_rankProcInNameOfFiles
	put the rank of the processor in generated files

double	M_real_time_per_iteration
	real time spent per iteration (in seconds)

bool	M_restart
	do a restart

bool	M_restartAtLastSave
	do restart with ti the last save

fs::path	M_restartPath
	restart path

int	M_saveFreq
	frequence of save solutions

bool	M_saveInFile
	Save solutions in file after each step.

BDFState	M_state
	Bdf state.

BDFStragegy	M_strategy
	BDF strategy (constant timestep or adaptative timestep)

double	M_Tf
	final time

double	M_Ti
	initial time to start

double	M_time
	time

std::vector< int >	M_time_orders
	vector that holds the time order at each bdf step

time_values_map_type	M_time_values_map
	vector that holds the time value at each bdf step

boost::timer	M_timer
	timer for real time per iteration

WorldComm	M_worldComm
	mpi communicator tool

Constructor & Destructor Documentation

template<typename SpaceType >

Feel::Bdf< SpaceType >::Bdf ( space_ptrtype const & space )

Constructor

Parameters

space	approximation space
n	order of the BDF

BDF_ORDER_FOUR:

template<typename SpaceType >

Feel::Bdf< SpaceType >::Bdf	(	po::variables_map const &	vm,
		space_ptrtype const &	space,
		std::string const &	name,
		std::string const &	prefix = `""`
	)

Constructor

Parameters

space	approximation space
n	order of the BDF

template<typename SpaceType >

Feel::Bdf< SpaceType >::Bdf	(	space_ptrtype const &	space,
		std::string const &	name
	)

Constructor

Parameters

space	approximation space
name	name of the BDF

Member Function Documentation

template<typename SpaceType >

Bdf< SpaceType >::element_type Feel::Bdf< SpaceType >::derivate	(	int	n,
		scalar_type	dt
	)		const

Returns the right hand side $\bar{p}$ of the time derivative formula

template<typename SpaceType >

Bdf< SpaceType >::element_type Feel::Bdf< SpaceType >::derivate ( int n ) const

Returns the right hand side $\bar{p} \Delta t$ of the time derivative formula. The timestep is taken into account elsewhere, e. g. in the mass matrix.

template<typename SpaceType >

Bdf< SpaceType >::element_type Feel::Bdf< SpaceType >::extrapolate ( int n ) const

Compute the polynomial extrapolation approximation of order n-1 of u^{n+1} defined by the n stored state vectors

References Feel::Vector< T >::size().

template<typename SpaceType >

void Feel::Bdf< SpaceType >::initialize ( element_type const & u0 )

Initialize all the entries of the unknown vector to be derived with the vector u0 (duplicated)

template<typename SpaceType >

void Feel::Bdf< SpaceType >::initialize ( unknowns_type const & uv0 )

Initialize all the entries of the unknown vector to be derived with a set of vectors uv0

template<typename SpaceType>

void Feel::Bdf< SpaceType >::initialize ( element_type const & u0 )

Initialize all the entries of the unknown vector to be derived with the vector u0 (duplicated)

template<typename SpaceType>

void Feel::Bdf< SpaceType >::initialize ( unknowns_type const & uv0 )

Initialize all the entries of the unknown vector to be derived with a set of vectors uv0

template<typename SpaceType>

BDFTimeScheme Feel::Bdf< SpaceType >::order ( ) const

inline

get the order of the BDF

Returns: order of the BDF

template<typename SpaceType >

Bdf< SpaceType >::element_type Feel::Bdf< SpaceType >::poly ( ) const

Compute the polynomial extrapolation approximation of order n-1 of u^{n+1} defined by the n stored state vectors

template<typename SpaceType >

Bdf< SpaceType >::element_type Feel::Bdf< SpaceType >::polyDeriv ( ) const

Returns the right hand side $\bar{p}$ of the time derivative formula

template<typename SpaceType >

double Feel::Bdf< SpaceType >::restart ( void )

restart the bdf

template<typename SpaceType >

template<typename container_type >

void Feel::Bdf< SpaceType >::shiftRight ( typename space_type::template Element< value_type, container_type > const & u_curr )

Update the vectors of the previous time steps by shifting on the right the old values.

Parameters

u_curr current (new) value of the state vector

template<typename SpaceType>

template<typename container_type >

void Feel::Bdf< SpaceType >::shiftRight ( typename space_type::template Element< value_type, container_type > const & u_curr )

Update the vectors of the previous time steps by shifting on the right the old values.

Parameters

u_curr current (new) value of the state vector

template<typename SpaceType >

double Feel::Bdf< SpaceType >::start ( )

start the bdf

The documentation for this class was generated from the following files:

Detailed Description

template<typename SpaceType> class Feel::Bdf< SpaceType >

Public Types

Public Member Functions

Friends

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

template<typename SpaceType>
class Feel::Bdf< SpaceType >