Feel::Aitken< fs_type > Class Template Reference

Aitken relaxation method for fixed point iterations. More...

#include <aitken2.hpp>

List of all members.

Public Types
typedef fs_type	functionspace_type
typedef boost::shared_ptr < functionspace_type >	functionspace_ptrtype
typedef functionspace_type::element_type	element_type
typedef functionspace_type::template Element< typename functionspace_type::value_type, typename VectorUblas< typename functionspace_type::value_type > ::range::type >	element_range_type
typedef fs_type	functionspace_type
typedef boost::shared_ptr < functionspace_type >	functionspace_ptrtype
typedef functionspace_type::element_type	element_type
typedef functionspace_type::template Element< typename functionspace_type::value_type, typename VectorUblas< typename functionspace_type::value_type > ::range::type >	element_range_type
Public Member Functions
	Aitken (functionspace_ptrtype _Xh, double _failsafeParameter=1)
	Aitken (Aitken const &tc)
	~Aitken ()
void	initialize (element_type const &residual, element_type const &elem)
void	initialize (element_type const &residual, element_range_type const &elem)
void	setElement (element_type const &residual, element_type const &elem)
void	setElement (element_type const &residual, element_range_type const &elem)
double	calculateParameter ()
void	relaxationStep (element_type &new_elem)
void	shiftRight ()
void	resetPreviousParameter ()
	Aitken (functionspace_ptrtype _Xh, double _failsafeParameter=0.1)
	Aitken (Aitken const &tc)
	~Aitken ()
void	initialize (element_type const &residual, element_type const &elem)
void	initialize (element_type const &residual, element_range_type const &elem)
void	setElement (element_type const &residual, element_type const &elem)
void	setElement (element_type const &residual, element_range_type const &elem)
double	calculateParameter ()
void	relaxationStep (element_type &new_elem)
void	shiftRight ()
void	resetPreviousParameter ()

---

Detailed Description

template<typename fs_type>
class Feel::Aitken< fs_type >

Aitken relaxation method for fixed point iterations.

 space_ptrtype Xh;
 space_type::element_type residual( Xh );
 space_type::element_type u_old( Xh );
 space_type::element_type u_new( Xh );
 Aitken<space_type> aitken( Xh );
 // initialize aitken
 aitken.initialize( residual, u_new );
 // reset aitken parameter before entering the fixed point loop
 aitken.resetPreviousParameter();
 // fixed point loop
 for( int i = 0; i < niter; ++i )
 {
   // do some computation
   aitken.SetElement( residual, u_new );
   theta = aitken.calculateParameter();
   // exploit aitken relaxation parameter
   u = theta * u_old + (1-theta)* u_new;
   aitken.shiftRight();
   u_old = u_new;
 }

Author:

Goncalo Pena

Christophe Prud'homme

 space_ptrtype Xh;
 space_type::element_type residual( Xh );
 space_type::element_type u_old( Xh );
 space_type::element_type u_new( Xh );
 Aitken<space_type> aitken( Xh );
 // initialize aitken
 aitken.initialize( residual, u_new );
 // reset aitken parameter before entering the fixed point loop
 aitken.resetPreviousParameter();
 // fixed point loop
 for( int i = 0; i < niter; ++i )
 {
   // do some computation
   aitken.SetElement( residual, u_new );
   theta = aitken.calculateParameter();
   // exploit aitken relaxation parameter
   u = theta * u_new + (1-theta)* u_old;
   aitken.shiftRight();
   u_old = u_new;
 }

Author:

Vincent Chabannes

---

Constructor & Destructor Documentation

template<typename fs_type >

Feel::Aitken< fs_type >::Aitken	(	functionspace_ptrtype	_Xh,
		double	_failsafeParameter = 1
	)		[inline]

Constructor

the _failsafeParameter is set to 1 by default. The _failsafeParameter parameter provides an upper value for the relaxation parameter that will not be exceeded.

Parameters:

_Xh	the function space from which the element will be used
_failsafeParameter	fail safe parameter value

template<typename fs_type >

Feel::Aitken< fs_type >::Aitken

(

Aitken< fs_type > const &

tc

)

[inline]

copy constructor

template<typename fs_type >

Feel::Aitken< fs_type >::~Aitken

(

)

[inline]

destructor

template<typename fs_type >

Feel::Aitken< fs_type >::Aitken	(	functionspace_ptrtype	_Xh,
		double	_failsafeParameter = 0.1
	)		[inline]

Constructor

the _failsafeParameter is set to 1 by default. The _failsafeParameter parameter provides an upper value for the relaxation parameter that will not be exceeded.

Parameters:

_Xh	the function space from which the element will be used
_failsafeParameter	fail safe parameter value

template<typename fs_type >

Feel::Aitken< fs_type >::Aitken

(

Aitken< fs_type > const &

tc

)

[inline]

copy constructor

template<typename fs_type >

Feel::Aitken< fs_type >::~Aitken

(

)

[inline]

destructor

---

Member Function Documentation

template<typename fs_type >

double Feel::Aitken< fs_type >::calculateParameter

(

)

Returns:

the Aitken parameter

References Feel::inner_product().

template<typename fs_type >

double Feel::Aitken< fs_type >::calculateParameter

(

)

Returns:

the Aitken parameter

template<typename fs_type >

void Feel::Aitken< fs_type >::initialize	(	element_type const &	residual,
		element_type const &	elem
	)		[inline]

initiliaze the aitken algorithm

Parameters:

residual	previous residual
elem	previous element

template<typename fs_type >

void Feel::Aitken< fs_type >::initialize	(	element_type const &	residual,
		element_type const &	elem
	)		[inline]

initiliaze the aitken algorithm

Parameters:

residual	previous residual
elem	previous element

template<typename fs_type >

void Feel::Aitken< fs_type >::relaxationStep

(

element_type &

new_elem

)

[inline]

Do a relaxation step

Parameters:

new_elem

new element to compute the relaxation step

template<typename fs_type >

void Feel::Aitken< fs_type >::relaxationStep

(

element_type &

new_elem

)

[inline]

Do a relaxation step

Parameters:

new_elem

new element to compute the relaxation step

template<typename fs_type >

void Feel::Aitken< fs_type >::resetPreviousParameter

(

)

[inline]

reset the previous parameter

template<typename fs_type >

void Feel::Aitken< fs_type >::resetPreviousParameter

(

)

[inline]

reset the previous parameter

template<typename fs_type >

void Feel::Aitken< fs_type >::setElement	(	element_type const &	residual,
		element_type const &	elem
	)		[inline]

Set the current element

Parameters:

residual	current residual
elem	current element

template<typename fs_type >

void Feel::Aitken< fs_type >::setElement	(	element_type const &	residual,
		element_type const &	elem
	)		[inline]

Set the current element

Parameters:

residual	current residual
elem	current element

template<typename fs_type >

void Feel::Aitken< fs_type >::shiftRight

(

)

[inline]

shift current step to previous step. After the call, we are ready for the next step.

template<typename fs_type >

void Feel::Aitken< fs_type >::shiftRight

(

)

[inline]

shift current step to previous step. After the call, we are ready for the next step.