Various arbitary wavelength polarization charge operators of delta-f (df) and full-f (ff) More...

Public Types
using	value_type = get_value_type< Container >

Public Member Functions
	PolCharge ()
	empty object ( no memory allocation) More...

	PolCharge (value_type alpha, std::vector< value_type > eps_gamma, const Geometry &g, direction dir=forward, value_type jfactor=1., std::string mode="df", bool commute=false)
	Construct from Grid. More...

	PolCharge (value_type alpha, std::vector< value_type > eps_gamma, const Geometry &g, bc bcx, bc bcy, direction dir=forward, value_type jfactor=1., std::string mode="df", bool commute=false)
	Construct from boundary conditions. More...

template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...

template<class ContainerType0 >
void	set_chi (const ContainerType0 &sigma)
	Change \(\chi\) in the elliptic or tensor elliptic operator. More...

template<class ContainerType0 >
void	set_chi (const SparseTensor< ContainerType0 > &tau)
	Change \(\chi\) in the elliptic or tensor elliptic operator. More...

template<class ContainerType0 >
void	set_iota (const ContainerType0 &sigma)
	Change \(\iota\) in the tensor elliptic operator. More...

void	set_commute (bool commute)
	Set the commute. More...

bool	get_commute () const
	Get the current state of commute. More...

const Container &	weights () const
	Return the vector making the matrix symmetric. More...

const Container &	precond () const
	Return the default preconditioner to use in conjugate gradient. More...

template<class ContainerType0 , class ContainerType1 >
void	variation (const ContainerType0 &phi, ContainerType1 &varphi)

template<class ContainerType0 , class ContainerType1 >
void	operator() (const ContainerType0 &x, ContainerType1 &y)
	Compute elliptic term and store in output. More...

template<class ContainerType0 , class ContainerType1 >
void	symv (const ContainerType0 &x, ContainerType1 &y)
	Compute elliptic term and store in output. More...

template<class ContainerType0 , class ContainerType1 >
void	symv (value_type alpha, const ContainerType0 &x, value_type beta, ContainerType1 &y)
	Compute elliptic term and add to output. More...

Detailed Description

template<class Geometry, class Matrix, class Container>
class dg::mat::PolCharge< Geometry, Matrix, Container >

Various arbitary wavelength polarization charge operators of delta-f (df) and full-f (ff)

"df"

\[ x = -\Delta \left(1+\alpha\Delta\right)^{-1} \phi \]

\[ \]

"ff"

\[ x = \sqrt{1+\alpha\Delta}^{-1}\left(-\nabla \cdot \chi \nabla\right)\sqrt{1+\alpha\Delta}^{-1}\phi \]

"ffO4"

\[ x = (1+\alpha\Delta)^{-1} \left(-\nabla \cdot \chi \nabla - \Delta \iota \Delta + \nabla \cdot\nabla \cdot 2\iota \nabla \nabla \right)(1+\alpha\Delta)^{-1} \phi \]

Member Typedef Documentation

◆ value_type

template<class Geometry , class Matrix , class Container >

using dg::mat::PolCharge< Geometry, Matrix, Container >::value_type = get_value_type<Container>

Constructor & Destructor Documentation

◆ PolCharge() [1/3]

template<class Geometry , class Matrix , class Container >

dg::mat::PolCharge< Geometry, Matrix, Container >::PolCharge ( )

inline

empty object ( no memory allocation)

◆ PolCharge() [2/3]

template<class Geometry , class Matrix , class Container >

dg::mat::PolCharge< Geometry, Matrix, Container >::PolCharge	(	value_type	alpha,
		std::vector< value_type >	eps_gamma,
		const Geometry &	g,
		direction	dir = `forward`,
		value_type	jfactor = `1.`,
		std::string	mode = `"df"`,
		bool	commute = `false`
	)

inline

Construct from Grid.

Parameters

alpha	alpha of the Helmholtz operator
eps_gamma	epsilon (-vector) for the Helmholtz operator inversion or the sqrt Helmholtz operator inversion
g	The Grid, boundary conditions are taken from here
dir	Direction of the right first derivative in x and y (i.e. `dg::forward`, `dg::backward` or `dg::centered`),
jfactor	( \( = \alpha \) ) scale jump terms (1 is a good value but in some cases 0.1 or 0.01 might be better)
mode	arbitrary wavelength polarization charge mode ("df" / "ff" / "ffO4" are implemented)
commute	false if Helmholtz operators (or their square root) are outside the elliptic or tensorelliptic operator and true otherwise

◆ PolCharge() [3/3]

template<class Geometry , class Matrix , class Container >

dg::mat::PolCharge< Geometry, Matrix, Container >::PolCharge	(	value_type	alpha,
		std::vector< value_type >	eps_gamma,
		const Geometry &	g,
		bc	bcx,
		bc	bcy,
		direction	dir = `forward`,
		value_type	jfactor = `1.`,
		std::string	mode = `"df"`,
		bool	commute = `false`
	)

inline

Construct from boundary conditions.

Parameters

alpha	alpha of the Helmholtz operator
eps_gamma	epsilon (-vector) for the Helmholtz operator inversion or the sqrt Helmholtz operator inversion
g	The Grid, boundary conditions are taken from here
bcx	boundary condition in x
bcy	boundary contition in y
dir	Direction of the right first derivative in x and y (i.e. `dg::forward`, `dg::backward` or `dg::centered`),
jfactor	( \( = \alpha \) ) scale jump terms (1 is a good value but in some cases 0.1 or 0.01 might be better)
mode	arbitrary wavelength polarization charge mode ("df" / "ff" / "ffO4" (O as in Order!) are implemented)
commute	false if Helmholtz operators (or their square root) are outside the elliptic or tensorelliptic operator and true otherwise

Member Function Documentation

◆ construct()

template<class Geometry , class Matrix , class Container >

template<class ... Params>

void dg::mat::PolCharge< Geometry, Matrix, Container >::construct ( Params &&... ps )

inline

Perfect forward parameters to one of the constructors.

Template Parameters

Params deduced by the compiler

Parameters

ps	parameters forwarded to constructors

◆ get_commute()

template<class Geometry , class Matrix , class Container >

bool dg::mat::PolCharge< Geometry, Matrix, Container >::get_commute ( ) const

inline

Get the current state of commute.

Returns: Either true or false.

◆ operator()()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::operator()	(	const ContainerType0 &	x,
		ContainerType1 &	y
	)

inline

Compute elliptic term and store in output.

i.e. y=M*x

Parameters

x	left-hand-side
y	result

Template Parameters

ContainerTypes must be usable with Container in The dg dispatch system

◆ precond()

template<class Geometry , class Matrix , class Container >

const Container & dg::mat::PolCharge< Geometry, Matrix, Container >::precond ( ) const

inline

Return the default preconditioner to use in conjugate gradient.

Currently returns the inverse scalar part of \( \chi\). This is especially good when \( \chi\) exhibits large amplitudes or variations

Returns: the inverse of \(\chi\).

◆ set_chi() [1/2]

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::set_chi ( const ContainerType0 & sigma )

inline

Change \(\chi\) in the elliptic or tensor elliptic operator.

Parameters

sigma The new scalar part in \(\chi\) (all elements must be >0)

Template Parameters

ContainerType0 must be usable with Container in The dg dispatch system

◆ set_chi() [2/2]

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::set_chi ( const SparseTensor< ContainerType0 > & tau )

inline

Change \(\chi\) in the elliptic or tensor elliptic operator.

Parameters

tau	The new tensor part in \(\chi\) (all elements must be >0)

Template Parameters

ContainerType0 must be usable in dg::assign to Container

◆ set_commute()

template<class Geometry , class Matrix , class Container >

void dg::mat::PolCharge< Geometry, Matrix, Container >::set_commute ( bool commute )

inline

Set the commute.

Parameters

commute Either true or false.

◆ set_iota()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::set_iota ( const ContainerType0 & sigma )

inline

Change \(\iota\) in the tensor elliptic operator.

Parameters

sigma The new scalar part in \(\chi\) (all elements must be >0)

Template Parameters

ContainerType0 must be usable with Container in The dg dispatch system

◆ symv() [1/2]

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::symv	(	const ContainerType0 &	x,
		ContainerType1 &	y
	)

inline

Compute elliptic term and store in output.

i.e. y=M*x

Parameters

x	left-hand-side
y	result

Template Parameters

ContainerTypes must be usable with Container in The dg dispatch system

◆ symv() [2/2]

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::symv	(	value_type	alpha,
		const ContainerType0 &	x,
		value_type	beta,
		ContainerType1 &	y
	)

inline

Compute elliptic term and add to output.

i.e. y=alpha*M*x+beta*y

Parameters

alpha	a scalar
x	left-hand-side
beta	a scalar
y	result

Template Parameters

ContainerTypes must be usable with Container in The dg dispatch system

◆ variation()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

void dg::mat::PolCharge< Geometry, Matrix, Container >::variation	(	const ContainerType0 &	phi,
		ContainerType1 &	varphi
	)

inline

◆ weights()

template<class Geometry , class Matrix , class Container >

const Container & dg::mat::PolCharge< Geometry, Matrix, Container >::weights ( ) const

inline

Return the vector making the matrix symmetric.

i.e. the volume form

Returns: volume form including weights

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

polarization.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ PolCharge() [1/3]

◆ PolCharge() [2/3]

◆ PolCharge() [3/3]

Member Function Documentation

◆ construct()

◆ get_commute()

◆ operator()()

◆ precond()

◆ set_chi() [1/2]

◆ set_chi() [2/2]

◆ set_commute()

◆ set_iota()

◆ symv() [1/2]

◆ symv() [2/2]

◆ variation()

◆ weights()