EXPERIMENTAL polarization solver class for N. More...

Public Types
using	geometry_type = Geometry

using	matrix_type = Matrix

using	container_type = Container

using	value_type = get_value_type< Container >

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

	PolChargeN (const Geometry &g, direction dir=forward, value_type jfactor=1.)
	Construct from Grid. More...

	PolChargeN (const Geometry &g, bc bcx, bc bcy, direction dir=forward, value_type jfactor=1.)
	Construct from grid and boundary conditions. More...

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

template<class ContainerType0 >
void	set_phi (const ContainerType0 &phi)

template<class ContainerType0 >
void	set_dxphi (const ContainerType0 &dxphi)

template<class ContainerType0 >
void	set_dyphi (const ContainerType0 &dyphi)

template<class ContainerType0 >
void	set_lapphi (const ContainerType0 &lapphi)

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	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::PolChargeN< Geometry, Matrix, Container >

EXPERIMENTAL polarization solver class for N.

Try to solve N \( -\nabla \cdot ( N \nabla \phi) = \rho\) for given phi and rho

Attention: Converges very slowly if at all

Member Typedef Documentation

◆ container_type

template<class Geometry , class Matrix , class Container >

using dg::mat::PolChargeN< Geometry, Matrix, Container >::container_type = Container

◆ geometry_type

template<class Geometry , class Matrix , class Container >

using dg::mat::PolChargeN< Geometry, Matrix, Container >::geometry_type = Geometry

◆ matrix_type

template<class Geometry , class Matrix , class Container >

using dg::mat::PolChargeN< Geometry, Matrix, Container >::matrix_type = Matrix

◆ value_type

template<class Geometry , class Matrix , class Container >

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

Constructor & Destructor Documentation

◆ PolChargeN() [1/3]

template<class Geometry , class Matrix , class Container >

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

inline

empty object ( no memory allocation)

◆ PolChargeN() [2/3]

template<class Geometry , class Matrix , class Container >

dg::mat::PolChargeN< Geometry, Matrix, Container >::PolChargeN	(	const Geometry &	g,
		direction	dir = `forward`,
		value_type	jfactor = `1.`
	)

inline

Construct from Grid.

Parameters

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)

Note: chi is assumed 1 per default

◆ PolChargeN() [3/3]

template<class Geometry , class Matrix , class Container >

dg::mat::PolChargeN< Geometry, Matrix, Container >::PolChargeN	(	const Geometry &	g,
		bc	bcx,
		bc	bcy,
		direction	dir = `forward`,
		value_type	jfactor = `1.`
	)

inline

Construct from grid and boundary conditions.

Parameters

g	The Grid
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)

Note: chi is assumed 1 per default

Member Function Documentation

◆ construct()

template<class Geometry , class Matrix , class Container >

template<class ... Params>

void dg::mat::PolChargeN< 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

◆ operator()()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

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

inline

Compute elliptic term and store in output.

i.e. \( y=f(x) = - \nabla \cdot (x \nabla_\perp \phi) \) or \( y=f(x) = x + (1+ \alpha \Delta_\perp )\nabla \cdot (x \nabla_\perp \phi) \)

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::PolChargeN< Geometry, Matrix, Container >::precond ( ) const

inline

Return the default preconditioner to use in conjugate gradient.

Currently returns the inverse weights without volume elment divided by the scalar part of \( \chi\). This is especially good when \( \chi\) exhibits large amplitudes or variations

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

◆ set_dxphi()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolChargeN< Geometry, Matrix, Container >::set_dxphi ( const ContainerType0 & dxphi )

inline

◆ set_dyphi()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolChargeN< Geometry, Matrix, Container >::set_dyphi ( const ContainerType0 & dyphi )

inline

◆ set_lapphi()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolChargeN< Geometry, Matrix, Container >::set_lapphi ( const ContainerType0 & lapphi )

inline

◆ set_phi()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::mat::PolChargeN< Geometry, Matrix, Container >::set_phi ( const ContainerType0 & phi )

inline

◆ symv() [1/2]

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

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

inline

Compute elliptic term and store in output.

i.e. \( y=M(phi) x \)

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::PolChargeN< 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. \( y=alpha*M(phi) x +beta*y \)

Parameters

alpha	a scalar
x	the chi term
beta	a scalar
y	result

Template Parameters

ContainerTypes must be usable with Container in The dg dispatch system

◆ weights()

template<class Geometry , class Matrix , class Container >

const Container & dg::mat::PolChargeN< 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_init.h

Public Types

Public Member Functions

Detailed Description

Member Typedef Documentation

◆ container_type

◆ geometry_type

◆ matrix_type

◆ value_type

Constructor & Destructor Documentation

◆ PolChargeN() [1/3]

◆ PolChargeN() [2/3]

◆ PolChargeN() [3/3]

Member Function Documentation

◆ construct()

◆ operator()()

◆ precond()

◆ set_dxphi()

◆ set_dyphi()

◆ set_lapphi()

◆ set_phi()

◆ symv() [1/2]

◆ symv() [2/2]

◆ weights()