dg::Poisson< Geometry, Matrix, Container > Struct Template Reference

Direct discretization of Poisson bracket \( \{ f,g\} \). 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
	Poisson ()=default
	Poisson (const Geometry &g)
	Create Poisson on a grid. More...
	Poisson (const Geometry &g, bc bcx, bc bcy)
	Create Poisson on a grid using different boundary conditions. More...
	Poisson (const Geometry &g, bc bcxlhs, bc bcylhs, bc bcxrhs, bc bcyrhs)
	Create Poisson on a grid using different boundary conditions. More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 >
void	operator() (const ContainerType0 &lhs, const ContainerType1 &rhs, ContainerType2 &result)
	Compute poisson's bracket. More...
template<class ContainerType0 >
void	set_chi (const ContainerType0 &new_chi)
	Change Chi. More...
const Matrix &	dxlhs () const
	Return internally used x - derivative. More...
const Matrix &	dylhs () const
	Return internally used y - derivative. More...
const Matrix &	dxrhs () const
	Return internally used x - derivative. More...
const Matrix &	dyrhs ()
	Return internally used y - derivative. More...

Detailed Description

template<class Geometry, class Matrix, class Container>
struct dg::Poisson< Geometry, Matrix, Container >

Direct discretization of Poisson bracket \( \{ f,g\} \).

Computes

\[ \{f,g\} := \chi/\sqrt{g_{2d}}\left(\partial_x f\partial_y g - \partial_y f\partial_x g\right) \]

where \( g_{2d} = g/g_{zz}\) is the two-dimensional volume element of the plane in 2x1 product space and \( \chi\) is an optional factor. Has the possitility to use mixed boundary conditions

    const dg::CartesianGrid2d grid( 0, lx, 0, ly, n, Nx, Ny);
    const dg::DVec lhs = dg::evaluate( left, grid);
    const dg::DVec rhs = dg::evaluate( right, grid);
    dg::DVec jac(lhs);
 
    dg::Poisson<dg::aGeometry2d, dg::DMatrix, dg::DVec> poisson( grid, bcxlhs, bcylhs,bcxrhs, bcyrhs );
    poisson( lhs, rhs, jac);

See also

A discussion of this and other advection schemes can also be found here https://mwiesenberger.github.io/advection

Template Parameters

Geometry	A type that is or derives from one of the abstract geometry base classes ( aGeometry2d, aGeometry3d, aMPIGeometry2d, ...). Geometry determines which Matrix and Container types can be used:
Matrix	A class for which the dg::blas2::symv functions are callable in connection with the Container class and to which the return type of dg::create::dx() can be converted using dg::blas2::transfer. The Matrix type can be one of: dg::HMatrix with dg::HVec and one of the shared memory geometries dg::DMatrix with dg::DVec and one of the shared memory geometries dg::MHMatrix with dg::MHVec and one of the MPI geometries dg::MDMatrix with dg::MDVec and one of the MPI geometries
Container	A data container class for which the blas1 functionality is overloaded and to which the return type of blas1::subroutine() can be converted using dg::assign. We assume that Container is copyable/assignable and has a swap member function. In connection with Geometry this is one of dg::HVec, dg::DVec when Geometry is a shared memory geometry dg::MHVec or dg::MDVec when Geometry is one of the MPI geometries

Member Typedef Documentation

container_type

template<class Geometry , class Matrix , class Container >

using dg::Poisson< Geometry, Matrix, Container >::container_type = Container

geometry_type

template<class Geometry , class Matrix , class Container >

using dg::Poisson< Geometry, Matrix, Container >::geometry_type = Geometry

matrix_type

template<class Geometry , class Matrix , class Container >

using dg::Poisson< Geometry, Matrix, Container >::matrix_type = Matrix

value_type

template<class Geometry , class Matrix , class Container >

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

Constructor & Destructor Documentation

Poisson() [1/4]

template<class Geometry , class Matrix , class Container >

dg::Poisson< Geometry, Matrix, Container >::Poisson ( )

default

Poisson() [2/4]

template<class Geometry , class Matrix , class Container >

dg::Poisson< Geometry, Matrix, Container >::Poisson

(

const Geometry &

g

)

Create Poisson on a grid.

Parameters

g

The grid

Note

chi defaults to 1

Poisson() [3/4]

template<class Geometry , class Matrix , class Container >

dg::Poisson< Geometry, Matrix, Container >::Poisson	(	const Geometry &	g,
		bc	bcx,
		bc	bcy
	)

Create Poisson on a grid using different boundary conditions.

Parameters

g	The grid
bcx	The boundary condition in x
bcy	The boundary condition in y

Note

chi defaults to 1

Poisson() [4/4]

template<class Geometry , class Matrix , class Container >

dg::Poisson< Geometry, Matrix, Container >::Poisson	(	const Geometry &	g,
		bc	bcxlhs,
		bc	bcylhs,
		bc	bcxrhs,
		bc	bcyrhs
	)

Create Poisson on a grid using different boundary conditions.

Parameters

g	The grid
bcxlhs	The lhs boundary condition in x
bcxrhs	The rhs boundary condition in x
bcylhs	The lhs boundary condition in y
bcyrhs	The rhs boundary condition in y

Note

chi defaults to 1

Member Function Documentation

dxlhs()

template<class Geometry , class Matrix , class Container >

const Matrix & dg::Poisson< Geometry, Matrix, Container >::dxlhs ( ) const

inline

Return internally used x - derivative.

The same as a call to dg::create::dx( g, bcxlhs)

Returns

derivative

dxrhs()

template<class Geometry , class Matrix , class Container >

const Matrix & dg::Poisson< Geometry, Matrix, Container >::dxrhs ( ) const

inline

Return internally used x - derivative.

The same as a call to dg::create::dx( g, bcxrhs)

Returns

derivative

dylhs()

template<class Geometry , class Matrix , class Container >

const Matrix & dg::Poisson< Geometry, Matrix, Container >::dylhs ( ) const

inline

Return internally used y - derivative.

The same as a call to dg::create::dy( g, bcylhs)

Returns

derivative

dyrhs()

template<class Geometry , class Matrix , class Container >

const Matrix & dg::Poisson< Geometry, Matrix, Container >::dyrhs ( )

inline

Return internally used y - derivative.

The same as a call to dg::create::dy( g, bcyrhs)

Returns

derivative

operator()()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 , class ContainerType2 >

void dg::Poisson< Geometry, Matrix, Container >::operator()	(	const ContainerType0 &	lhs,
		const ContainerType1 &	rhs,
		ContainerType2 &	result
	)

Compute poisson's bracket.

Computes

\[ [f,g] := 1/\sqrt{g_{2d}}\left(\partial_x f\partial_y g - \partial_y f\partial_x g\right) \]

where \( g_{2d} = g/g_{zz}\) is the two-dimensional volume element of the plane in 2x1 product space.

Parameters

lhs	left hand side in x-space
rhs	rights hand side in x-space
result	Poisson's bracket in x-space

Template Parameters

ContainerTypes

must be usable with Container in The dg dispatch system

set_chi()

template<class Geometry , class Matrix , class Container >

template<class ContainerType0 >

void dg::Poisson< Geometry, Matrix, Container >::set_chi ( const ContainerType0 &  new_chi )

inline

Change Chi.

Parameters

new_chi

The new chi

Template Parameters

ContainerTypes

must be usable with Container in The dg dispatch system

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

• poisson.h