dg::Helmholtz2< Geometry, Matrix, Container > Struct Template Reference

DEPRECATED, Matrix class that represents a more general Helmholtz-type operator. More...

Public Types
using	container_type = Container
using	geometry_type = Geometry
using	matrix_type = Matrix
using	value_type = get_value_type< Container >

Public Member Functions
	Helmholtz2 ()
	empty object ( no memory allocation) More...
	Helmholtz2 (const Geometry &g, value_type alpha=1., direction dir=dg::forward, value_type jfactor=1.)
	Construct Helmholtz2 operator. More...
	Helmholtz2 (const Geometry &g, bc bcx, bc bcy, value_type alpha=1., direction dir=dg::forward, value_type jfactor=1.)
	Construct Helmholtz2 operator. More...
void	construct (const Geometry &g, bc bcx, bc bcy, value_type alpha=1, direction dir=dg::forward, value_type jfactor=1.)
	Construct Helmholtz2 operator. More...
void	construct (const Geometry &g, value_type alpha=1, direction dir=dg::forward, value_type jfactor=1.)
	Construct Helmholtz2 operator. More...
void	symv (const Container &x, Container &y)
	apply operator More...
const Container &	weights () const
	Return the weights making the operator self-adjoint. More...
const Container &	precond () const
	Preconditioner to use in conjugate gradient solvers. More...
value_type &	alpha ()
	Change alpha. More...
value_type	alpha () const
	Access alpha. More...
void	set_chi (const Container &chi)
	Set Chi in the above formula. More...
const Container &	chi () const
	Access chi. More...

Detailed Description

template<class Geometry, class Matrix, class Container>
struct dg::Helmholtz2< Geometry, Matrix, Container >

DEPRECATED, Matrix class that represents a more general Helmholtz-type operator.

Discretization of

\[ \left[ \chi +2 \alpha\Delta + \alpha^2\Delta \left(\chi^{-1}\Delta \right)\right] \]

where \( \chi\) is a function and \(\alpha\) a scalar.

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

Note

The Laplacian in this formula is positive as opposed to the negative sign in the Elliptic operator

Attention

It is MUCH better to solve the normal Helmholtz operator twice, consecutively, than solving the Helmholtz2 operator once. The following code snippet shows how to do it:

    std::cout << "Alternative test with two Helmholtz operators\n";
    dg::Helmholtz< dg::CartesianGrid2d, dg::DMatrix, dg::DVec > gamma1inv(alpha, {grid2d, dg::centered});
    gamma1inv.set_chi( chi);
    dg::PCG<dg::DVec> pcgO(  x, grid2d.size());
    dg::PCG<dg::DVec> pcgOO( x, grid2d.size());
    t.tic();
    unsigned number1 = pcgO.solve( gamma1inv, phi, rholap, 1., w2d, eps/100);
    dg::blas1::pointwiseDot( phi, chi, phi);
    unsigned number2 = pcgOO.solve( gamma1inv, x, phi, 1., w2d, eps/100);
    t.toc();
    //Evaluation
    dg::blas1::axpby( 1., sol, -1., x);

Member Typedef Documentation

container_type

template<class Geometry , class Matrix , class Container >

using dg::Helmholtz2< Geometry, Matrix, Container >::container_type = Container

geometry_type

template<class Geometry , class Matrix , class Container >

using dg::Helmholtz2< Geometry, Matrix, Container >::geometry_type = Geometry

matrix_type

template<class Geometry , class Matrix , class Container >

using dg::Helmholtz2< Geometry, Matrix, Container >::matrix_type = Matrix

value_type

template<class Geometry , class Matrix , class Container >

using dg::Helmholtz2< Geometry, Matrix, Container >::value_type = get_value_type<Container>

Constructor & Destructor Documentation

Helmholtz2() [1/3]

template<class Geometry , class Matrix , class Container >

dg::Helmholtz2< Geometry, Matrix, Container >::Helmholtz2 ( )

inline

empty object ( no memory allocation)

Helmholtz2() [2/3]

template<class Geometry , class Matrix , class Container >

dg::Helmholtz2< Geometry, Matrix, Container >::Helmholtz2 ( const Geometry &  g, value_type  alpha = 1., direction  dir = dg::forward, value_type  jfactor = 1.  )

inline

Construct Helmholtz2 operator.

Parameters

g	The grid to use
alpha	Scalar in the above formula
dir	Direction of the Laplace operator
jfactor	The jfactor used in the Laplace operator (probably 1 is always the best factor but one never knows...)

Note

The default value of \(\chi\) is one

Helmholtz2() [3/3]

template<class Geometry , class Matrix , class Container >

dg::Helmholtz2< Geometry, Matrix, Container >::Helmholtz2 ( const Geometry &  g, bc  bcx, bc  bcy, value_type  alpha = 1., direction  dir = dg::forward, value_type  jfactor = 1.  )

inline

Construct Helmholtz2 operator.

Parameters

g	The grid to use
bcx	boundary condition in x
bcy	boundary contition in y
alpha	Scalar in the above formula
dir	Direction of the Laplace operator
jfactor	The jfactor used in the Laplace operator (probably 1 is always the best factor but one never knows...)

Note

The default value of \(\chi\) is one

Member Function Documentation

alpha() [1/2]

template<class Geometry , class Matrix , class Container >

value_type & dg::Helmholtz2< Geometry, Matrix, Container >::alpha ( )

inline

Change alpha.

Returns

reference to alpha

alpha() [2/2]

template<class Geometry , class Matrix , class Container >

value_type dg::Helmholtz2< Geometry, Matrix, Container >::alpha ( ) const

inline

Access alpha.

Returns

alpha

chi()

template<class Geometry , class Matrix , class Container >

const Container & dg::Helmholtz2< Geometry, Matrix, Container >::chi ( ) const

inline

Access chi.

Returns

chi

construct() [1/2]

template<class Geometry , class Matrix , class Container >

void dg::Helmholtz2< Geometry, Matrix, Container >::construct ( const Geometry &  g, bc  bcx, bc  bcy, value_type  alpha = 1, direction  dir = dg::forward, value_type  jfactor = 1.  )

inline

Construct Helmholtz2 operator.

Parameters

g	The grid to use
bcx	boundary condition in x
bcy	boundary contition in y
alpha	Scalar in the above formula
dir	Direction of the Laplace operator
jfactor	The jfactor used in the Laplace operator (probably 1 is always the best factor but one never knows...)

Note

The default value of \(\chi\) is one

construct() [2/2]

template<class Geometry , class Matrix , class Container >

void dg::Helmholtz2< Geometry, Matrix, Container >::construct ( const Geometry &  g, value_type  alpha = 1, direction  dir = dg::forward, value_type  jfactor = 1.  )

inline

Construct Helmholtz2 operator.

Parameters

g	The grid to use
alpha	Scalar in the above formula
dir	Direction of the Laplace operator
jfactor	The jfactor used in the Laplace operator (probably 1 is always the best factor but one never knows...)

Note

The default value of \(\chi\) is one

precond()

template<class Geometry , class Matrix , class Container >

const Container & dg::Helmholtz2< Geometry, Matrix, Container >::precond ( ) const

inline

Preconditioner to use in conjugate gradient solvers.

Returns

1 by default

set_chi()

template<class Geometry , class Matrix , class Container >

void dg::Helmholtz2< Geometry, Matrix, Container >::set_chi ( const Container &  chi )

inline

Set Chi in the above formula.

Parameters

chi	new container

symv()

template<class Geometry , class Matrix , class Container >

void dg::Helmholtz2< Geometry, Matrix, Container >::symv ( const Container &  x, Container &  y  )

inline

apply operator

Computes

\[ y = \left[ \chi +2 \alpha\Delta + \alpha^2\Delta \left(\chi^{-1}\Delta \right)\right] x \]

to make the matrix symmetric

Parameters

x	lhs (is constant up to changes in ghost cells)
y	rhs contains solution

Note

Takes care of sign in laplaceM and thus multiplies by -alpha

weights()

template<class Geometry , class Matrix , class Container >

const Container & dg::Helmholtz2< Geometry, Matrix, Container >::weights ( ) const

inline

Return the weights making the operator self-adjoint.

i.e. the volume form

Returns

volume form including weights

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

• helmholtz.h