dg::GeneralHelmholtz< Matrix, Container > Struct Template Reference

A general Helmholtz-type operator \( (\chi-\alpha F) \). More...

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

Public Member Functions
	GeneralHelmholtz ()=default
	empty object ( no memory allocation) More...
	GeneralHelmholtz (value_type alpha, Matrix matrix)
	Construct from given Matrix object. More...
template<class ... Params>
void	construct (Params &&...ps)
	Perfect forward parameters to one of the constructors. More...
const Container &	weights () const
	Call weights() of Matrix class. More...
const Container &	precond () const
	Call precond() of Matrix class. More...
template<class ContainerType0 , class ContainerType1 >
void	symv (const ContainerType0 &x, ContainerType1 &y)
	Compute. More...
Matrix &	matrix ()
	Write access to Matrix object. More...
const Matrix &	matrix () const
	Read access to Matrix object. More...
value_type &	alpha ()
	Change alpha. More...
value_type	alpha () const
	Access alpha. More...
template<class ContainerType0 >
void	set_chi (const ContainerType0 &chi)
	Set Chi in the above formula. More...
const Container &	chi () const
	Access chi. More...

Detailed Description

template<class Matrix, class Container>
struct dg::GeneralHelmholtz< Matrix, Container >

A general Helmholtz-type operator \( (\chi-\alpha F) \).

where \( \chi\) is a vector and \(\alpha\) a scalar and \(F\) is an operator.

Attention

If \( F\) is the Elliptic operator then the Laplacian in this formula becomes positive as opposed to the negative sign in the Elliptic operator

Can be used by the dg::PCG class. The following example shows how the class can be used to act as a Helmholtz2 operator:

    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);

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 intention is for Matrix to be one of the Elliptic classes with the weights() and precond() methods defined. If Matrix is to be an arbitrary functor then it is more convenient to simply directly use a lambda function to achieve the computation of \( y = (\chi - \alpha F)x\)

Member Typedef Documentation

container_type

template<class Matrix , class Container >

using dg::GeneralHelmholtz< Matrix, Container >::container_type = Container

matrix_type

template<class Matrix , class Container >

using dg::GeneralHelmholtz< Matrix, Container >::matrix_type = Matrix

value_type

template<class Matrix , class Container >

using dg::GeneralHelmholtz< Matrix, Container >::value_type = get_value_type<Container>

Constructor & Destructor Documentation

GeneralHelmholtz() [1/2]

template<class Matrix , class Container >

dg::GeneralHelmholtz< Matrix, Container >::GeneralHelmholtz ( )

default

empty object ( no memory allocation)

GeneralHelmholtz() [2/2]

template<class Matrix , class Container >

dg::GeneralHelmholtz< Matrix, Container >::GeneralHelmholtz ( value_type  alpha, Matrix  matrix  )

inline

Construct from given Matrix object.

Parameters

alpha	Scalar in the above formula
matrix	an existing elliptic operator

Member Function Documentation

alpha() [1/2]

template<class Matrix , class Container >

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

inline

Change alpha.

Returns

reference to alpha

alpha() [2/2]

template<class Matrix , class Container >

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

inline

Access alpha.

Returns

alpha

chi()

template<class Matrix , class Container >

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

inline

Access chi.

Returns

chi

construct()

template<class Matrix , class Container >

template<class ... Params>

void dg::GeneralHelmholtz< 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

matrix() [1/2]

template<class Matrix , class Container >

Matrix & dg::GeneralHelmholtz< Matrix, Container >::matrix ( )

inline

Write access to Matrix object.

matrix() [2/2]

template<class Matrix , class Container >

const Matrix & dg::GeneralHelmholtz< Matrix, Container >::matrix ( ) const

inline

Read access to Matrix object.

precond()

template<class Matrix , class Container >

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

inline

Call precond() of Matrix class.

set_chi()

template<class Matrix , class Container >

template<class ContainerType0 >

void dg::GeneralHelmholtz< Matrix, Container >::set_chi ( const ContainerType0 &  chi )

inline

Set Chi in the above formula.

Parameters

chi	new Container

Template Parameters

ContainerTypes

must be usable with Container in The dg dispatch system

symv()

template<class Matrix , class Container >

template<class ContainerType0 , class ContainerType1 >

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

inline

Compute.

\[ y = ( \chi - \alpha M) x \]

Parameters

x	lhs
y	rhs contains solution

Template Parameters

ContainerTypes

must be usable with Container_type in The dg dispatch system

weights()

template<class Matrix , class Container >

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

inline

Call weights() of Matrix class.

---

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

• helmholtz.h