hp1D::LevelRiesz Class Referenceabstract

This class creates a linearform corresponding to the integral: More...

#include <levelRiesz.hh>

Inheritance diagram for hp1D::LevelRiesz:

Public Member Functions
	LevelRiesz (const concepts::Space< Real > &space2D, const concepts::ElementFormulaContainer< Real > &levelFunction, const concepts::ElementFormulaContainer< Real2d > &levelFunctionGrad, const concepts::ElementFormulaContainer< Real > &observable)
	Constructor The level function $\psi$ and it's gradient are defined on a 2D space. More...
virtual void	operator() (const concepts::Element< Real > &elm, concepts::ElementMatrix< Real > &em) const
	This method loops over all elements of the 2D space and cells levelRieszElement on each one of them. More...
virtual void	operator() (const Element< typename Realtype< concepts::Real >::type > &elm, ElementMatrix< concepts::Real > &em) const=0
	Computes the element contribution to the function. More...
	~LevelRiesz ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const

Private Attributes
const concepts::ElementFormulaContainer< Real >	levelFunction_
const concepts::ElementFormulaContainer< Real2d >	levelFunctionGrad_
const concepts::ElementFormulaContainer< Real >	observable_
const concepts::Space< Real > &	space2D_

Detailed Description

This class creates a linearform corresponding to the integral:

,

where $\psi$ is a given 2D-function (must take values between 0 and 1 !) and f the function to be integrated.

These integrals, called geometric coefficients, are computed for all y in [0,1] via a Galerkin-projection on a polynomial space.

As polynomials spaces one can choose the space of orthonormal Legendre-polynomials (hp1D::hpAdaptiveSpaceL2) or the space of Karniadakis-polynomials (hp1D::Space).

Author

Lukas Drescher, 2015, Felix Baumann 2017

Definition at line 34 of file levelRiesz.hh.

Constructor & Destructor Documentation

LevelRiesz()

hp1D::LevelRiesz::LevelRiesz	(	const concepts::Space< Real > &	space2D,
		const concepts::ElementFormulaContainer< Real > &	levelFunction,
		const concepts::ElementFormulaContainer< Real2d > &	levelFunctionGrad,
		const concepts::ElementFormulaContainer< Real > &	observable
	)

Constructor The level function $\psi$ and it's gradient are defined on a 2D space.

$\psi$ must take values in [0,1]. The observable corresponds to the integrand.

Parameters

space2D	2D domain, on which level function is given
levelFunction	levelset function. must take values in [0,1]
levelFunctionGrad	gradient of levelset function
observable	integrand over level sets of levelFunction

~LevelRiesz()

hp1D::LevelRiesz::~LevelRiesz ( )

inline

Definition at line 52 of file levelRiesz.hh.

Member Function Documentation

info()

virtual std::ostream& hp1D::LevelRiesz::info ( std::ostream &  os ) const

protectedvirtual

Reimplemented from concepts::LinearForm< concepts::Real >.

operator()() [1/2]

virtual void hp1D::LevelRiesz::operator() ( const concepts::Element< Real > &  elm, concepts::ElementMatrix< Real > &  em  ) const

virtual

This method loops over all elements of the 2D space and cells levelRieszElement on each one of them.

These local contributions are added together to get the overall value.

operator()() [2/2]

virtual void concepts::LinearForm< concepts::Real , typename Realtype<concepts::Real >::type >::operator() ( const Element< G > &  elm, ElementMatrix< F > &  em  ) const

pure virtualinherited

Computes the element contribution to the function.

Parameters

elm	Element on which the computations should be performed
em	The local matrix

Member Data Documentation

levelFunction_

const concepts::ElementFormulaContainer<Real> hp1D::LevelRiesz::levelFunction_

private

Definition at line 69 of file levelRiesz.hh.

levelFunctionGrad_

const concepts::ElementFormulaContainer<Real2d> hp1D::LevelRiesz::levelFunctionGrad_

private

Definition at line 70 of file levelRiesz.hh.

observable_

const concepts::ElementFormulaContainer<Real> hp1D::LevelRiesz::observable_

private

Definition at line 71 of file levelRiesz.hh.

space2D_

const concepts::Space<Real>& hp1D::LevelRiesz::space2D_

private

Definition at line 68 of file levelRiesz.hh.

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

• levelSets/levelRiesz.hh