Given a elliptic equation: More...

#include <explicitResidual.hh>

Inheritance diagram for hp2D::ExplicitResidual2D< F >:

Classes
class	Distance
	Weight class for 2d Elements. More...

class	EdgeWeight
	Weight class for 1d Elements. More...

Public Types
typedef HashMap< Real >::const_iterator	const_iterator

typedef concepts::Realtype< F >::type	G

typedef HashMap< Real >::iterator	iterator

typedef F	value_type

enum	weight { DIAM, DIAM_HP, DIAM_P }

Public Member Functions
void	addHNData (const Set< uint > &nSet)
	Add attributes for homogen neumann boundary conditions. More...

void	addHNData (uint attrb)

void	addINData (const Set< uint > &nSet, concepts::ElementFormulaContainer< F > frm)
	Add inhomogen Neumanndata if exist. More...

iterator	begin ()

const_iterator	begin () const

virtual ExplicitResidual2D< F > *	clone () const
	Virtual constructor. More...

virtual ElementFormula< F, concepts::Realtype< F >::type > *	clone () const=0
	Virtual copy constructor. More...

void	compute ()

virtual F &	dflt_value ()
	Gives default value. More...

virtual const F &	dflt_value () const
	Gives default value. More...

iterator	end ()

const_iterator	end () const

	ExplicitResidual2D (const concepts::SpaceOnCells< F > &spc, const concepts::Vector< F > &sol, const concepts::ElementFormulaContainer< F > res, const concepts::ElementFormulaContainer< F > *a=0, bool square=false, enum weight w=DIAM, Real alpha=0)
	Constructor of the 2d explicit residual a posteriori Error estimator. More...

const Real	getGlobal () const

uint	nelm () const

virtual const Real	operator() () const

virtual F	operator() (const Connector &cntr, const Real p, const Real t=0.0) const
	Gives the value in an particular cell on a particular point. More...

virtual F	operator() (const Connector &cntr, const Real2d &p, const Real t=0.0) const

virtual F	operator() (const Connector &cntr, const Real3d &p, const Real t=0.0) const

virtual F	operator() (const ElementWithCell< concepts::Realtype< F >::type > &elm, const Real p, const Real t=0.0) const=0
	Evaluates the formula. More...

virtual F	operator() (const ElementWithCell< concepts::Realtype< F >::type > &elm, const Real2d &p, const Real t=0.0) const=0
	Evaluates the formula. More...

virtual F	operator() (const ElementWithCell< concepts::Realtype< F >::type > &elm, const Real3d &p, const Real t=0.0) const=0
	Evaluates the formula. More...

virtual F	operator() (const ElementWithCell< G > &elm, const Real p, const Real t=0.0) const

virtual F	operator() (const ElementWithCell< G > &elm, const Real2d &p, const Real t=0.0) const

virtual F	operator() (const ElementWithCell< G > &elm, const Real3d &p, const Real t=0.0) const

const Real	operator() (uint key) const
	Return the error on given local element, that belongs to the input key. More...

virtual	~ExplicitResidual2D ()

Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream. More...

Protected Attributes
Sequence< ElementFormulaContainer< F > >	frms_

Real	globError_

Set< uint >	hNAttrbs_

Sequence< Set< uint > >	iNAttrbs_

concepts::HashMap< Real >	locError_

const ElementFormulaContainer< F >	res_

const concepts::Vector< F > &	sol_

const concepts::SpaceOnCells< F > &	spc_

Private Member Functions
virtual void	computeError_ (const concepts::ElementFormulaContainer< F > &res, concepts::HashMap< Real > &jumpResidual)

virtual void	computeJumpPart_ (concepts::HashMap< Real > &jumpResidual) const

Private Attributes
const concepts::ElementFormulaContainer< F > *	a_

concepts::Set< uint >	allNattrb_

Real	alpha_

F	dflt_value_
	default value More...

bool	square_

enum weight	weight_

Detailed Description

template<class F>
class hp2D::ExplicitResidual2D< F >

Given a elliptic equation:

     Lu = f  in \Omega
    u = 0  on \Gamma_D  (Dirichletboundary)

\partial_n u = g on \Gamma_N (Neumannboundary)

Let highest order operator be given as div(alpha(x,y)*grad(.)), so consider isotropic case.

For more general case div ( IK * grad(.) ), one may think of a diffusion-tensor IK, this class is not builded up so far. MatrixFormulas will be needed. We just consider the special case IK = I*alpha so far.

Remarks: Interior edges are assumed to have attribute zero only. Boundary edges are assumed to have non zero attribute.

Given a FEM solution u_h, the error estimator local on a element K becomes

eta_K^2 := w_K^2*||f-Lu_h||_L^2(K)^2

sum\limits_{E \subset \partial K\ w_E*||[[n^T * alpha grad u_h]]_K||_L^2(E)^2

where [[.]]_K is defined as [[.]] local on a element K where

 { [n^T * alpha grad u_h]     on inner edges E (i.e two underylying Elements)

[[v]] = { g - [n^T * alpha grad u_h] on neumann edges E (one underlying Element) { 0 on dirichlet boundary

while [.] denotes the jump and grad_n the normal derivative.

As weight w_K we may choose

w_K= diam(K)
w_K= diam(K)/(1+p_K) where p_K is minimum polynomial degree along one direction.

For weight w_E we may choose

w_E = diam(E)/2
w_E= diam(E)/2*(1+p_E) where p_E is polynomial degree along the Edge E.

The second weights are motivated from : An hp-Efficient Residual-Based A Posteriori Error Estimator for Maxwell’s Equations, Markus Bürg

and the inverse polynomial Interpolation estimates within. They may have to be taken with care for reliably error estimator, this is not checked.

Author: Robert Gruhlke, 2014

Definition at line 169 of file explicitResidual.hh.

Member Typedef Documentation

◆ const_iterator

template<class F >

typedef HashMap<Real>::const_iterator concepts::LocalEstimator< F >::const_iterator

inherited

Definition at line 96 of file estimator.hh.

◆ G

template<typename F >

typedef concepts::Realtype<F>::type concepts::PiecewiseFormulaBase< F >::G

inherited

Definition at line 45 of file piecewiseFormula.hh.

◆ iterator

template<class F >

typedef HashMap<Real>::iterator concepts::LocalEstimator< F >::iterator

inherited

Definition at line 95 of file estimator.hh.

◆ value_type

typedef F concepts::ElementFormula< F, concepts::Realtype< F >::type >::value_type

inherited

Definition at line 37 of file elementFormula.hh.

Member Enumeration Documentation

◆ weight

template<class F >

enum hp2D::ExplicitResidual2D::weight

Enumerator
DIAM
DIAM_HP
DIAM_P

Definition at line 187 of file explicitResidual.hh.

Constructor & Destructor Documentation

◆ ExplicitResidual2D()

template<class F >

hp2D::ExplicitResidual2D< F >::ExplicitResidual2D	(	const concepts::SpaceOnCells< F > &	spc,
		const concepts::Vector< F > &	sol,
		const concepts::ElementFormulaContainer< F >	res,
		const concepts::ElementFormulaContainer< F > *	a = `0`,
		bool	square = `false`,
		enum weight	w = `DIAM`,
		Real	alpha = `0`
	)

Constructor of the 2d explicit residual a posteriori Error estimator.

Parameters

spc	The FEM space
sol	the solution vector representing the FEM solution
res	The residual formula, res = f-Lu_h
a	The coefficient function in the highest derivative operator div ( a * grad(.)) if no function `a` is given, by default `a` is const and therefore set to ONE.
square	Addition flag information marking that all Elements in the space are squared, this increases the diameter computation time.
weight	form of the weight for the local contributions
alpha	\in [0,1] exponent of the weight in the error estimator, only comes into account for weight w = DIAM_HP

◆ ~ExplicitResidual2D()

template<class F >

virtual hp2D::ExplicitResidual2D< F >::~ExplicitResidual2D ( )

inlinevirtual

Definition at line 215 of file explicitResidual.hh.

Member Function Documentation

◆ addHNData() [1/2]

template<class F >

void concepts::ExplicitResidual< F >::addHNData ( const Set< uint > & nSet )

inlineinherited

Add attributes for homogen neumann boundary conditions.

Definition at line 41 of file explicitResidual.hh.

◆ addHNData() [2/2]

template<class F >

void concepts::ExplicitResidual< F >::addHNData ( uint attrb )

inlineinherited

Definition at line 44 of file explicitResidual.hh.

◆ addINData()

template<class F >

void concepts::ExplicitResidual< F >::addINData	(	const Set< uint > &	nSet,
		concepts::ElementFormulaContainer< F >	frm
	)

inlineinherited

Add inhomogen Neumanndata if exist.

This is needed for computing the jump terms

Definition at line 33 of file explicitResidual.hh.

◆ begin() [1/2]

template<class F >

iterator concepts::LocalEstimator< F >::begin ( )

inlineinherited

Definition at line 100 of file estimator.hh.

◆ begin() [2/2]

template<class F >

const_iterator concepts::LocalEstimator< F >::begin ( ) const

inlineinherited

Definition at line 104 of file estimator.hh.

◆ clone() [1/2]

template<class F >

virtual ExplicitResidual2D<F>* hp2D::ExplicitResidual2D< F >::clone ( ) const

inlinevirtual

Virtual constructor.

Returns a pointer to a copy of itself. The caller is responsible to destroy this copy.

Implements concepts::ExplicitResidual< F >.

Definition at line 332 of file explicitResidual.hh.

◆ clone() [2/2]

virtual ElementFormula<F,concepts::Realtype< F >::type >* concepts::ElementFormula< F, concepts::Realtype< F >::type >::clone ( ) const

pure virtualinherited

Virtual copy constructor.

◆ compute()

template<class F >

void hp2D::ExplicitResidual2D< F >::compute ( )

◆ computeError_()

template<class F >

virtual void hp2D::ExplicitResidual2D< F >::computeError_	(	const concepts::ElementFormulaContainer< F > &	res,
		concepts::HashMap< Real > &	jumpResidual
	)

privatevirtual

◆ computeJumpPart_()

template<class F >

virtual void hp2D::ExplicitResidual2D< F >::computeJumpPart_ ( concepts::HashMap< Real > & jumpResidual ) const

privatevirtual

◆ dflt_value() [1/2]

template<typename F >

virtual F& concepts::PiecewiseFormulaBase< F >::dflt_value ( )

inlinevirtualinherited

Gives default value.

Definition at line 83 of file piecewiseFormula.hh.

◆ dflt_value() [2/2]

template<typename F >

virtual const F& concepts::PiecewiseFormulaBase< F >::dflt_value ( ) const

inlinevirtualinherited

Gives default value.

Definition at line 81 of file piecewiseFormula.hh.

◆ end() [1/2]

template<class F >

iterator concepts::LocalEstimator< F >::end ( )

inlineinherited

Definition at line 108 of file estimator.hh.

◆ end() [2/2]

template<class F >

const_iterator concepts::LocalEstimator< F >::end ( ) const

inlineinherited

Definition at line 112 of file estimator.hh.

◆ getGlobal()

template<typename F >

const Real concepts::Estimator< F >::getGlobal ( ) const

inlineinherited

Definition at line 22 of file estimator.hh.

◆ info()

template<class F >

virtual std::ostream& hp2D::ExplicitResidual2D< F >::info ( std::ostream & os ) const

inlineprotectedvirtual

Returns information in an output stream.

Reimplemented from concepts::ExplicitResidual< F >.

Definition at line 335 of file explicitResidual.hh.

◆ nelm()

template<class F >

uint concepts::LocalEstimator< F >::nelm ( ) const

inlineinherited

Definition at line 116 of file estimator.hh.

◆ operator()() [1/11]

template<class F >

virtual const Real hp2D::ExplicitResidual2D< F >::operator() ( ) const

inlinevirtual

Definition at line 330 of file explicitResidual.hh.

◆ operator()() [2/11]

template<class F >

virtual F concepts::LocalEstimator< F >::operator()	(	const Connector &	cntr,
		const Real	p,
		const Real	t = `0.0`
	)		const

inlinevirtualinherited

Gives the value in an particular cell on a particular point.

Parameters

cell	topological cell
p	physical coordinates
t	time

Implements concepts::PiecewiseFormulaBase< F >.

Definition at line 132 of file estimator.hh.

◆ operator()() [3/11]

template<class F >

virtual F concepts::LocalEstimator< F >::operator()	(	const Connector &	cntr,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const

inlinevirtualinherited

Implements concepts::PiecewiseFormulaBase< F >.

Definition at line 135 of file estimator.hh.

◆ operator()() [4/11]

template<class F >

virtual F concepts::LocalEstimator< F >::operator()	(	const Connector &	cntr,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const

inlinevirtualinherited

Implements concepts::PiecewiseFormulaBase< F >.

Definition at line 138 of file estimator.hh.

◆ operator()() [5/11]

virtual F concepts::ElementFormula< F, concepts::Realtype< F >::type >::operator()	(	const ElementWithCell< G > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const

pure virtualinherited

Evaluates the formula.

Parameters

elm	Element
p	Point in space in local element coordinates
t	Point in time

◆ operator()() [6/11]

virtual F concepts::ElementFormula< F, concepts::Realtype< F >::type >::operator()	(	const ElementWithCell< G > &	elm,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const

pure virtualinherited

Evaluates the formula.

Parameters

elm	Element
p	Point in space in local element coordinates
t	Point in time

◆ operator()() [7/11]

virtual F concepts::ElementFormula< F, concepts::Realtype< F >::type >::operator()	(	const ElementWithCell< G > &	elm,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const

pure virtualinherited

Evaluates the formula.

Parameters

elm	Element
p	Point in space in local element coordinates
t	Point in time

◆ operator()() [8/11]

template<typename F >

virtual F concepts::PiecewiseFormulaBase< F >::operator()	(	const ElementWithCell< G > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const

inlinevirtualinherited

Definition at line 52 of file piecewiseFormula.hh.

◆ operator()() [9/11]

template<typename F >

virtual F concepts::PiecewiseFormulaBase< F >::operator()	(	const ElementWithCell< G > &	elm,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const

inlinevirtualinherited

Definition at line 57 of file piecewiseFormula.hh.

◆ operator()() [10/11]

template<typename F >

virtual F concepts::PiecewiseFormulaBase< F >::operator()	(	const ElementWithCell< G > &	elm,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const

inlinevirtualinherited

Definition at line 63 of file piecewiseFormula.hh.

◆ operator()() [11/11]

template<class F >

const Real concepts::LocalEstimator< F >::operator() ( uint key ) const

inlineinherited

Return the error on given local element, that belongs to the input key.

Definition at line 123 of file estimator.hh.

Member Data Documentation

◆ a_

template<class F >

const concepts::ElementFormulaContainer<F>* hp2D::ExplicitResidual2D< F >::a_

private

Definition at line 344 of file explicitResidual.hh.

◆ allNattrb_

template<class F >

concepts::Set<uint> hp2D::ExplicitResidual2D< F >::allNattrb_

private

Definition at line 352 of file explicitResidual.hh.

◆ alpha_

template<class F >

Real hp2D::ExplicitResidual2D< F >::alpha_

private

Definition at line 349 of file explicitResidual.hh.

◆ dflt_value_

template<typename F >

F concepts::PiecewiseFormulaBase< F >::dflt_value_

privateinherited

default value

Definition at line 88 of file piecewiseFormula.hh.

◆ frms_

template<class F >

Sequence<ElementFormulaContainer<F> > concepts::ExplicitResidual< F >::frms_

protectedinherited

Definition at line 77 of file explicitResidual.hh.

◆ globError_

template<typename F >

Real concepts::Estimator< F >::globError_

protectedinherited

Definition at line 37 of file estimator.hh.

◆ hNAttrbs_

template<class F >

Set<uint> concepts::ExplicitResidual< F >::hNAttrbs_

protectedinherited

Definition at line 81 of file explicitResidual.hh.

◆ iNAttrbs_

template<class F >

Sequence<Set<uint> > concepts::ExplicitResidual< F >::iNAttrbs_

protectedinherited

Definition at line 79 of file explicitResidual.hh.

◆ locError_

template<class F >

concepts::HashMap<Real> concepts::LocalEstimator< F >::locError_

protectedinherited

Definition at line 151 of file estimator.hh.

◆ res_

template<class F >

const ElementFormulaContainer<F> concepts::ExplicitResidual< F >::res_

protectedinherited

Definition at line 74 of file explicitResidual.hh.

◆ sol_

template<typename F >

const concepts::Vector<F>& concepts::Estimator< F >::sol_

protectedinherited

Definition at line 35 of file estimator.hh.

◆ spc_

template<typename F >

const concepts::SpaceOnCells<F>& concepts::Estimator< F >::spc_

protectedinherited

Definition at line 33 of file estimator.hh.

◆ square_

template<class F >

bool hp2D::ExplicitResidual2D< F >::square_

private

Definition at line 342 of file explicitResidual.hh.

◆ weight_

template<class F >

enum weight hp2D::ExplicitResidual2D< F >::weight_

private

Definition at line 344 of file explicitResidual.hh.

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

estimator/explicitResidual.hh

hp2D::ExplicitResidual2D< F > Class Template Referenceabstract

Classes

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

template<class F> class hp2D::ExplicitResidual2D< F >

Member Typedef Documentation

◆ const_iterator

◆ G

◆ iterator

◆ value_type

Member Enumeration Documentation

◆ weight

Constructor & Destructor Documentation

◆ ExplicitResidual2D()

◆ ~ExplicitResidual2D()

Member Function Documentation

◆ addHNData() [1/2]

◆ addHNData() [2/2]

◆ addINData()

◆ begin() [1/2]

◆ begin() [2/2]

◆ clone() [1/2]

◆ clone() [2/2]

◆ compute()

◆ computeError_()

◆ computeJumpPart_()

◆ dflt_value() [1/2]

◆ dflt_value() [2/2]

◆ end() [1/2]

◆ end() [2/2]

◆ getGlobal()

◆ info()

◆ nelm()

◆ operator()() [1/11]

◆ operator()() [2/11]

◆ operator()() [3/11]

◆ operator()() [4/11]

◆ operator()() [5/11]

◆ operator()() [6/11]

◆ operator()() [7/11]

◆ operator()() [8/11]

◆ operator()() [9/11]

◆ operator()() [10/11]

◆ operator()() [11/11]

Member Data Documentation

◆ a_

◆ allNattrb_

◆ alpha_

◆ dflt_value_

◆ frms_

◆ globError_

◆ hNAttrbs_

◆ iNAttrbs_

◆ locError_

◆ res_

◆ sol_

◆ spc_

◆ square_

◆ weight_

template<class F>
class hp2D::ExplicitResidual2D< F >