Class for PML in polar coordinates. More...

#include <pml_formula.h>

Inheritance diagram for concepts::FormulaPMLRadia:

Public Types
enum	PMLMode { AD1, AD2, AS, IDENT, AD1, AD2, AS1, AS2, IDENT }

enum	PMLMode { AD1, AD2, AS, IDENT, AD1, AD2, AS1, AS2, IDENT }

typedef Cmplx	value_type

Public Member Functions
Real	c_c (Real2d &p) const

virtual FormulaPMLRadia *	clone () const
	Virtual constructor. More...

virtual FormulaPMLRadia *	clone () const
	Virtual constructor. More...

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

	FormulaPMLRadia (const ElementFormulaContainer< Cmplx > coeff_a, const ElementFormulaContainer< Cmplx > coeff_b, RCP< concepts::Formula< Real > > sigma, RCP< concepts::Formula< Real > > sigmaB, PMLMode mode, double omega)
	Constructor. More...

	FormulaPMLRadia (RCP< Formula< Real > > sigma, RCP< Formula< Real > > sigmaB, PMLMode mode, const Real2d &center=Real2d(0, 0))
	Constructor. More...

Cmplx	gamma (Real2d &p) const
	Returns the parameter gamma in page 2067(no equation number) of the above article. More...

Cmplx	gammaB (Real2d &p) const
	Returns the parameter gamma bar in page 2067(no equation number) of the above article. More...

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

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

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

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

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

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

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

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

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

Real	s_c (Real2d &p) const

Real	s_s (Real2d &p) const

RCP< Formula< Real > >	sigma () const

RCP< Formula< Real > >	sigmaB () const

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

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

Private Member Functions
Cmplx	gamma_ (Real2d &p) const
	Returns the parameter $\gamma$ on page 2067 (no equation number) of the above article. More...

Cmplx	gammaB_ (Real2d &p) const
	Returns the parameter $\overline{gamma}$ on page 2067 (no equation number) of the above article. More...

Private Attributes
Real2d	center_
	Center of PML. More...

const ElementFormulaContainer< Cmplx >	coeff_a
	globally defined material, piecewise constant dielectric More...

const ElementFormulaContainer< Cmplx >	coeff_b

PMLMode	mode
	The choosen mode. More...

PMLMode	mode_
	The choosen mode. More...

double	omega
	The wave number. More...

RCP< concepts::Formula< Real > >	sigma
	sigma function, which takes the general form of $PMLstrength*(\rho-PMLdist)^{powercoeff}$ More...

RCP< Formula< Real > >	sigma_
	Function $\sigma: \mathbb{R}^2\to\mathbb{R}$ . More...

RCP< concepts::Formula< Real > >	sigmaB
	sigma bar function, given in the above article page 2067, the average of sigma More...

RCP< Formula< Real > >	sigmaB_
	Function $\overline{\sigma}: \mathbb{R}^2\to\mathbb{R}$ . More...

Detailed Description

Class for PML in polar coordinates.

Class for radial PML in polar coordinates.

The class is either one of the formulas needed for PML in polar coordinates, which are determined by one of the following modes.

There are four modes of the formula. AD1 First diagonal entry of matrix A. AD2 Second diagonal entry of matrix A. AS A12 = A21 = AS IDENT The term for MASS matrix

Taken from the article: F.Collino and P.Monk, The perfectly matched layer in curvilinear coordinates, SIAM J.Sci Comput. 19(6)(1998)2061-2090"

Author: Mengyu Wang, 2010

The class provides formulas for radial PML in polar coordinates, which are determined by one of the following modes:

AD1 First diagonal entry of matrix A. AD2 Second diagonal entry of matrix A. AS Both off-diagonal entries of matrix A. IDENT The term for mass matrix

Author: Mengyu Wang, 2010

Definition at line 834 of file pml_formula.h.

Member Typedef Documentation

◆ value_type

typedef Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::type >::value_type

inherited

Definition at line 37 of file elementFormula.hh.

Member Enumeration Documentation

◆ PMLMode [1/2]

enum concepts::FormulaPMLRadia::PMLMode

Enumerator
AD1
AD2
AS
IDENT
AD1
AD2
AS1
AS2
IDENT

Definition at line 836 of file pml_formula.h.

◆ PMLMode [2/2]

enum concepts::FormulaPMLRadia::PMLMode

Enumerator
AD1
AD2
AS
IDENT
AD1
AD2
AS1
AS2
IDENT

Definition at line 434 of file pml_formula.hh.

Constructor & Destructor Documentation

◆ FormulaPMLRadia() [1/2]

concepts::FormulaPMLRadia::FormulaPMLRadia	(	const ElementFormulaContainer< Cmplx >	coeff_a,
		const ElementFormulaContainer< Cmplx >	coeff_b,
		RCP< concepts::Formula< Real > >	sigma,
		RCP< concepts::Formula< Real > >	sigmaB,
		PMLMode	mode,
		double	omega
	)

inline

Constructor.

Parameters

coeff_a	Element formula for material alpha in the global domain
coeff_b	Element formula for material beta in the global domain
sigma	Formula for sigma, which takes the general form of $PMLstrength*(\rho-PMLdist)^{powercoeff}$
sigmaB	Formula for sigmabar in the above article, page 2067
mode	Mode
omega	Wave number

Definition at line 849 of file pml_formula.h.

◆ FormulaPMLRadia() [2/2]

concepts::FormulaPMLRadia::FormulaPMLRadia	(	RCP< Formula< Real > >	sigma,
		RCP< Formula< Real > >	sigmaB,
		PMLMode	mode,
		const Real2d &	center = `Real2d(0, 0)`
	)

Constructor.

Parameters

sigma	Function $\sigma: \mathbb{R}^2\to\mathbb{R}$
sigmaB	Function $\overline{\sigma}: \mathbb{R}^2\to\mathbb{R}$
mode	One of the four modes

In the report of Monk & Collino (see page 2067) the functions and $\overline{sigma}$ are weighted by $1/\omega$ . To do so, multiply the formulas in advance by this factor.

Member Function Documentation

◆ c_c()

Real concepts::FormulaPMLRadia::c_c ( Real2d & p ) const

inline

Definition at line 888 of file pml_formula.h.

◆ clone() [1/3]

virtual FormulaPMLRadia* concepts::FormulaPMLRadia::clone ( ) const

inlinevirtual

Virtual constructor.

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

Implements concepts::Cloneable.

Definition at line 864 of file pml_formula.h.

◆ clone() [2/3]

virtual FormulaPMLRadia* concepts::FormulaPMLRadia::clone ( ) const

inlinevirtual

Virtual constructor.

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

Implements concepts::Cloneable.

Definition at line 450 of file pml_formula.hh.

◆ clone() [3/3]

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

pure virtualinherited

Virtual copy constructor.

◆ gamma()

Cmplx concepts::FormulaPMLRadia::gamma ( Real2d & p ) const

inline

Returns the parameter gamma in page 2067(no equation number) of the above article.

Definition at line 880 of file pml_formula.h.

◆ gamma_()

Cmplx concepts::FormulaPMLRadia::gamma_ ( Real2d & p ) const

inlineprivate

Returns the parameter $\gamma$ on page 2067 (no equation number) of the above article.

Definition at line 479 of file pml_formula.hh.

◆ gammaB()

Cmplx concepts::FormulaPMLRadia::gammaB ( Real2d & p ) const

inline

Returns the parameter gamma bar in page 2067(no equation number) of the above article.

Definition at line 884 of file pml_formula.h.

◆ gammaB_()

Cmplx concepts::FormulaPMLRadia::gammaB_ ( Real2d & p ) const

inlineprivate

Returns the parameter $\overline{gamma}$ on page 2067 (no equation number) of the above article.

Definition at line 485 of file pml_formula.hh.

◆ info() [1/2]

virtual std::ostream& concepts::FormulaPMLRadia::info ( std::ostream & os ) const

inlineprotectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Definition at line 914 of file pml_formula.h.

◆ info() [2/2]

virtual std::ostream& concepts::FormulaPMLRadia::info ( std::ostream & os ) const

protectedvirtual

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

◆ operator()() [1/9]

virtual Cmplx concepts::FormulaPMLRadia::operator()	(	const ElementWithCell< Real > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const

inlinevirtual

Definition at line 874 of file pml_formula.h.

◆ operator()() [2/9]

virtual Cmplx concepts::FormulaPMLRadia::operator()	(	const ElementWithCell< Real > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const

virtual

◆ operator()() [3/9]

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

inlinevirtual

Definition at line 900 of file pml_formula.h.

◆ operator()() [4/9]

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

virtual

◆ operator()() [5/9]

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

inlinevirtual

Definition at line 868 of file pml_formula.h.

◆ operator()() [6/9]

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

virtual

◆ operator()() [7/9]

virtual Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::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()() [8/9]

virtual Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::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()() [9/9]

virtual Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::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

◆ s_c()

Real concepts::FormulaPMLRadia::s_c ( Real2d & p ) const

inline

Definition at line 896 of file pml_formula.h.

◆ s_s()

Real concepts::FormulaPMLRadia::s_s ( Real2d & p ) const

inline

Definition at line 892 of file pml_formula.h.

◆ sigma()

RCP<Formula<Real> > concepts::FormulaPMLRadia::sigma ( ) const

inline

Definition at line 461 of file pml_formula.hh.

◆ sigmaB()

RCP<Formula<Real> > concepts::FormulaPMLRadia::sigmaB ( ) const

inline

Definition at line 462 of file pml_formula.hh.

Member Data Documentation

◆ center_

Real2d concepts::FormulaPMLRadia::center_

private

Center of PML.

Definition at line 473 of file pml_formula.hh.

◆ coeff_a

const ElementFormulaContainer<Cmplx> concepts::FormulaPMLRadia::coeff_a

private

globally defined material, piecewise constant dielectric

Definition at line 920 of file pml_formula.h.

◆ coeff_b

const ElementFormulaContainer<Cmplx> concepts::FormulaPMLRadia::coeff_b

private

Definition at line 921 of file pml_formula.h.

◆ mode

PMLMode concepts::FormulaPMLRadia::mode

private

The choosen mode.

Definition at line 927 of file pml_formula.h.

◆ mode_

PMLMode concepts::FormulaPMLRadia::mode_

private

The choosen mode.

Definition at line 471 of file pml_formula.hh.

◆ omega

double concepts::FormulaPMLRadia::omega

private

The wave number.

Definition at line 929 of file pml_formula.h.

◆ sigma

RCP<concepts::Formula<Real> > concepts::FormulaPMLRadia::sigma

private

sigma function, which takes the general form of $PMLstrength*(\rho-PMLdist)^{powercoeff}$

Definition at line 923 of file pml_formula.h.

◆ sigma_

RCP<Formula<Real> > concepts::FormulaPMLRadia::sigma_

private

Function $\sigma: \mathbb{R}^2\to\mathbb{R}$ .

Definition at line 467 of file pml_formula.hh.

◆ sigmaB

RCP<concepts::Formula<Real> > concepts::FormulaPMLRadia::sigmaB

private

sigma bar function, given in the above article page 2067, the average of sigma

Definition at line 925 of file pml_formula.h.

◆ sigmaB_

RCP<Formula<Real> > concepts::FormulaPMLRadia::sigmaB_

private

Function $\overline{\sigma}: \mathbb{R}^2\to\mathbb{R}$ .

Definition at line 469 of file pml_formula.hh.

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

applications/pml_formula.h
waveprop/pml_formula.hh

concepts::FormulaPMLRadia Class Referenceabstract

Public Types

Public Member Functions

Protected Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ value_type

Member Enumeration Documentation

◆ PMLMode [1/2]

◆ PMLMode [2/2]

Constructor & Destructor Documentation

◆ FormulaPMLRadia() [1/2]

◆ FormulaPMLRadia() [2/2]

Member Function Documentation

◆ c_c()

◆ clone() [1/3]

◆ clone() [2/3]

◆ clone() [3/3]

◆ gamma()

◆ gamma_()

◆ gammaB()

◆ gammaB_()

◆ info() [1/2]

◆ info() [2/2]

◆ operator()() [1/9]

◆ operator()() [2/9]

◆ operator()() [3/9]

◆ operator()() [4/9]

◆ operator()() [5/9]

◆ operator()() [6/9]

◆ operator()() [7/9]

◆ operator()() [8/9]

◆ operator()() [9/9]

◆ s_c()

◆ s_s()

◆ sigma()

◆ sigmaB()

Member Data Documentation

◆ center_

◆ coeff_a

◆ coeff_b

◆ mode

◆ mode_

◆ omega

◆ sigma

◆ sigma_

◆ sigmaB

◆ sigmaB_