Class for PML in polar coordinates. More...

#include <pml_formula.h>

Inheritance diagram for concepts::FormulaPMLRadia:

Collaboration diagram for concepts::FormulaPMLRadia:

Public Types
enum	PMLMode { AD1, AD2, AS, IDENT, AD1, AD2, AS, IDENT }
enum	PMLMode { AD1, AD2, AS, IDENT, AD1, AD2, AS, IDENT }
typedef Cmplx	value_type
Public Member Functions
Real	c_c (Real2d &p) const
Real	c_c (Real2d &p) const
virtual FormulaPMLRadia *	clone () const
	Virtual copy constructor.
virtual FormulaPMLRadia *	clone () const
	Virtual copy constructor.
	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.
	FormulaPMLRadia (const ElementFormulaContainer< Cmplx > coeff_a, const ElementFormulaContainer< Cmplx > coeff_b, RCP< Formula< Real > > sigma, RCP< Formula< Real > > sigmaB, PMLMode mode, double omega)
	Constructor.
Cmplx	gamma (Real2d &p) const
	Returns the parameter gamma in page 2067(no equation number) of the above article.
Cmplx	gamma (Real2d &p) const
	Returns the parameter gamma in page 2067(no equation number) of the above article.
Cmplx	gammaB (Real2d &p) const
	Returns the parameter gamma bar in page 2067(no equation number) of the above article.
Cmplx	gammaB (Real2d &p) const
	Returns the parameter gamma bar in page 2067(no equation number) of the above article.
virtual Cmplx	operator() (const ElementWithCell< typename Realtype< Cmplx >::type > &elm, const Real3d &p, const Real t=0.0) const =0
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< Real > &elm, const Real2d &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< typename Realtype< Cmplx >::type > &elm, const Real p, const Real t=0.0) const =0
	Evaluates the formula.
virtual Cmplx	operator() (const ElementWithCell< Real > &elm, const Real p, const Real t=0.0) const
virtual Cmplx	operator() (const ElementWithCell< typename Realtype< Cmplx >::type > &elm, const Real2d &p, const Real t=0.0) const =0
Real	s_c (Real2d &p) const
Real	s_c (Real2d &p) const
Real	s_s (Real2d &p) const
Real	s_s (Real2d &p) const
Protected Member Functions
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
virtual std::ostream &	info (std::ostream &os) const
	Returns information in an output stream.
Private Attributes
const ElementFormulaContainer < Cmplx >	coeff_a
	globally defined material, piecewise constant dielectric
const ElementFormulaContainer < Cmplx >	coeff_a_
	globally defined material, piecewise constant dielectric
const ElementFormulaContainer < Cmplx >	coeff_b
const ElementFormulaContainer < Cmplx >	coeff_b_
PMLMode	mode
	The choosen mode.
PMLMode	mode_
	The choosen mode.
double	omega
	The wave number.
double	omega_
	The wave number.
RCP< concepts::Formula< Real > >	sigma
	sigma function, which takes the general form of $PMLstrength*(\rho-PMLdist)^{powercoeff}$
RCP< Formula< Real > >	sigma_
	sigma function, which takes the general form of $PMLstrength*(\rho-PMLdist)^{powercoeff}$
RCP< concepts::Formula< Real > >	sigmaB
	sigma bar function, given in the above article page 2067, the average of sigma
RCP< Formula< Real > >	sigmaB_
	sigma bar function, given in the above article page 2067, the average of sigma

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 A12 = A21 = AS IDENT The term for MASS matrix

Author:: Mengyu Wang, 2010

Definition at line 823 of file pml_formula.h.

Member Typedef Documentation

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

Definition at line 31 of file elementFormula.hh.

Member Enumeration Documentation

enum concepts::FormulaPMLRadia::PMLMode

Enumerator:

AD1
AD2
AS
IDENT
AD1
AD2
AS
IDENT

Definition at line 825 of file pml_formula.h.

enum concepts::FormulaPMLRadia::PMLMode

Enumerator:

AD1
AD2
AS
IDENT
AD1
AD2
AS
IDENT

Definition at line 376 of file pml_formula.hh.

Constructor & Destructor Documentation

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 838 of file pml_formula.h.

concepts::FormulaPMLRadia::FormulaPMLRadia	(	const ElementFormulaContainer< Cmplx >	coeff_a,
		const ElementFormulaContainer< Cmplx >	coeff_b,
		RCP< Formula< Real > >	sigma,
		RCP< 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 389 of file pml_formula.hh.

Member Function Documentation

Real concepts::FormulaPMLRadia::c_c ( Real2d & p ) const [inline]

Definition at line 877 of file pml_formula.h.

Real concepts::FormulaPMLRadia::c_c ( Real2d & p ) const [inline]

Definition at line 428 of file pml_formula.hh.

virtual FormulaPMLRadia* concepts::FormulaPMLRadia::clone ( ) const [inline, virtual]

Virtual copy constructor.

Implements concepts::ElementFormula< Cmplx >.

Definition at line 404 of file pml_formula.hh.

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virtual FormulaPMLRadia* concepts::FormulaPMLRadia::clone ( ) const [inline, virtual]

Virtual copy constructor.

Implements concepts::ElementFormula< Cmplx >.

Definition at line 853 of file pml_formula.h.

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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 869 of file pml_formula.h.

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 420 of file pml_formula.hh.

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 873 of file pml_formula.h.

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 424 of file pml_formula.hh.

virtual std::ostream& concepts::FormulaPMLRadia::info ( std::ostream & os ) const [inline, protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Definition at line 454 of file pml_formula.hh.

virtual std::ostream& concepts::FormulaPMLRadia::info ( std::ostream & os ) const [inline, protected, virtual]

Returns information in an output stream.

Reimplemented from concepts::OutputOperator.

Definition at line 903 of file pml_formula.h.

virtual Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::type >::operator()	(	const ElementWithCell< typename Realtype<Cmplx >::type > &	elm,
		const Real	p,
		const Real	t = `0.0`
	)		const `[pure virtual, inherited]`

Evaluates the formula.

Parameters:

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

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

Definition at line 414 of file pml_formula.hh.

virtual Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::type >::operator()	(	const ElementWithCell< typename Realtype<Cmplx >::type > &	elm,
		const Real3d &	p,
		const Real	t = `0.0`
	)		const `[pure virtual, inherited]`

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

Definition at line 857 of file pml_formula.h.

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

Definition at line 889 of file pml_formula.h.

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virtual Cmplx concepts::ElementFormula< Cmplx , typename Realtype<Cmplx >::type >::operator()	(	const ElementWithCell< typename Realtype<Cmplx >::type > &	elm,
		const Real2d &	p,
		const Real	t = `0.0`
	)		const `[pure virtual, inherited]`

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

Definition at line 863 of file pml_formula.h.

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

Definition at line 440 of file pml_formula.hh.

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