The mapping function propsed by Bermudez et al, appears to be the best and so this will be the default mapping (see definition of PMLHelmholtzEquations) More...

#include <pml_fourier_decomposed_helmholtz_elements.h>

Inheritance diagram for oomph::BermudezPMLMappingAndTransformedCoordinate:

Public Member Functions
	BermudezPMLMappingAndTransformedCoordinate ()
	Default constructor (empty) More...

std::complex< double >	gamma (const double &nu_i, const double &pml_width_i, const double &k_squared)
	Overwrite the pure PML mapping coefficient function to return the mapping function proposed by Bermudez et al. More...

std::complex< double >	transformed_coordinate (const double &nu_i, const double &pml_width_i, const double &pml_inner_boundary, const double &k_squared)
	Overwrite the pure PML mapping coefficient function to return the transformed coordinate proposed by Bermudez et al. More...

Public Member Functions inherited from oomph::PMLMappingAndTransformedCoordinate
	PMLMappingAndTransformedCoordinate ()
	Default constructor (empty) More...

Detailed Description

The mapping function propsed by Bermudez et al, appears to be the best and so this will be the default mapping (see definition of PMLHelmholtzEquations)

Definition at line 108 of file pml_fourier_decomposed_helmholtz_elements.h.

Constructor & Destructor Documentation

◆ BermudezPMLMappingAndTransformedCoordinate()

oomph::BermudezPMLMappingAndTransformedCoordinate::BermudezPMLMappingAndTransformedCoordinate ( )

inline

Default constructor (empty)

Definition at line 113 of file pml_fourier_decomposed_helmholtz_elements.h.

Member Function Documentation

◆ gamma()

std::complex<double> oomph::BermudezPMLMappingAndTransformedCoordinate::gamma	(	const double &	nu_i,
		const double &	pml_width_i,
		const double &	k_squared
	)

inlinevirtual

Overwrite the pure PML mapping coefficient function to return the mapping function proposed by Bermudez et al.

return $\gamma=1 + (1/k)(i/|outer_boundary - x|)$ or more abstractly $\gamma = 1 + \frac i {k\delta_{pml}}(1/|1-\bar\nu|)$

Implements oomph::PMLMappingAndTransformedCoordinate.

Definition at line 117 of file pml_fourier_decomposed_helmholtz_elements.h.

◆ transformed_coordinate()

std::complex<double> oomph::BermudezPMLMappingAndTransformedCoordinate::transformed_coordinate	(	const double &	nu_i,
		const double &	pml_width_i,
		const double &	pml_inner_boundary,
		const double &	k_squared
	)

inlinevirtual

Overwrite the pure PML mapping coefficient function to return the transformed coordinate proposed by Bermudez et al.

return $\tilde x = h + \nu + \log(1-|\nu / \delta|)$