oomph::BermudezPMLMappingAndTransformedCoordinate Class Reference

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

Constructor & Destructor Documentation

BermudezPMLMappingAndTransformedCoordinate()

oomph::BermudezPMLMappingAndTransformedCoordinate::BermudezPMLMappingAndTransformedCoordinate ( )

inline

Default constructor (empty)

{};

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.

    {
      return 1.0 +
             std::complex<double>(1.0 / sqrt(k_squared), 0) *
               std::complex<double>(0.0, 1.0 / (std::fabs(pml_width_i - nu_i)));
    }

References boost::multiprecision::fabs(), and sqrt().

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

Implements oomph::PMLMappingAndTransformedCoordinate.

    {
      double log_arg = 1.0 - std::fabs(nu_i / pml_width_i);
      return std::complex<double>(pml_inner_boundary + nu_i,
                                  -log(log_arg) / sqrt(k_squared));
    }

References boost::multiprecision::fabs(), Eigen::bfloat16_impl::log(), and sqrt().

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

• pml_fourier_decomposed_helmholtz_elements.h