pml_mapping_functions.h
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26#ifndef OOMPH_PML_MAPPING_FUNCTIONS_HEADER
27#define OOMPH_PML_MAPPING_FUNCTIONS_HEADER
28
29// Config header generated by autoconfig
30#ifdef HAVE_CONFIG_H
31#include <oomph-lib-config.h>
32#endif
33
34#include "complex_matrices.h"
35#include "oomph_utilities.h"
36
37namespace oomph
38{
39 //
40 //=======================================================================
41 /// Class to hold the mapping function (gamma) for the Pml which defines
42 /// how the coordinates are transformed in the Pml. This class holds
43 /// the one dimensional or uniaxial case which is the most common
44 //=======================================================================
46 {
47 public:
48 /// Default constructor (empty)
50
51 /// Pure virtual to return Pml mapping gamma, where gamma is the
52 /// \f$d\tilde x / d x\f$ as function of \f$\nu\f$ where \f$\nu = x - h\f$
53 /// where h is the vector from the origin to the start of the Pml
54 virtual std::complex<double> gamma(const double& nu_i,
55 const double& pml_width_i,
56 const double& wavenumber_squared,
57 const double& alpha_shift = 0.0) = 0;
58 };
59
60 //=======================================================================
61 /// A mapping function propsed by Bermudez et al, appears to be the best
62 /// for the Helmholtz equations and so this will be the default mapping
63 /// (see definition of PmlHelmholtzEquations)
64 //=======================================================================
66 {
67 public:
68 /// Default constructor (empty)
70
71 /// Overwrite the pure Pml mapping coefficient function to return the
72 /// coeffcients proposed by Bermudez et al
73 std::complex<double> gamma(const double& nu_i,
74 const double& pml_width_i,
75 const double& wavenumber_squared,
76 const double& alpha_shift = 0.0)
77 {
78 /// return \f$\gamma=1 + (1/k)(i/|outer_boundary - x|)\f$
79 return 1.0 + MathematicalConstants::I / sqrt(wavenumber_squared) *
80 (1.0 / std::fabs(pml_width_i - nu_i));
81 }
82 };
83
84 //=======================================================================
85 /// A mapping function proposed by Bermudez et al, similar to the one above
86 /// but is continuous across the inner Pml boundary
87 /// appears to be the best for TimeHarmonicLinearElasticity
88 /// and so this will be the default mapping
89 //=======================================================================
91 {
92 public:
93 /// Default constructor (empty)
95
96 /// Overwrite the pure Pml mapping coefficient function to return the
97 /// coeffcients proposed by Bermudez et al
98 std::complex<double> gamma(const double& nu_i,
99 const double& pml_width_i,
100 const double& wavenumber_squared,
101 const double& alpha_shift = 0.0)
102 {
103 /// return \f$\gamma=1 + (i/k)(1/|outer_boundary - x|-1/|pml width|)\f$
104 return 1.0 + MathematicalConstants::I / sqrt(wavenumber_squared) *
105 (1.0 / std::fabs(pml_width_i - nu_i) -
106 1.0 / std::fabs(pml_width_i));
107 }
108 };
109
110} // namespace oomph
111
112#endif
A mapping function propsed by Bermudez et al, appears to be the best for the Helmholtz equations and ...
BermudezPMLMapping()
Default constructor (empty)
std::complex< double > gamma(const double &nu_i, const double &pml_width_i, const double &wavenumber_squared, const double &alpha_shift=0.0)
Overwrite the pure Pml mapping coefficient function to return the coeffcients proposed by Bermudez et...
A mapping function proposed by Bermudez et al, similar to the one above but is continuous across the ...
std::complex< double > gamma(const double &nu_i, const double &pml_width_i, const double &wavenumber_squared, const double &alpha_shift=0.0)
Overwrite the pure Pml mapping coefficient function to return the coeffcients proposed by Bermudez et...
ContinuousBermudezPMLMapping()
Default constructor (empty)
Class to hold the mapping function (gamma) for the Pml which defines how the coordinates are transfor...
virtual std::complex< double > gamma(const double &nu_i, const double &pml_width_i, const double &wavenumber_squared, const double &alpha_shift=0.0)=0
Pure virtual to return Pml mapping gamma, where gamma is the as function of where where h is the v...
PMLMapping()
Default constructor (empty)
const std::complex< double > I(0.0, 1.0)
The imaginary unit.
//////////////////////////////////////////////////////////////////// ////////////////////////////////...