On the stability of the high-order Higdon Absorbing Boundary Conditions

Baffet, Daniel H.; Givoli, Dan

doi:10.1016/j.apnum.2011.01.010

Cited by 14 publications

(11 citation statements)

References 29 publications

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“…This can effect the stability of the system. For the time dependent wave equation this has been investigated in [1].…”

Section: Appendix a Self-adjointness Of Abcs For Helmholtz Equationmentioning

confidence: 98%

“…Sommerfeld [32, §28] shows that the following "radiation condition" is sufficient for the well-posedness of the Helmholtz equation (1) in an exterior unbounded region when the RHS function F (x, y, z) has a compact support.…”

Section: The Sommerfeld Radiation Conditionmentioning

confidence: 99%

“…We consider compact high order absorbing boundary conditions (ABCs) for the Helmholtz equation in a finite domain D: u + k 2 u = F , (1) where k(x, y, z) is the wavenumber, and F (x, y, z) is typically the displacement at a point or region of D. We consider various high order absorbing boundary conditions (ABCs) and introduce a new technique called "the gradient method" (GM) as a new approach to ABCs for the Helmholtz equation, and possibly, for other partial differential equations of physics. GM is based on the principle of using directional derivatives of u in the direction of the wavefront propagation, i.e., the direction of ∇u (the gradient of u).…”

Section: Introductionmentioning

confidence: 99%

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Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Gordon

Turkel

2015

Journal of Computational Physics

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“…This can effect the stability of the system. For the time dependent wave equation this has been investigated in [1].…”

Section: Appendix a Self-adjointness Of Abcs For Helmholtz Equationmentioning

confidence: 98%

Section: The Sommerfeld Radiation Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Gordon

Turkel

2015

Journal of Computational Physics

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“…The energy method has been successfully used to analyze problems with freesurface [413], PML [414,415], and absorbing boundary conditions [28,37,379,411,416]. Besides finite differences, the analysis with energy method is present in finite [35] and spectral [417] elements, finite volumes [266], and discontinuous Galerkin methods [418].…”

Section: Stabilitymentioning

confidence: 99%

Numerical modeling of mechanical wave propagation

Seriani

Oliveira

2020

Riv. Nuovo Cim.

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The numerical modeling of mechanical waves is currently a fundamental tool for the study and investigation of their propagation in media with heterogeneous physical properties and/or complex geometry, as, in these cases, analytical methods are usually not applicable. These techniques are used in geophysics (geophysical interpretation, subsoil imaging, development of new methods of exploration), seismology (study of earthquakes, regional and global seismology, accurate calculation of synthetic seismograms), in the development of new methods for ultrasonic diagnostics in materials science (non-destructive methods) and medicine (acoustic tomography). In this paper we present a review of numerical methods that have been developed and are currently used. In particular we review the key concepts and pioneering ideas behind finite-difference methods, pseudospectral methods, finite-volume methods, Galerkin continuous and discontinuous finite-element methods (classical or based on spectral interpolation), and still others such as physics-compatible, and multiscale methods. We focus on their formulations in time domain along with the main temporal discretization schemes. We present the theory and implementation for some of these methods. Moreover, their computational characteristics are evaluated in order to aid the choice of the method for each practical situation.

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“…Although the Higdon's ABC [6] was proved to be energystable up to any order on the continuous level, instability of implementing the high-order Higdon's ABC with Eqn. (1) was found in [2], [7], [8].…”

Section: Introductionmentioning

confidence: 99%

A stable implementation of multiple Higdon’s absorbing boundary condition for Maxwell’s equations

Rengang¹

2021

Preprint

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Highlights 1) This letter presents a stable implementation of Higdon’s ABC at multiple layers without attenuation factor. 2) The multiple Higdon’s ABC works well with wide-band frequency and ultra-thin layers, such as three. 3) Optimal parameters of the multiple Higdon’s ABC are presented in this letter. 4) The optimal angels of the multiple Higdon’s ABC satisfy a circle equation.

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On the stability of the high-order Higdon Absorbing Boundary Conditions

Cited by 14 publications

References 29 publications

Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions

Numerical modeling of mechanical wave propagation

A stable implementation of multiple Higdon’s absorbing boundary condition for Maxwell’s equations

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