Stability analysis of the Green's Function Method (GFM) used as an ABC for arbitrarily shaped boundaries

Ronen Holtzman; Raphael Kastner; Ehud Heyman; Richard W. Ziolkowski

doi:10.1109/TAP.2002.802272

Stability analysis of the Green's Function Method (GFM) used as an ABC for arbitrarily shaped boundaries

Ronen Holtzman, Raphael Kastner, Ehud Heyman, Richard W. Ziolkowski

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

The time-domain discrete Green's function of the external region beyond a given boundary has been recently introduced as a discretized version of the impedance condition. It is incorporated within the framework of the finite-difference time-domain (FDTD) as a quasi-local, single-layer boundary condition, termed the Green's function method (GFM). The stability characteristics of this method are provided. The analysis is based on the general representation of the method in matrix form, whose eigenvalues are investigated. This formulation helps detect and remove possible instabilities of the algorithm. A demonstration of the GFM absorbing boundary condition's (ABCs) ability to deal with re-entrant corner problems is given.

Original language	English (US)
Pages (from-to)	1017-1029
Number of pages	13
Journal	IEEE Transactions on Antennas and Propagation
Volume	50
Issue number	7
DOIs	https://doi.org/10.1109/TAP.2002.802272
State	Published - Jul 2002

Keywords

Absorbing boundary conditions (ABCs)
Finite-difference time-domain (FDTD)
Green's function
Stability

ASJC Scopus subject areas

Electrical and Electronic Engineering

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10.1109/TAP.2002.802272

Cite this

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title = "Stability analysis of the Green's Function Method (GFM) used as an ABC for arbitrarily shaped boundaries",

abstract = "The time-domain discrete Green's function of the external region beyond a given boundary has been recently introduced as a discretized version of the impedance condition. It is incorporated within the framework of the finite-difference time-domain (FDTD) as a quasi-local, single-layer boundary condition, termed the Green's function method (GFM). The stability characteristics of this method are provided. The analysis is based on the general representation of the method in matrix form, whose eigenvalues are investigated. This formulation helps detect and remove possible instabilities of the algorithm. A demonstration of the GFM absorbing boundary condition's (ABCs) ability to deal with re-entrant corner problems is given.",

keywords = "Absorbing boundary conditions (ABCs), Finite-difference time-domain (FDTD), Green's function, Stability",

author = "Ronen Holtzman and Raphael Kastner and Ehud Heyman and Ziolkowski, {Richard W.}",

note = "Funding Information: Manuscript received April 3, 2000; revised March 29, 2001. This work was supported by Grant No. 1999420, under the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel.",

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AU - Kastner, Raphael

AU - Heyman, Ehud

AU - Ziolkowski, Richard W.

N1 - Funding Information: Manuscript received April 3, 2000; revised March 29, 2001. This work was supported by Grant No. 1999420, under the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel.

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N2 - The time-domain discrete Green's function of the external region beyond a given boundary has been recently introduced as a discretized version of the impedance condition. It is incorporated within the framework of the finite-difference time-domain (FDTD) as a quasi-local, single-layer boundary condition, termed the Green's function method (GFM). The stability characteristics of this method are provided. The analysis is based on the general representation of the method in matrix form, whose eigenvalues are investigated. This formulation helps detect and remove possible instabilities of the algorithm. A demonstration of the GFM absorbing boundary condition's (ABCs) ability to deal with re-entrant corner problems is given.

AB - The time-domain discrete Green's function of the external region beyond a given boundary has been recently introduced as a discretized version of the impedance condition. It is incorporated within the framework of the finite-difference time-domain (FDTD) as a quasi-local, single-layer boundary condition, termed the Green's function method (GFM). The stability characteristics of this method are provided. The analysis is based on the general representation of the method in matrix form, whose eigenvalues are investigated. This formulation helps detect and remove possible instabilities of the algorithm. A demonstration of the GFM absorbing boundary condition's (ABCs) ability to deal with re-entrant corner problems is given.

KW - Absorbing boundary conditions (ABCs)

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KW - Green's function

KW - Stability

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Stability analysis of the Green's Function Method (GFM) used as an ABC for arbitrarily shaped boundaries

Abstract

Keywords

ASJC Scopus subject areas

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