The efficient evaluation of Green’s functions is a crucial aspect in the numerical analysis of periodic electromagnetic structures through integral-equation methods. In fact, the extremely slow converging behavior of the simple space-domain summation of non-periodic Green’s functions requires the use of suitable acceleration techniques, in order to reduce to acceptable values the calculation time of the reaction integrals involved in the method of moments. Although a number of such techniques has been known for a long time, various aspects still deserve investigation and the research in this field is ongoing. Among the various acceleration techniques, the Ewald method stands for its robustness and efficiency. In this work we study and optimize its application to the calculation of the Green function for the study of structures periodic along three axes (3D periodic Green’s function). This is an important case that finds application, e.g., in problems involving cavities (waveguide resonators and filters, shielding configurations) and artificial materials (3D electromagnetic band-gap structures, bulk metamaterials). As is known, the Ewald method is based on the splitting of the Green function calculation in two parts, expressed by a spatial series and a spectral series, respectively, whose relative computational burden is regulated by the so-called splitting (or Ewald) parameter E. In this work, limitations on the numerical accuracy occurring when the E parameter is chosen to have maximal asymptotic convergence are discussed, and an optimal choice for E is proposed to overcome them. The best ways of summing the resulting three-indices spatial and spectral series are also considered. Comparisons with other acceleration techniques applicable to 3D periodic Green’s functions are presented.

Efficient numerical evaluation of the 3D periodic green’s function in free space through the Ewald technique / Lovat, Giampiero; Burghignoli, Paolo; Araneo, Rodolfo. - ELETTRONICO. - (2008), pp. 1-1. (Intervento presentato al convegno 2008 USNC/URSI National Radio Science Meeting tenutosi a San Diego, CA, USA nel 5-12 luglio 2008).

Efficient numerical evaluation of the 3D periodic green’s function in free space through the Ewald technique

LOVAT, GIAMPIERO;BURGHIGNOLI, Paolo;ARANEO, Rodolfo
2008

Abstract

The efficient evaluation of Green’s functions is a crucial aspect in the numerical analysis of periodic electromagnetic structures through integral-equation methods. In fact, the extremely slow converging behavior of the simple space-domain summation of non-periodic Green’s functions requires the use of suitable acceleration techniques, in order to reduce to acceptable values the calculation time of the reaction integrals involved in the method of moments. Although a number of such techniques has been known for a long time, various aspects still deserve investigation and the research in this field is ongoing. Among the various acceleration techniques, the Ewald method stands for its robustness and efficiency. In this work we study and optimize its application to the calculation of the Green function for the study of structures periodic along three axes (3D periodic Green’s function). This is an important case that finds application, e.g., in problems involving cavities (waveguide resonators and filters, shielding configurations) and artificial materials (3D electromagnetic band-gap structures, bulk metamaterials). As is known, the Ewald method is based on the splitting of the Green function calculation in two parts, expressed by a spatial series and a spectral series, respectively, whose relative computational burden is regulated by the so-called splitting (or Ewald) parameter E. In this work, limitations on the numerical accuracy occurring when the E parameter is chosen to have maximal asymptotic convergence are discussed, and an optimal choice for E is proposed to overcome them. The best ways of summing the resulting three-indices spatial and spectral series are also considered. Comparisons with other acceleration techniques applicable to 3D periodic Green’s functions are presented.
2008
2008 USNC/URSI National Radio Science Meeting
04 Pubblicazione in atti di convegno::04d Abstract in atti di convegno
Efficient numerical evaluation of the 3D periodic green’s function in free space through the Ewald technique / Lovat, Giampiero; Burghignoli, Paolo; Araneo, Rodolfo. - ELETTRONICO. - (2008), pp. 1-1. (Intervento presentato al convegno 2008 USNC/URSI National Radio Science Meeting tenutosi a San Diego, CA, USA nel 5-12 luglio 2008).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/227980
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