Comparative Analysis of Acceleration Techniques for 2-D and 3-D Green's Functions in Periodic Structures Along One and Two Directions

2007/06/01 by Guido Valerio, Paolo Baccarelli, Paolo Burghignoli +1 · 112 citations
Engineering · Mathematics · Physics and Astronomy · #Acceleration #Advanced Antenna and Metasurface Technologies #Classical mechanics #Combinatorics #Computer science #Electromagnetic Compatibility and Measurements #Electromagnetic Scattering and Analysis #Function (biology) #Mathematical analysis #Mathematics #Phase space #Physics #Quantum mechanics #Skew #Space (punctuation) #Telecommunications #Topology (electrical circuits)

paper · doi:10.1109/tap.2007.897340

published in IEEE Transactions on Antennas and Propagation 55(6), 1630-1643 (IEEE Antennas & Propagation Society)

openalex publication_date 2007/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

The problem of accelerating the calculation of the periodic Green's function is addressed here for both 3-D and 2-D free-space configurations. In the 3-D case, periodicity is considered both along one axis and along two, generally skew, axes. A comprehensive review of the existing methods is first presented and some extensions are developed. The possibility of treating the case of complex phase shifts between unit cells, necessary for the study of complex modes in periodic structures, is also investigated. Comparisons among the various acceleration methods are performed, thus providing fundamental information on their actual efficiency in typical problems.

Citations

• Die Berechnung optischer und elektrostatischer Gitterpotentiale
• A new acceleration technique with exponential convergence rate to evaluate periodic Green functions

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