A new acceleration technique with exponential convergence rate to evaluate periodic Green functions

2005/01/01 by M.G. Silveirinha, Mário G. Silveirinha, C.A. Fernandes +1 · 54 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Acceleration #Antenna Design and Optimization #Applied mathematics #Classical mechanics #Computer science #Convergence (economics) #Exponential function #Exponential growth #Function (biology) #Gaussian #Gaussian function #Geometry #Mathematical analysis #Mathematics #Metamaterials and Metasurfaces Applications #Orbital Angular Momentum in Optics #Physics #Point (geometry) #Position (finance) #Rate of convergence #Telecommunications

paper · doi:10.1109/tap.2004.838793

published in IEEE Transactions on Antennas and Propagation 53(1), 347-355 (IEEE Antennas & Propagation Society)

openalex publication_date 2005/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

We propose a new approach to compute the dynamic potential (Green function) from two- and three-dimensional periodic arrays of point sources in a three-dimensional space. The method has at least exponential convergence rate (in some cases it has Gaussian convergence rate). The convergence rate is independent of the position of the observation point in the unit cell. The proposed approach can also be used to calculate the derivatives of the Green function very efficiently.

Citations

• Die Berechnung optischer und elektrostatischer Gitterpotentiale

Cited by

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