A broadband ML-FMA for 3-D periodic green's function in 2-D lattice using ewald summation

Michael Wei, Weng C. Chew

Research output: Contribution to journalArticle

Abstract

A periodic fast multipole algorithm (P-FMA) is devised for evaluating 3-D periodic Green's function (PGF) for a 2-D lattice which can be used to solve scattering by a structure with 2-D periodicity. The introduction of periodicity in the Green's function formulation produces image sources at each lattice site. Like multilevel FMA (ML-FMA), P-FMA takes advantage of the distance between image sources and observation points to factorize the field using multipoles. By substituting known factorizations of the free-space Green's function into the expression for PGF, one can isolate the summation over the lattice into the translation phase of the FMA. For both plane wave and multipole factorizations, a common term known as lattice constant appears. The lattice constant is an infinite sum over the lattice which does not converge absolutely when expressed as a spatial sum. Using the Ewald summation technique, the lattice constants can be evaluated with exponential convergence and high accuracy. The resulting P-FMA is between O(N) and O(N log N) in memory use and computational complexity, depending on the object size relative to the wavelength.

Original languageEnglish (US)
Article number7891536
Pages (from-to)3134-3145
Number of pages12
JournalIEEE Transactions on Antennas and Propagation
Volume65
Issue number6
DOIs
StatePublished - Jan 1 2017

Fingerprint

periodic functions
Green's function
Green's functions
Lattice constants
broadband
multipoles
Factorization
factorization
periodic variations
Crystal lattices
Computational complexity
Scattering
Data storage equipment
Wavelength
plane waves
formulations
scattering
wavelengths

Keywords

  • Ewald summation
  • Fast multipole method (ML-FMA)
  • Lattice sum
  • Method of moments (MoM)
  • Multilevel
  • Periodic Green's function (PGF)
  • Periodic scattering
  • Periodic structures

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

A broadband ML-FMA for 3-D periodic green's function in 2-D lattice using ewald summation. / Wei, Michael; Chew, Weng C.

In: IEEE Transactions on Antennas and Propagation, Vol. 65, No. 6, 7891536, 01.01.2017, p. 3134-3145.

Research output: Contribution to journalArticle

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