Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space


Journal Article

© 2016 The Author(s) Published by the Royal Society. This work, part I in a two-part series, presents: (i) a simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) an associated boundary-integral equation method for the numerical solution of problems of scattering of waves by doubly periodic arrays of scatterers in three-dimensional space. Except for certain 'Wood frequencies' at which the quasi-periodic Green function ceases to exist, the proposed approach, which is based on smooth windowing functions, gives rise to tapered lattice sums which converge superalgebraically fast to the Green function-that is, faster than any power of the number of terms used. This is in sharp contrast to the extremely slow convergence exhibited by the lattice sums in the absence of smooth windowing. (The Wood-frequency problem is treated in part II.) This paper establishes rigorously the superalgebraic convergence of the windowed lattice sums. A variety of numerical results demonstrate the practical efficiency of the proposed approach.

Full Text

Duke Authors

Cited Authors

  • Bruno, OP; Shipman, SP; Turc, C; Venakides, S

Published Date

  • July 1, 2016

Published In

Volume / Issue

  • 472 / 2191

PubMed ID

  • 27493573

Pubmed Central ID

  • 27493573

Electronic International Standard Serial Number (EISSN)

  • 1471-2946

International Standard Serial Number (ISSN)

  • 1364-5021

Digital Object Identifier (DOI)

  • 10.1098/rspa.2016.0255

Citation Source

  • Scopus