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

Oscar P. Bruno, Stephen P. Shipman, Catalin Turc, Stephanos Venakides

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number20160255
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2191
DOIs
StatePublished - Jul 1 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Keywords

  • Scattering,Periodic Green function,Lattice sum,Smooth truncation,Super-algebraic convergence,Boundary-integral equations

Fingerprint

Dive into the research topics of 'Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space'. Together they form a unique fingerprint.

Cite this