Superalgebraically convergent smoothly windowed lattice sums for doubly periodic Green functions in three-dimensional space
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.
Additional Information
© 2016 The Author(s). Published by the Royal Society. Received April 8, 2016. Accepted June 2, 2016. Published 6 July 2016. The authors gratefully acknowledge support from AFOSR and NSF under contracts FA9550-15-1-0043 and DMS-1411876 (O.P.B.); NSF DMS-0807325 (S.P.S.); NSF DMS-1008076 (C.T.) and NSF DMS-0707488 and NSF DMS-1211638 (S.V.). Data accessibility: All data applicable to this paper are included in the article. Authors' contributions: All authors are equally considered co-contributors in this article. There are no competing interests relevant to this article.Attached Files
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Additional details
- PMCID
- PMC4971249
- Eprint ID
- 71113
- Resolver ID
- CaltechAUTHORS:20161014-131501720
- FA9550-15-1-0043
- Air Force Office of Scientific Research (AFOSR)
- DMS-1411876
- NSF
- DMS-0807325
- NSF
- DMS-1008076
- NSF
- DMS-0707488
- NSF
- DMS-1211638
- NSF
- Created
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2016-10-14Created from EPrint's datestamp field
- Updated
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2022-04-26Created from EPrint's last_modified field