Dienstfrey, A.
, Hang, F.
and Huang, J.
(2001),
Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation, Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=901516
(Accessed May 9, 2025)
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Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation
Published
Author(s)
, Fengbo Hang, Jingfang Huang
Abstract
Many algorithms that are currently used for the solution of the Helmholtz equation in periodic domains require the evaluation of the Green s function, G(x, x0). The fact that the natural representation of G via the method of images gives rise to a conditionally convergent series whose direct evaluation is prohibitive has inspired the search for more efficient procedures for evaluating this Green s function. Recently, the evaluation of G through the lattice-sum representation has proven to be both accurate and fast. As a consequence, the computation of the requisite, also conditionally convergent, lattice sums has become an active area of research. We describe a new integral representation for these sums, and compare our results with other techniques for evaluating similar quantities.Citation
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences
Volume
457
Pub Type
Journals
Download Paper
Keywords
Helmholtz equation, lattice sums, plane-wave expansion
Citation
Issues
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Created January 16, 2001, Updated June 2, 2021