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Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation
Published
Author(s)
Andrew M. Dienstfrey, 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
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 June 1, 2023)