Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation

Published

January 16, 2001

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

Volume

457

Pub Type

Journals

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Keywords

Helmholtz equation, lattice sums, plane-wave expansion

Citation

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)