Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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
Volume
457

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 March 3, 2024)
Created January 16, 2001, Updated June 2, 2021