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|Author(s):||Andrew M. Dienstfrey; Fengbo Hang; Jingfang Huang;|
|Title:||Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation|
|Published:||January 16, 2001|
|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|
|Pages:||pp. 67 - 85|
|Keywords:||Helmholtz equation, lattice sums, plane-wave expansion|
|PDF version:||Click here to retrieve PDF version of paper (254KB)|