| 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 |
| Volume: |
457 |
| Pages: |
pp. 67 - 85 |
| Keywords: |
Helmholtz equation; lattice sums; plane-wave expansion |
| Research Areas: |
Math |
| PDF version: |
 Click here to retrieve PDF version of paper (248KB) |
