×

The Green’s function for the two-dimensional Helmholtz equation in periodic domains. (English) Zbl 0922.76274

Summary: Analytical techniques are described for transforming the Green’s function for the two-dimensional Helmholtz equation in periodic domains from the slowly convergent representation as a series of images into forms more suitable for computation. In particular, methods derived from Kummer’s transformation are described, and integral representations, lattice sums and the use of Ewald’s method are discussed. We also consider Green’s functions suitable for problems in parallel-plate acoustic waveguides, and present numerical results comparing the accuracy of the various methods.

MSC:

76Q05 Hydro- and aero-acoustics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
PDFBibTeX XMLCite
Full Text: DOI