Lattice Sums for the Helmholtz Equation

A survey of different representations for lattice sums for the Helmholtz equation is given. These sums arise naturally when dealing with wave scattering by periodic structures. One of the main objectives is to show how the various forms depend on the dimension d of the underlying space and the lattice dimension d. Lattice sums are related to, and can be calculated from, the quasi-periodic Green's function and this object serves as the starting point of the analysis. Key words. Lattice, Helmholtz equation, Ewald summation, quasi-periodic Green's function AMS subject classifications.

• Type: Journal
• Year: 2010
• Where: SIAMREV
• Authors: Chris M. Linton
• Keywords: Helmholtz Equation, Lattice Dimension, Lattice Sums, SIAMREV 2010