Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green's function
journal contributionposted on 19.03.2015, 13:42 by Christopher Linton
A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green's function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of Θ-functions which are significant generalisations of known results.
- Mathematical Sciences