2134/17057
Christopher Linton
Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green's function
2015
Loughborough University
untagged
2015-03-19 13:42:12
article
https://repository.lboro.ac.uk/articles/Two-dimensional_phase_modulated_lattice_sums_with_application_to_the_Helmholtz_Green_s_function/9385340
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.