TUESDAY Feb. 13 : | Analysis Seminar |

Title: | Efficient computation of diffraction near cutoff (Wood anomaly) frequencies |

Stephen Shipman
Luisiana State University Abstract: We present an efficient method for computing wave scattering by 2D-periodic diffraction gratings in 3D space near cutoff frequencies, at which a Rayleigh wave is at grazing incidence to the grating. At these frequencies (a.k.a. Wood-anomaly frequencies), the quasi-periodic Green function does not exist, although a solution to the diffraction problem typically does. This is manifest in the divergence of a doubly infinite spatial lattice sum that represents the Green function at generic frequencies. We present a modification of this lattice sum by adding two types of terms to it. The first type adds weighted spatial shifts of the Green function to itself. The shifts are such that the spatial singularities introduced by these terms are located below the grating and therefore out of the spatial domain of interest. With suitable choices of the weights, these terms produce algebraic convergence of the lattice sum. The degree of the algebraic convergence depends on the number of added shifts. The second type of terms are quasi-periodic plane wave solutions of the Helmholtz equation. They reinstate the grazing modes, effectively eliminated by the terms of the first type. These modes are needed for guaranteeing the well-posedness of the boundary-integral equation for the scattered field that involves the Green function. This is joint work with O. Bruno, C. Turc, and S. Venakides. | |

Time and Place: | 03:30 PM CW 131 |