| Abstract: | The Helmholtz equation is widely used to model wave propagation problems in application areas like electro-magnetics, geophysics and acoustics. Numerical simulation of Helmholtz becomes expensive when the frequency of the waves is high. In this talk we present the recent construction of the Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source, under the assumption of non-trapping rays we show error estimates between the exact outgoing solution and Gaussian beams in terms of the wave number k, both for single beams and superposition of beams. The main result is that the relative local L2 error in the beam approximations decay as k^{?N/2} independent of dimension and presence of caustics, for N-th order beams. This is a joint work with J. Ralston, O. Runborg and N. Tanushev. |
