Gaussian Beam Methods for the Helmholtz Equation

In this work we construct 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.