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 nontrapping 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 Nth order beams. [ABSTRACT FROM AUTHOR]