Title: Asymptotic Green's function methods for high frequency wave propagation 

Abstract: We will present asymptotic methods for simulating high frequency wave propagation. The Huygens' principle or the Feymann's path integral is used as the time propagator for the wavefunction, where the Green's functions are approximated by asymptotic approximations. Upon obtaining analytic approximations for the phase and amplitude of the Green's functions, the resulting integral can be evaluated by fast Fourier transform after appropriate low rank approximations.  The perfectly matched layer method is incorporated to restrict the computation onto a bounded domain of interest. Numerical example will be presented to demonstrate the asymptotic Green's function methods.

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