### Abstract

The numerical approximation of high frequency wave propagation is important in many applications, including geophysics, electromagnetics and acoustics. When the wavelength is short compared to the overall size of the computational domain direct simulation using standard wave equations is very expensive. Fortunately, there are computationally much less costly models, that are good approximations of many wave equations precisely for very high frequencies. In this talk I will focus on the geometrical optics approximation, which is the infinite frequency limit of wave equations. Geometrical optics has traditionally been simulated using ray tracing. More recently numerical procedures based on various partial differential equations have been introduced. In this talk I will survey such numerical methods for geometrical optics and also briefly discuss finite frequency corrections and some other models