Geometrical optics and geometrical theory of diffraction are approximations for high frequency wave propagation, which are used in a number of applications. We shall first discuss numerical computations of wave propagation in general with the emphasis on applications in the simulation of electromagnetic and seismic wave fields. The equations of geometrical optics and geometrical theory of diffraction will then be introduced. Different formulations in the forms of ordinary and partial differential equations will be discussed. Classical and modern computational techniques for these differential equations will be surveyed. This will include traditional ray tracing and the recently introduced methods based directly on the eikonal equation or the geometrically based motion of wave fronts. Finally there will be a discussion on hybridizing high frequency methods with other techniques for wave propagation and on important applications.
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