  We present a new methodology, based on the WKB approximation and Fast Fourier
Transforms, for the evaluation of wave propagation through inhomogeneous media.
This method can accurately resolve fields containing caustics, while still
enjoying the computational advantages of the WKB approximation, namely, the
ability to resolve arbitrarily high-frequency problems in computing times which
are orders-of-magnitude shorter than those required by other algorithms
presently available. For example, the proposed approach can simulate with high
accuracy (with errors such as e.g. 0.1\%--0.001\%) the propagation of 5 cm
radar signals across two-dimensional configurations resembling atmospheric
ducting conditions, spanning hundreds of kilometers and millions of wavelengths
in electrical size, in computing times of a few minutes in a single CPU core.
[Preliminary version]
