Windowed oscillatory integral: an approach to compute high-frequency wave fields

We revise known approaches to compute high- frequency wave-fields and propose a new one. The approach is uniform in the sense that, in contrary to the conventional ray-tracing method, it can be applied globally and independently of ray-field singularities (caustics). The obtained representation has the form of an integral over rays, only rays passing through a vicinity of the observation point contribute. The integral representation differs, however, from analogous ones (such as Maslov's canonical operator and Gaussian-beams method) and provides efficient tool for computation of electromagnetic, acoustic and elastic high-frequency waves.