Asymptotic high-frequency methods

A review is given of a wide variety of asymptotic methods used in high-frequency scattering. Following brief descriptions of the saddle point method, Watson transformation, and residue series, a survey of the literature is made in which these methods have been employed. The desirability of using high-frequency approximate methods is pointed out. A critical discussion of geometrical optics, physical optics, and the geometrical theory of diffraction is presented. The relationship of these methods to the asymptotic solution of Maxwell´s equations is examined. Their applicability and limitations are discussed by referring to numerous examples in the literature.