Efficient evaluation of edge diffraction integrals using the numerical method of steepest descent

Abstract

For the problem of edge diffraction from an edge of finite length a frequency-domain solution, obtained from an analytical time-domain solution, has been presented by Svensson et al. [Acta. Acust. Acust. 95, 568-572]. This formulation takes the form of a Fourier-type integral whose evaluation is expensive in the high frequency range. This paper demonstrates that by using tailored highly oscillatory quadrature methods based on asymptotic properties of the integral, accurate approximations in the high frequency case can be obtained with little computational effort.