Applying the numerical method of steepest descent on multivariate oscillatory integrals in scattering theory

2013/02/05 by Asheim, Andreas
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1302.1019

Abstract

In this paper we demonstrate that the numerical method of steepest descent fails when applied in a straight forward fashion to the most commonly occurring highly oscillatory integrals in scattering theory. Through a polar change of variables, however, the integral can be brought on a form that can be solved efficiently using a mix of oscillatory integration techniques and classical quadrature. The approach is described in detail and demonstrated numerically on integration problems taken from applications.

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