Applying the numerical method of steepest descent on multivariate oscillatory integrals in scattering theory
Numerical Analysis
2013-02-06 v1
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.
Keywords
Cite
@article{arxiv.1302.1019,
title = {Applying the numerical method of steepest descent on multivariate oscillatory integrals in scattering theory},
author = {Andreas Asheim},
journal= {arXiv preprint arXiv:1302.1019},
year = {2013}
}