English

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}
}