PathFinder: A toolbox for highly oscillatory integrals
Andrew Gibbs, University College London
Sala conferenze IMATI-CNR, Pavia – Martedì 12 Novembre 2019 h.15:00
Abstract. Highly oscillatory integrals arise when modelling short-wavelength phenomena, for example creeping waves, whispering gallery waves or molecular collisions. Standard numerical quadrature rules are very expensive for highly oscillatory integrals, typically requiring the cost to grow in proportion with frequency. A range of specialised methods exist for the evaluation of such integrals, although care and prior analysis are necessary to implement these methods robustly.
In this talk I will present PathFinder, a Matlab toolbox for the evaluation of highly oscillatory integrals. I will assume no prior knowledge of the subject, and so will begin by introducing the method of numerical steepest descent (NSD), on which the toolbox is based. The general idea behind NSD is to deform the path of integration into the complex plane, onto a contour where the integrand is exponentially decaying, which is much easier to evaluate by numerical quadrature. Once I have demonstrated the effectiveness of NSD, I will explain how the process is automated robustly in PathFinder, for a general class of oscillatory integrals.