Multivariate highly oscillatory integration

The aim of this talk is to describe several methods for numerically approximating

the integral of a multivariate highly oscillatory function. We begin with a review

of the asymptotic and Filon-type methods developed by Iserles and Nørsett. Using a

method developed by Levin as a point of departure we will construct a new method that

uses the same information as the Filon-type method, and obtains the same asymptotic

order, while not requiring moments. This allows us to integrate over nonsimplicial

domains, and with complicated oscillators.