Friday October 28 2005, 11h-12h (Celestijnenlaan 200S00.03, 3001 Heverlee)
The efficient evaluation of oscillatory integrals
By Daan Huybrechs (TWR)
Oscillatory integrals abound in numerical methods for the solution of engineering problems, including in electromagnetism, quantum physics, acoustics and wave phenomenas in general. The solution of these problems often requires an accurate and quick evaluation of the integral. Recently, much progress has been made in this field: oscillatory integrals can be approximated with regular quadrature rules using only few quadrature points, irrespective of the frequency of the oscillations.
In this seminar we present two new methods to evaluate highly oscillatory integrals, based on results from the field of complex analysis. Contrary to most classical approaches, the accuracy of these methods actually increases with increasing frequency. The second method gives rise to a quadrature formula of a conventional form that can be used as a computational tool in other numerical methods. An application involving high frequency wave scattering is briefly presented.