Math-Sci Seminar

        (ATTENTION TO UNUSUAL DATE, PLACE and TIME)

Speaker: Dr. Fatih Ecevit, Max Plank Institute, Leipzig, Germany
Title: Analysis of Multiple Scattering Iterations for High-frequency Scattering Problems
Date: Tue 26 Dec, 2006
Time: 15:30
Place: Engineering Building, Room B15

Abstract:

We present an analysis of a recently proposed integral-equation method for the solution of high-frequency
electromagnetic and acoustic scattering problems that delivers error-controllable solutions in
frequency-independent computational times. Within single scattering configurations the method is based on
the use of an appropriate ansatz for the unknown surface densities and on suitable extensions of the method
of stationary phase. The extension to multiple-scattering configurations, in turn, is attained through consideration
of an iterative (Neumann) series that successively accounts for further geometrical wave reflections.
As we show, for a collection of convex obstacles, this series can be rearranged
into a sum of periodic orbits (of increasing period), each corresponding to contributions arising from waves
that reflect off a fixed subset of scatterers when these are transversed sequentially in a periodic manner.
Here, we analyze the properties of these periodic orbits in the high-frequency regime, by deriving precise
asymptotic expansions for the “currents” (i.e. the normal derivative of the fields) that they induce on the
surface of the obstacles. As we demonstrate these expansions can be used to provide accurate estimates of
the rate at which their magnitude decreases with increasing number of reflections, which defines the overall
rate of convergence of the multiple-scattering series. Moreover, we show that the detailed asymptotic
knowledge of these currents can be used to accelerate this convergence and, thus, to reduce the number of
iterations necessary to attain a prescribed accuracy.


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