Scientific Computing Group Seminars - Detail View

Speaker: A. Ditkowski

Affiliation: Tel Aviv University

Talk Title: Electromagnetic Scattering by Randomly Shaped Objects

Invited by: Jan S Hesthaven

Time: Sept. 11 2009 11 a.m.

Location: 182 George Street, Room 110

Abstract:

We propose a new numerical approach for the approximation of the scattered radiation by objects of uncertain shape. We model the uncertainty by representing it in terms of a known random variable, and employ the polynomial chaos expansion method. This later method has proved, in the majority of cases, to be computationally superior to the conventional Monte-Carlo sampling method. We consider the scattering phenomenon from a macroscopic point of view which is governed by Maxwell’s equations, and accordingly use the approximation to solve Maxwell’s Equations numerically. We show that the discontinuous nature of the problem’s domain causes a dramatic reduction in accuracy when the standard polynomial chaos expansion is employed. In order to obtain spectral convergence, we introduce a new implicit approach in which the approximation is obtained indirectly by expanding the interface fields at all possible states of the object’s shape. The presented new variant of the polynomial chaos expansion not only handles the discontinuity more accurately then the standard method, but also proves to be beneficiary in other aspects. First, the original problem in the unbounded domain is transformed to evaluation of one-dimensional integrals over a finite interval, thus efficiently reducing the computational domain. Furthermore, the approximation automatically satisfies the far-field radiation conditions and therefore its accuracy is not jeopardized by the reduction of the computational domain. Joined work with Yuval Harness