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Talk Abstract

Calculation of Electromagnetic and Acoustic Scattering via Boundary Variations and Analytic Continuation

Calculation of Electromagnetic and Acoustic Scattering via Boundary Variations and Analytic Continuation

School of Mathematics

University of Minnesota

reitich@math.umn.edu

In this talk we will present a numerical method we introduced
recently for the solution of problems of electromagnetic and
acoustic wave propagation. Our approach is based on the observation
that electromagnetic and acoustic fields behave analytically
with respect to variations of a scattering surface, so that
they can be represented in the form of * convergent* power
series in a perturbation parameter. We will show that these
series expansions can be made into the basis for very efficient
numerical algorithms. In fact, a second element in our theory
consists of simple recursive formulas which allow us to obtain
the power series by considering a sequence of easily solvable
scattering problems. The analytic extension of the fields to
large perturbations can then be achieved via Padé approximation.
We shall present two- and three-dimensional numerical examples
that demonstrate that our algorithms lead to accurate predictions
for a wide variety of scattering configurations.

This is joint work with **Oscar Bruno**
(Applied Mathematics, Caltech).

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