Title: A new high-order high-frequency integral equation method for the solution of wave scattering problems


			    Fernando Reitich
                       Department of Mathematics 
                        University of Minnesota
                         Minneapolis, MN 55455 
                     E-Mail: reitich@math.umn.edu 
             Web page: http://www.math.umn.edu/~reitich/


Abstract:
The effort and interest in the design of improved algorithms for
computational electromagnetics and acoustics applications has
consistently grown over the last twenty years as these simulations
have become relevant in an increasing number of fields and have
been facilitated by remarkable developments in computing resources.
Still, current state-of-the-art algorithms are limited by the
competing demands of accuracy, which typically requires an
increasing number of degrees of freedom to resolve on the scale
of a wavelength, and efficiency, which favors coarse discretizations.
In this talk we will present a new strategy for the solution of
the integral equations of electromagnetic and acoustic scattering
that successfully deals with these requirements by {\it avoiding\/}
the need to discretize on the scale of the wavelength at
high-frequencies, while retaining error-controllability and
high-order convergence characteristics. The approach is based the
derivation of an appropriate ansatz for the phase of the (unknown)
currents, on explicit treatment of shadow boundaries, and on
localized high-order integration around critical points.
[Joint work with O. Bruno and C. Geuzaine (Caltech)].