June 18,  19,  20   2003
 
 
 

12:00 AM - Wednesday, June 18, 2003 - Amphitheater Darboux

Oscar Bruno

Applied and Computational Mathematics
Caltech
Pasadena, CA 91125, USA

bruno@acm.caltech.edu

New High-order, High frequency Methods in Computational Electromagnetism

We present a set of new algorithms and methodologies for the numerical solution of problems of scattering by complex bodies in three-dimensional space. These methods, which are based on integral equations, high-order integration, fast Fourier transforms and highly accurate high-frequency methods, can be used in the solution of problems of electromagnetic and acoustic scattering by surfaces and penetrable scatterers --- even in cases in which the scatterers contain geometric singularities such as corners and edges. In all cases the solvers exhibit high-order convergence, they run on low memories and reduced operation counts, and they result in solutions with a high degree of accuracy. In particular, our algorithms can evaluate accurately in a personal computer scattering from hundred-wavelength-long objects by direct solution of integral equations --- a goal, otherwise achievable today only by supercomputing. A class of new high-order surface representation methods will be discussed, which allows for accurate high-order description of surfaces from a given CAD representation. Finally, we will discuss certain high-order high-frequency methods we introduced recently, which are efficient where our direct methods become costly, and thus lead to a general computational methodology which is applicable and accurate throughout the electromagnetic spectrum.