New High-Order, High-Frequency Methods In Computational Electromagnetism

Abstract

We present a new set of 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 ob jects by
direct solution of integral equations–a goal, otherwise achievable today only by supercomputing.
A new class of high-order surface representation methods will be discussed, which allows
for accurate high-order description of surfaces from a given CAD representation. A class of
high-order high-frequency methods which we developed recently, finally, are efficient where our
direct methods become costly, thus leading to a general computational methodology which is
applicable and accurate for the whole range of frequencies in the electromagnetic spectrum.