Abstract:
We present a new set of algorithms and methodologies
for the numerical solution of problems of scattering
by complex bodies in threedimensional space. These
methods, which are based on integral equations,
highorder integration, fast Fourier transforms and
highly accurate highfrequency 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 highorder
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 hundredwavelengthlong
objects by direct solution of integral equations 
a goal, otherwise achievable today only by
supercomputing. A new class of highorder surface
representation methods will be discussed, which
allows for accurate highorder description of
surfaces from a given CAD representation. A class of
highorder highfrequency methods which we developed
recently, finally, are efficient where our direct
methods become costly, thus leading to a general and
accurate computational methodology which is
applicable and accurate for the whole range of
frequencies in the electromagnetic spectrum.
[LECTURE SLIDES]
