Wave scattering by inhomogeneous media: efficient algorithms and applications

We review 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--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. A class of high-order high-frequency methods currently under development, in turn, are efficient where our direct methods become costly, and they thus lead to an overall computational methodology which is applicable and accurate throughout the electromagnetic spectrum