Fast, High-Order, High-Frequency Integral Methods for Computational Acoustics and Electromagnetics
Part of the
Lecture Notes in Computational Science and Engineering
book series (LNCSE, volume 31)
We review a set of algorithms and methodologies developed recently 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 integrators, 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 comers and edges. All of the solvers presented here 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 approach to direct solution of integral equations results in algorithms that can evaluate accurately in a personal computer scattering from hundred-wavelength-long objects — a goal, otherwise achievable today only by super-computing. The high-order high-frequency methods we present, in turn, are efficient where our direct methods become costly, thus leading to an overall computational methodology which is applicable and accurate throughout the electromagnetic spectrum.
KeywordsFourier Series Trapezoidal Rule Helmholtz Equation Singular Surface Fast Multipole Method
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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