Abstract

A review of different methods of solving for the solution of scattering by three-dimensional objects is presented. There are two main classes of methods: one is for solving the differential equation directly, and the other is for solving the integral equation derived from the differential equation. The differential equation method has the advantage of generating a sparse matrix but could potentially suffer from grid-dispersion error. The radiation condition in the differential equation approach is sometimes approximated. The alternative approach, which is the integral equation approach, provides a solution that satisfies the radiation condition immediately and possibly with less grid-dispersion error. However, it gives rise to a dense matrix that is more computationally intensive to solve and to invert. Recent methods developed for inverting and solving the integral equation efficiently are discussed. They involve the recursive method, the nesting method, and the iterative method. The recursive method seeks the solution of (n + 1) subscatterers from the solution of n subscatterers. The nesting method nests a smaller problem within a larger problem. The iterative method uses the conjugate gradient method but exploits recursion and nesting to expedite the matrix-vector multiply in the conjugate gradient method. Some results for solving three-dimensional scattering of electromagnetic fields are presented.

© 1994 Optical Society of America

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