An Iterative Technique Based on the Method of Least Squares Applied to Scattering Problems Using the k-Space Approach

Abstract

An iterative technique based on the method of least squares and utilizing variational trial functions is presented. It is applied in the solution of scattering problems involving arbitrarily shaped homogeneous or inhomogeneous penetrable obstacles, utilizing a volume formulation and the k-space approach. The method minimizes a squared error over subspaces of the range of the operator, and is guaranteed to converge under certain conditions. For the class of problems for which it was designed, namely scattering problems for dielectrics using a volume formulation, the method performs better than other iterative techniques. Numerical results are presented for infinitely long homogeneous circular cylinders with TE plane wave excitation. A comparison of the performance of the iterative technique with the conjugate gradient method is made. Modifications of the iterative method which involve increasing the number of trial functions are discussed and numerical results are presented which demonstrate the effects of the modifications.