Efficient Preconditioning of the Method of Auxiliary Sources (MAS) for Cylindrical Scatterers of Quasi- Circular Cross-Section

ABSTRACT

Two different forms of a preconditioning process (i.e. standard preconditioning and quasi-diagonalization) are presented, in conjunction with the Method of Auxiliary Sources (MAS), when the latter is applied to a specific class of two-dimensional scattering problems. The method enhances the efficiency of MAS, when the linear system becomes illconditioned, due to distancing of the auxiliary surface from the outer boundary. If the cross-sectional boundary is geometrically close to a circle, it is proven that the MAS matrix becomes quasi-circulant, as intuition dictates. By exploiting the properties of the exactly circulant matrix, pertaining to the original circular configuration, the perturbed system is transformed to a quasi-diagonal one, whose inversion is a numerically stable operation.