A General-Purpose Preconditioner for Method of Moments Matrices and a Novel Approach to Resolving the Low Frequency Breakdown Problem

This paper presents a general-purpose preconditioner for Method of Moments (MoM) matrices to speed up iterative solutions of the same. The proposed preconditioner is constructed by inverting a sparsified version of the impedance matrix, which is found to retain all the important singular values of the original impedance matrix. The preconditioner is shown to significantly reduce the number of iterations while using an iterative solver such as Generalized Minimal Residual (GMRES). We test the efficacy of the preconditioner for a variety of ill-conditioned MoM problems, including those arising from internal resonance and non-uniform meshing of multiscale problems. Additionally, we show that a further speedup of the convergence can be achieved, without compromising the accuracy, by using an alternative convergence criterion. Finally, the problem of ill-conditioning arising from the low-frequency breakdown problem is also examined, and a novel strategy for handling such problems is proposed as an alternative to using the loop-star basis function.