Numerically efficient solution of dense linear system of equations arising in a class of electromagnetic scattering problems

Abstract

In this paper we present an efficient technique for solving a dense complex-symmetric linear system of equations arising in the method of moments (MoM) formulation. To illustrate the application of the method, we consider a finite array of scatterers, which gives rise to a large number of unknowns. The solution procedure utilizes preconditioned transpose-free QMR (PTFQMR) iterations and computes the matrix-vector products by employing a compressed impedance matrix. The compression is achieved by reduced-rank representation of the off-diagonal blocks, based on a partial-QR decomposition, which is followed by an iterative refinement. Both the preconditioning and the compression steps take advantage of the block structure of the matrix. The convergence of the iterative procedure is investigated and the performance of the proposed algorithm is compared to that achieved by other schemes. The effectiveness of the preconditioner and the degree of matrix compression are quantified. Finite arrays of variable shape and sizes are considered, and it is demonstrated that the ability to solve large problems using this technique enables one to evaluate the edge effects in the finite array. Such array is basically flat and periodic, but the algorithm is still efficient when variation with strict periodicity or flatness exists.