NUMERICALLY EFFICIENT SOLUTION OF DENSE LINEAR-SYSTEM OF EQUATIONS ARISING IN A CLASS OF ELECTROMAGNETIC SCATTERING PROBLEMS

In this paper we present an efficient technique for solving dense comp lex-symmetric linear system of equations arising in the method of mome nts (MoM) formulation. To illustrate the application of the method, we consider a finite array of scatterers, which gives rise to a large nu mber of unknowns. The solution procedure utilizes preconditioned trans pose-free QMR (PTFQMR) iterations and computes the matrix-vector produ cts by employing a compressed impedance matrix. The compression is ach ieved by reduced-rank representation of the off-diagonal blocks, based on a partial-QR decomposition, which is followed by an iterative refi nement. Both the preconditioning and the compression steps take advant age of the block structure of the matrix. The convergence of the itera tive procedure is investigated and the performance of the proposed alg orithm is compared to that achieved by other schemes. The effectivenes s of the preconditioner and the degree of matrix compression are quant ified. Finite arrays of variable shape and sizes are considered, and i t 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 stil l efficient when variation with strict periodicity or flatness exists.