On the Convergence Properties of the Multiple Sweep Method of Moments
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On the Convergence Properties of the Multiple Sweep Method of MomentsAbstract
This paper investigates the convergence properties of the Multiple Sweep Method of Moments (MSMM), both analytically and numerically, and presents some numerical results for various 2D scattering geometries, such as a strip, a cylinder, and a rough surface with and without a target on it. The MSMM is an O(N2) iterative method for solving the large matrix equations which arise in the method of moments (MM) analysis of electrically large bodies. In the MSMM, the body is split into P sections and the currents on these sections are found in a recursive fashion. Although the MSMM is a frequency domain solution, it has a time domain interpretation. The first sweep includes the dominant scattering mechanisms and each subsequent sweep includes higher order mechanisms. A connection between the MSMM and classical iterative methods is established in this paper. Under certain conditions, the MSMM is shown to be mathematically equivalent to a block Jacobi preconditioned system of equations that results from the moment method, and solved via the method of symmetric successive over-relaxation (SSOR) with relaxation factor ! = 1. Based on this connection, the convergence is analyzed by examining the eigenvalue distribution of the iteration matrix for different classes of 2D geometries, and for electric and magnetic field integral equation formulations and TEz and TMz polarizations. In addition, the MSMM is compared with other recently used iterative methods for rough surface scattering problems, namely the Method of Ordered Multiple Interactions (MOMI), or the Forward-Backward (FB) Method. The results show that the MSMM converges for some problems for which the MOMI (and FB) fails to converge, e.g., the rough surface with a target on it, or when the surface becomes multi-valued which causes large offdiagonal elements in the interaction matrix.
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