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PIERS Online
Vol. 4
No. 7
2008
pp: 771-774Convergence of Krylov Solvers and Choice of Basis and Weighting Set of Functions in the Moment Method Solution of Electrical Field Integral EquationGiovanni Angiulli and Salvatore Tringali doi:10.2529/PIERS071220023303 Downloads: 628 Abstract:In Computational Electromagnetics, iterative techniques for solving algebraic linear system of equations are of fundamental importance, since actual problems give rise to linear systems too large to be practically solved by direct methods. In this work we investigate as performances of the major Krylov subspace iterative solver (i.e., GMRES), is affected by different choice of these set of functions. Specifically, we consider the algebraic linear system of equations obtained by reducing the electrical field integral equation (EFIE) from the TMz scattering of a plane wave by a metallic strip. It can be observed that exists a critical threshold Δ0 such that, whenever either the basis or the weight pulses are given with an amplitude greater than Δ0, then the total number of internal loops necessary for taking the relative residual under a definite tolerance ε>0 increases all of a sudden, in such a dramatic way that it can even prevent the process at all from convergence. We try to explain this numerical behavior by inquiring the relationship between the MoM matrix condition number and the number of overall iterations necessary to numerical convergence.References:1. Chew, W. C., J. M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001. 2. Klein, C. A. and R. Mittra, "The effect of different testing functions in the moment method solution of thin-wire antenna problems," IEEE Trans. on Antennas and Propagation, 258-261, March, 1975. 3. Peterson, A. F., C. F. Smith, and R. Mittra, "Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm," IEEE Trans. on Antennas and Propagation, Vol. 36, No. 8, 1177-1179, 1988. 4. Saad, J., Iterative Methods for Sparse Linear Systems, SIAM, 2003. 5. Balanis, C. A., Advanced Engineering Electromagnetics, Wiley, 1989. 6. Harrington, R. F., Field Computation by Moment Methods, Krieger, Malabar, FL, 1982. |
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