Fast analysis of electromagnetic scattering of 3-D dielectric bodies with augmented GMRES-FFT method

The problem of electromagnetic scattering by three-dimensional dielectric bodies is formulated in terms of a weak formulation of the domain-integral equation. Applying Galerkin's method with rooftop functions as basis and testing functions, the integral equation can be solved by the Krylov-subspace iterative fast Fourier transform (FFT) methods. However, poor convergence is observed when the relative permittivity of the scatterer becomes large. In order to relieve this trouble, an augmented generalized minimum residual method (AGMRES) is presented. Comparisons between several typical iterative methods are made to show the efficiency of our proposed method.

[1]  Y. Saad.  Krylov subspace methods for solving large unsymmetric linear systems , 1981 .

[2]  Jian-Ming Jin,et al.  Simple and efficient computation of electromagnetic fields in arbitrarily shaped inhomogeneous dielectric bodies using transpose-free QMR and FFT , 1998 .

[3]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[4]  Z. Q. Zhang,et al.  Three‐dimensional weak‐form conjugate‐ and biconjugate‐gradient FFT methods for volume integral equations , 2001 .

[5]  Wayne Joubert,et al.  On the convergence behavior of the restarted GMRES algorithm for solving nonsymmetric linear systems , 1994, Numer. Linear Algebra Appl..

[6]  J. Kong.  Electromagnetic Wave Theory , 1986 .

[7]  C. Balanis.  Advanced Engineering Electromagnetics , 1989 .

[8]  Qing Huo Liu,et al.  RCS computation of large inhomogeneous objects using a fast integral equation solver , 2003 .

[9]  Johnson J. H. Wang.  Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations , 1991 .

[10]  M. Cátedra,et al.  A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform , 1989 .

[11]  Yousef Saad,et al.  Deflated and Augmented Krylov Subspace Techniques , 1997, Numer. Linear Algebra Appl..

[12]  Ronald B. Morgan,et al.  A Restarted GMRES Method Augmented with Eigenvectors , 1995, SIAM J. Matrix Anal. Appl..

[13]  Edward K. N. Yung,et al.  Analysis of electromagnetic scattering of three-dimensional dielectric bodies using Krylov subspace FFT iterative methods , 2003 .

[14]  P. M. Berg,et al.  The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems , 1992 .