A Comparative Assessment Among Iterative Linear Solvers Dealing with Electromagnetic Integral Equations in 3D Inhomogeneous Anisotropic Media

This paper deals with full-vectorial, three-dimensional, electromagnetic scattering problems formulated in terms of integral scattering equations. The weak formulation is applied in order to effectively deal with inhomogeneous anisotropic media and the arising set of algebraic linear equations is solved through some of the most recent and effective iterative linear solvers for allowing a detailed assessment of their performances when facing with three-dimensional complex scenarios.

[1]  J. Richmond Scattering by a dielectric cylinder of arbitrary cross section shape , 1965 .

[2]  K.A. Michalski,et al.  Electromagnetic wave theory , 1987, Proceedings of the IEEE.

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

[4]  W. Chew Waves and Fields in Inhomogeneous Media , 1990 .

[5]  A conjugate gradient procedure for the analysis of planar conductors with alternating patch and aperture formulations (EM scattering) , 1988 .

[6]  Norbert N. Bojarski,et al.  The k-space formulation of the scattering problem in the time domain , 1982 .

[7]  P. M. Berg,et al.  Iterative forward and inverse algorithms based on domain integral equations for three-dimensional electric and magnetic objects , 2004 .

[8]  R. Freund,et al.  QMR: a quasi-minimal residual method for non-Hermitian linear systems , 1991 .

[9]  P. M. van den Berg,et al.  A weak form of the conjugate gradient FFT method for two-dimensional TE scattering problems , 1991 .

[10]  L. Nuno,et al.  A scheme to analyze conducting plates of resonant size using the conjugate-gradient method and the fast Fourier transform , 1988 .

[11]  John L. Volakis,et al.  Application of a conjugate gradient FFT method to scattering from thin planar material plates , 1988 .

[12]  Weng Cho Chew,et al.  A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems , 1995 .

[13]  P. M. Berg Iterative Schemes Based on the Minimization of the Error in Field Problems , 1985 .

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

[15]  T. Sarkar,et al.  Comments on "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies" , 1986 .

[16]  Aria Abubakar,et al.  Three‐dimensional nonlinear inversion in cross‐well electrode logging , 1998 .

[17]  Qing Huo Liu,et al.  Applications of the BCGS-FFT method to 3-D induction well logging problems , 2003, IEEE Trans. Geosci. Remote. Sens..

[18]  Dominique Lesselier,et al.  Buried, 2-D penetrable objects illuminated by line-sources: FFT-based iterative computations of the anomalous field , 1991 .

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