A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

Abstract

In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.

Keywords:

• Dense matrices
• Electromagnetics
• Integral formulation
• Multilevel fast multipole algorithm
• Preconditioning techniques

Acknowledgements

The research work of JZ was supported in part by the US National Science Foundation under grants CCR-0092532 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under grants KSEF-148-502-05-132 and KSEF-148-502-06-186, and in part by the Alzheimer's Association under a New Investigator Research Grant NIGR-06-25460.