A Short Survey on Preconditioning Techniques for Large
Scale Dense Complex Linear Systems in Electromagnetics

Yin Wang and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Jeonghwa Lee
Department of Computer Science
Shippensburg University
Shippensburg, PA 17257, USA


In solving systems of linear equations arising from practical scientific and engineering modeling and simulations such as electromagnetics applications, it is critical 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 on 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.

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Technical Report 471-07, Department of Computer Science, University of Kentucky, Lexington, KY, 2007.

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