Performance of Preconditioned Krylov Iterative Methods
for Solving Hybrid Integral Equations in Electromagnetics

Jeonghwa Lee 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

Cai-Cheng Lu
Department of Electrical and Computer Engineering
University of Kentucky
Lexington, KY 40506-0046, USA


In solving systems of linear equations arising from practical engineering models such as the electromagnetic wave scattering problems, it is critical to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov iterative methods are most suitable. The Krylov iterative methods require the computation of matrix-vector product operations at each iteration, which account for the major computational cost of this class of methods. We use the multilevel fast multipole algorithm (MLFMA) to reduce the computational complexity of the matrix-vector product operations. We conduct an experimental study on the behavior of three Krylov iterative methods, BiCG, BiCGSTAB, and TFQMR, and of two preconditioners, the ILUT preconditioner, and the sparse approximate inverse (SAI) preconditioner. The preconditioners are constructed by using the near part matrix numerically generated in the MLFMA. Our experimental results indicate that a well chosen preconditioned Krylov iterative method maintains the computational complexity of the MLFMA and effectively reduces the overall simulation time.

Key words: Krylov methods, sparse approximate inverse preconditioning, multilevel fast multipole algorithm, electromagnetic scattering

Mathematics Subject Classification: 65F10, 65R20, 65F30, 77C10

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Technical Report 373-03, Department of Computer Science, University of Kentucky, Lexington, KY, 2003. This paper has been published in Journal of the Applied Computational Electromagnetics Society, Vol. 18, No. 4, pp. 54-61 (2003).

The research work of Lee and Zhang was supported in part by the U.S. National Science Foundation under the grant CCR-9988165, CCR-0092532, and ACR-0202934, in part by the U.S. Department of Energy under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee. Lu's research work was supported in part by the U.S. National Science Foundation under grant ECS-0093692, and in part by the U.S. Office of Naval Research under grant N00014-00-1-0605.