Incomplete LU Preconditioning for Large Scale Dense Complex
Linear Systems from Electromagnetic Wave Scattering Problems

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


We consider preconditioned iterative solution of the linear system $Ax = b$, where the coefficient matrix $A$ is a large scale dense complex valued matrix arising from discretizing the integral equation of electromagnetic scattering. For some scattering structures this matrix can be poorly conditioned. The main purpose of this study is to evaluate the efficiency of a class of incomplete LU (ILU) factorization preconditioners for solving this type of matrices. We solve the electromagnetic wave equations using the BiCG method with an ILU preconditioner in the context of a multilevel fast multipole algorithm (MLFMA). The novelty of this work is that the ILU preconditioner is constructed using the near part block diagonal submatrix generated from the MLFMA. Experimental results show that the ILU preconditioner reduces the number of BiCG iterations substantially, compared to the block diagonal preconditioner. The preconditioned iteration scheme also maintains the computational complexity of the MLFMA, and consequently reduces the total CPU time.

Key words: Krylov subspace methods, ILU preconditioning, multilevel fast multipole algorithm, electromagnetic wave equation

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

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This paper has been published in Journal of Computational Physics, Vol. 185, pp. 158-175 (2003).

Technical Report 342-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002. The research work of Lee and Zhang was supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-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.