Incomplete LU preconditioning for large scale dense complex linear systems from electromagnetic wave scattering problems

Authors:
Jeonghwa Lee;Jun Zhang;Cai-Cheng Lu
Affiliations:
Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY;Laboratory for High Performance Scientific Computing and Computer Simulation, Department of Computer Science, University of Kentucky, 773 Anderson Hall, Lexington, KY;Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY
Venue:
Journal of Computational Physics
Year:
2003

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Abstract

We consider the preconditioned iterative solution of large dense linear systems, where the coefficient matrix is a 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 as constructed using the near part block diagonal submatrices 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.