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

Jeonghwa Lee, Jun Zhang, Cai Cheng Lu

Research output: Contribution to journalArticlepeer-review

139 Scopus citations

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 is 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.

Original languageEnglish
Pages (from-to)158-175
Number of pages18
JournalJournal of Computational Physics
Volume185
Issue number1
DOIs
StatePublished - Feb 10 2003

Keywords

  • Electromagnetic scattering
  • ILU preconditioning
  • Krylov subspace methods
  • Multilevel fast multiple algorithm

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy (all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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