On preconditioning and the eigensystems of electromagnetic radiation problems

Andrew J. Hesford, Weng C. Chew

Research output: Contribution to journalArticlepeer-review


A formulation of the Method of Moments (MoM) impedance matrix is presented that facilitates discussion of the behavior of its eigenvalues and eigenvectors. This provides insight into the difficulties of producing iterative solutions to electromagnetic radiation problems, which typically involve nonuniform meshes. Based on this analysis, a localized self-box inclusion (SBI) preconditioner is developed to overcome the aforementioned issues. Numerical results are shown using a parallel multilevel fast multipole algorithm (MLFMA) library, coupled with an implementation of the SBI preconditioner. Using these parallel libraries allows the solution of very large problems, due to both excessive size and poor conditioning. A model of an XM antenna, mounted atop an automobile above a very large ground plane, establishes the effectiveness of these methods for more than 3.5 million unknowns.

Original languageEnglish (US)
Pages (from-to)2413-2420
Number of pages8
JournalIEEE Transactions on Antennas and Propagation
Issue number8 I
StatePublished - 2008
Externally publishedYes


  • Electromagnetic radiation
  • Fast solvers
  • Iterative methods
  • Moment methods
  • Preconditioner

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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