Efficient solution of the electric and magnetic current combined‐field integral equation with the multilevel fast multipole algorithm and block‐diagonal preconditioning

Date
2009-12
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Source Title
Print ISSN
0048-6604
Electronic ISSN
1944-799X
Publisher
Wiley-Blackwell Publishing, Inc.
Volume
44
Issue
06
Pages
1 - 15
Language
English
Type
Article
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Abstract

We consider the efficient solution of electromagnetics problems involving dielectric and composite dielectric-metallic structures, formulated with the electric and magnetic current combined-field integral equation (JMCFIE). Dense matrix equations obtained from the discretization of JMCFIE with Rao-Wilton-Glisson functions are solved iteratively, where the matrix-vector multiplications are performed efficiently with the multilevel fast multipole algorithm. JMCFIE usually provides well conditioned matrix equations that are easy to solve iteratively. However, iteration counts and the efficiency of solutions depend on the contrast, i.e., the relative variation of electromagnetic parameters across dielectric interfaces. Owing to the numerical imbalance of off-diagonal matrix partitions, solutions of JMCFIE become difficult with increasing contrast. We present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. 4PBDP is useful, especially when the contrast increases, and the standard block-diagonal preconditioner fails to provide a rapid convergence.

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Keywords
Integral equations, Multilevel fast multipole algorithm (MLFMA), Iterative solvers
Citation
Published Version (Please cite this version)