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

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      Author
      Ergül, Özgür
      Gürel, Levent
      Date
      2009-12
      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.
      Keywords
      Integral equations
      Multilevel fast multipole algorithm (MLFMA)
      Iterative solvers
      Permalink
      http://hdl.handle.net/11693/48312
      Published Version (Please cite this version)
      https://doi.org/10.1029/2009RS004143
      Collections
      • Computational Electromagnetics Research Center (BiLCEM) 85
      • Department of Electrical and Electronics Engineering 3524
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