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      Sequential and parallel preconditioners for large-scale integral-equation problems

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      Author(s)
      Malas, Tahir
      Ergül, Özgür
      Gürel, Levent
      Date
      2007
      Source Title
      Proceedings of the Computational Electromagnetics Workshop, IEEE 2007
      Publisher
      IEEE
      Pages
      35 - 43
      Language
      English
      Type
      Conference Paper
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      Abstract
      For efficient solutions of integral-equation methods via the multilevel fast multipole algorithm (MLFMA), effective preconditioners are required. In this paper we review appropriate preconditioners that have been used for sparse systems and developed specially in the context of MLFMA. First we review the ILU-type preconditioners that are suitable for sequential implementations. We can make these preconditioners robust and efficient for integral-equation methods by making appropriate selections and by employing pivoting to suppress the instability problem. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes insufficient to approximate the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to MLFMA to be used as an effective preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve problems with tens of millions of unknowns in a few hours. We report the solution of integral-equation problems that are among the largest in their classes. © 2007 IEEE.
      Keywords
      Large-scale systems
      Integral equations
      Virtual manufacturing
      MLFMA
      Linear systems
      Sparse matrices
      Tin
      Computational electromagnetics
      Robustness
      Boundary conditions
      Permalink
      http://hdl.handle.net/11693/27034
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/CEM.2007.4387648
      Collections
      • Computational Electromagnetics Research Center (BiLCEM) 84
      • Department of Electrical and Electronics Engineering 3702
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