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      Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning

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      Author(s)
      Malas, T.
      Gürel, Levent
      Date
      2009
      Source Title
      SIAM Journal on Scientific Computing
      Print ISSN
      1064-8275
      Electronic ISSN
      1095-7197
      Publisher
      Society for Industrial and Applied Mathematics
      Volume
      31
      Issue
      3
      Pages
      1968 - 1984
      Language
      English
      Type
      Article
      Item Usage Stats
      199
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      114
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      Abstract
      With the help of the multilevel fast multipole algorithm, integral-equation methods can be used to solve real-life electromagnetics problems both accurately and efficiently. Increasing problem dimensions, on the other hand, necessitate effective parallel preconditioners with low setup costs. In this paper, we consider sparse approximate inverses generated from the sparse near-field part of the dense coefficient matrix. In particular, we analyze pattern selection strategies that can make efficient use of the block structure of the near-field matrix, and we propose a load-balancing method to obtain high scalability during the setup. We also present some implementation details, which reduce the computational cost of the setup phase. In conclusion, for the open-surface problems that are modeled by the electric-field integral equation, we have been able to solve ill-conditioned linear systems involving millions of unknowns with moderate computational requirements. For closed surface problems that can be modeled by the combined-field integral equation, we reduce the solution times significantly compared to the commonly used block-diagonal preconditioner.
      Keywords
      Preconditioning
      Sparse-approximate-inverse preconditioners
      Integral-equation methods
      Computational electromagnetics
      Parallel computation
      31A10
      65F10
      78A45
      78M05
      65Y05
      Permalink
      http://hdl.handle.net/11693/48309
      Published Version (Please cite this version)
      https://doi.org/10.1137/070711098
      Collections
      • Computational Electromagnetics Research Center (BiLCEM) 84
      • Department of Electrical and Electronics Engineering 3702
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