Browsing by Subject "Sparse approximate inverse"

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    Effective preconditioners for large integral-equation problems
    (IET, 2007-11) Malas, Tahir; Ergül, Özgür; Gürel, Levent
    We consider effective preconditioning schemes for the iterative solution of integral-equation methods. 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 too crude approximation to the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to the multilevel fast multipole algorithm (MLFMA) to be used as a 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 targets with tens of millions of unknowns in a few hours.
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    Efficient surface integral equation methods for the analysis of complex metamaterial structures
    (IEEE, 2009) Yla-Oijala, P.; Ergül, Özgür; Gürel, Levent; Taskinen, M.
    Two approaches, the multilevel fast multipole algorithm with sparse approximate inverse preconditioner and the surface equivalence principle algorithm, are applied to analyze complex three-dimensional metamaterial structures. The efficiency and performance of these methods are studied and discussed.