Browsing by Subject "Multiscale problem"

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    Broadband multilevel fast multipole algorithm for large-scale problems with nonuniform discretizations
    (IEEE, 2016) Ergül, Ö.; Karaosmanoğlu, B.; Takrimi, Manouchehr; Ertürk, Vakur B.
    We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA solvers employing conventional tree structures, are demonstrated on practical problems.
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    A novel broadband multilevel fast multipole algorithm with incomplete-leaf tree structures for multiscale electromagnetic problems
    (Institute of Electrical and Electronics Engineers Inc., 2016) Takrimi, M.; Ergül, Ö.; Ertürk, V. B.
    An efficient and versatile broadband multilevel fast multipole algorithm (MLFMA), which is capable of handling large multiscale electromagnetic problems with a wide dynamic range of mesh sizes, is presented. By invoking a novel concept of incomplete-leaf tree structures, where only the overcrowded boxes are divided into smaller ones for a given population threshold, versatility of using variable-sized boxes is achieved. Consequently, for geometries containing highly overmeshed local regions, the proposed method is always more efficient than the conventional MLFMA for the same accuracy, while it is always more accurate if the efficiency is comparable. Furthermore, in such a population-based clustering scenario, the error is controllable regardless of the number of levels. Several canonical examples are provided to demonstrate the superior efficiency and accuracy of the proposed algorithm in comparison with the conventional MLFMA. � 2016 IEEE.