Browsing by Subject "Multiple-precision arithmetic (MPA)"

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    Error control of multiple-precision MLFMA
    (Institute of Electrical and Electronics Engineers, 2018) Kalfa, M.; Ergül, Ö.; Ertürk, Vakur
    We introduce and demonstrate a new error control scheme for the computation of far-zone interactions in the multilevel fast multipole algorithm when implemented within a multiple-precision arithmetic framework. The proposed scheme provides the optimum truncation numbers as well as the machine precisions given the desired relative error thresholds and the box sizes for the translation operator at all frequencies. In other words, unlike the previous error control schemes which are valid only for high-frequency problems, the proposed scheme can be used to control the error across both low- A nd high-frequency problems. Optimum truncation numbers and machine precisions are calculated for a wide range of box sizes and desired relative error thresholds with the proposed error control scheme. The results are compared with the previously available methods and numerical surveys.
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    ItemOpen Access
    Multiple-precision arithmetic implementation of the multilevel fast multipole algorithm
    (IEEE, 2024-01-01) Kalfa, Mert; Ergül, Özgür; Ertürk, Vakur Behçet
    We propose and demonstrate a multiple-precision arithmetic (MPA) framework applied to the inherent hierarchical tree structure of the multilevel fast multipole algorithm (MLFMA), dubbed the MPA-MLFMA that provides an unconventional but elegant treatment to both the low-frequency breakdown (LFB) and the efficiency limitations of MLFMA for electrically large problems with fine geometrical details. We show that a distinct machine precision (MP) can be assigned to each level of the tree structure of MPA-MLFMA, which, in turn, enables controlled accuracy and efficiency over arbitrarily large frequency bandwidths. We present the capabilities of MPA-MLFMA over a wide range of broadband and multiscale scattering problems. We also discuss the implications of a multiple-precision framework implemented in software and hardware platforms.