Error control in MLFMA with multiple-precision arithmetic

Date

2018-04-13

Author

Kalfa, Mert
Ergül, Özgür Salih
Ertürk, Vakur B.

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We present a new error control method that provides the truncation numbers as well as the required digits of machine precision for the translation operator of the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems (i.e., electrically large translation distances). When combined with a multiple-precision implementation of MLFMA, the proposed method can be used to solve low-frequency problems that are problematic with a fixed-precision implementation. Numerical results in the form of optimal truncation numbers and machine precisions for a variety of box sizes and desired relative error thresholds are presented and compared with the methods or numerical surveys available in the literature.

Subject Keywords

Diagonalization, Error analysis, Low-frequency breakdown, Multilevel fast multipole algorithm, Multiple-precision arithmetic

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85057329884&origin=inward
https://hdl.handle.net/11511/82894

DOI

https://doi.org/10.1049/cp.2018.0645

Conference Name

12th European Conference on Antennas and Propagation, EuCAP 2018 (9 - 13 Nisan 2018)

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

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Error Control of MLFMA within a Multiple-Precision Arithmetic Framework Kalfa, Mert; ERTÜRK, VAKUR BEHÇET; Ergül, Özgür Salih (2018-07-13) We present a new error control scheme that provides the truncation numbers as well as the required digits of machine precision for the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems. When combined with a multiple-precision arithmetic framework, the proposed method can be used to solve low-frequency problems that would otherwise experience overflow issues. Numerical results...
Error Control of Multiple-Precision MLFMA Kalfa, Mert; Ergül, Özgür Salih; Erturk, Vakur B. (Institute of Electrical and Electronics Engineers (IEEE), 2018-10) 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-frequenc...
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Citation Formats

M. Kalfa, Ö. S. Ergül, and V. B. Ertürk, “Error control in MLFMA with multiple-precision arithmetic,” London, İngiltere, 2018, vol. 2018, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85057329884&origin=inward.