Error Control of Multiple-Precision MLFMA

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Date

2018-10

Author

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

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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- and 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 proposal error control scheme. The results are compared with the previously available methods and numerical surveys.

Subject Keywords

Diagonalization, Error analysis, Fast multipole method (FMM), Low-frequency breakdown, Multiple-precision arithmetic (MPA)

URI

https://hdl.handle.net/11511/28380

Journal

IEEE Transactions on Antennas and Propagation

DOI

https://doi.org/10.1109/tap.2018.2854405

Collections

Department of Electrical and Electronics Engineering, Article

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Citation Formats

M. Kalfa, Ö. S. Ergül, and V. B. Erturk, “Error Control of Multiple-Precision MLFMA,” IEEE Transactions on Antennas and Propagation, pp. 5651–5656, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/28380.