Error Control of Multiple-Precision MLFMA

Kalfa, Mert
Ergül, Özgür Salih
Erturk, Vakur B.
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.
IEEE Transactions on Antennas and Propagation


Error control in MLFMA with multiple-precision arithmetic
Kalfa, Mert; Ergül, Özgür Salih; Ertürk, Vakur B. (null; 2018-04-13)
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-frequ...
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Error Analysis of MLFMA with Closed-Form Expressions
Kalfa, Mert; Erturk, Vakur B.; Ergül, Özgür Salih (2021-01-01)
The current state-of-the-art error control of Multilevel Fast Multipole Algorithm (MLFMA) is valid for any given error threshold at any frequency, but it requires a multiple-precision arithmetic framework to be implemented. In this work, we use asymptotic approximations and curve-fitting techniques to derive accurate closed-form expressions for the error control of MLFMA that can be implemented in common fixed-precision computers. Moreover, using the proposed closed-form expressions in conjunction with the ...
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: