Multiple-Precision Arithmetic Implementation of the Multilevel Fast Multipole Algorithm

Date

2023-01-01

Author

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

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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We propose and demonstrate a multiple-precision arithmetic framework applied to the inherent hierarchical tree structure of the multilevel fast multipole algorithm (MLFMA), dubbed the multiple-precision arithmetic MLFMA (MPA-MLFMA) that provides an unconventional but elegant treatment to both the low-frequency breakdown and the efficiency limitations of MLFMA for electrically large problems with fine geometrical details. We show that a distinct machine precision 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 multi-scale scattering problems. We also discuss the implications of a multiple-precision framework implemented in software and hardware platforms.

Subject Keywords

error analysis, low-frequency breakdown, multilevel fast multipole algorithm, multiple-precision arithmetic

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85164413213&origin=inward
https://hdl.handle.net/11511/104709

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Department of Electrical and Electronics Engineering, Article