Multiple-Precision Arithmetic Implementation of the Multilevel Fast Multipole Algorithm

Kalfa M., Ergul O., Erturk V. B.

IEEE Transactions on Antennas and Propagation, vol.72, no.1, pp.11-21, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 72 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1109/tap.2023.3291077
  • Journal Name: IEEE Transactions on Antennas and Propagation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, PASCAL, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.11-21
  • Keywords: Error analysis, low-frequency breakdown (LFB), multilevel fast multipole algorithm (MLFMA), multiple-precision arithmetic (MPA)
  • Middle East Technical University Affiliated: Yes

Abstract

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.