Error Analysis of MLFMA With Closed-Form Expressions


Kalfa M., Erturk V. B. , Ergul Ö. S.

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol.69, no.10, pp.6618-6623, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 10
  • Publication Date: 2021
  • Doi Number: 10.1109/tap.2021.3070086
  • Journal Name: IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
  • Journal Indexes: Science Citation Index 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.6618-6623
  • Keywords: Error correction, Closed-form solutions, Antennas, Frequency control, Green's function methods, Finite wordlength effects, Complexity theory, Error analysis, low-frequency breakdown, multilevel fast multipole algorithm (MLFMA), multiple-precision arithmetic, ELECTROMAGNETIC SCATTERING, MULTIPOLE

Abstract

The current state-of-the-art error control of the 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 state-of-the-art scheme, we report novel design curves for MLFMA that can be used to determine achievable error limits, as well as the minimum box sizes that can be solved with a given desired error threshold for a wide range of machine precision levels.