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Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12953))

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Abstract

In this paper, we show an efficient application of multiple-precision arithmetic to numerical computation of the Biot-Savart integral, which is a mathematical model of motion of vortex filaments. Since it is a non-linear integro-differential equation, numerical methods play a significant role in analysis. Hence reliable schemes are desired even though their computational costs are high. Multiple-precision arithmetic enables us to estimate rounding errors quantitatively, and comparing various precision arithmetic. Thus we conclude reliability of numerical results. In particular, reconnection of vortex filaments is investigated, and we meet oscillation of numerical solutions due to singularity. The proposed method clarifies that the divergence immediately after reconnection is still reliable in terms of rounding errors.

The second author was supported in part by JSPS KAKENHI Grant Numbers JP19H00641 and JP20H01821.

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Acknowledgments

The authors would like to express their gratitude for Professor Yoshifumi Kimura (Nagoya University) for his fruitful suggestions and discussions.

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Yu-Hsun Lee & Hiroshi Fujiwara

Authors
  1. Yu-Hsun Lee
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  2. Hiroshi Fujiwara
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Corresponding author

Correspondence to Yu-Hsun Lee .

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Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Lee, YH., Fujiwara, H. (2021). Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12953. Springer, Cham. https://doi.org/10.1007/978-3-030-86976-2_13

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  • DOI: https://doi.org/10.1007/978-3-030-86976-2_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86975-5

  • Online ISBN: 978-3-030-86976-2

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