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

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 ana...

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Published inComputational Science and Its Applications - ICCSA 2021 Vol. 12953; pp. 191 - 201
Main Authors Lee, Yu-Hsun, Fujiwara, Hiroshi
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 2021
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Computational fluid dynamics
Multiple-precision arithmetic
Numerical instability and reliability
Vortex reconnection
Online AccessGet full text
ISBN303086975X
9783030869755
ISSN0302-9743
1611-3349
DOI10.1007/978-3-030-86976-2_13

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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.
AbstractList 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.
Author Fujiwara, Hiroshi
Lee, Yu-Hsun
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Editor Misra, Sanjay
Apduhan, Bernady O
Murgante, Beniamino
Torre, Carmelo Maria
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Taniar, David
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Notes The second author was supported in part by JSPS KAKENHI Grant Numbers JP19H00641 and JP20H01821.
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Snippet In this paper, we show an efficient application of multiple-precision arithmetic to numerical computation of the Biot-Savart integral, which is a mathematical...
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StartPage 191
SubjectTerms Computational fluid dynamics
Multiple-precision arithmetic
Numerical instability and reliability
Vortex reconnection
Title Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments
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