Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments
Multiple-Precision Arithmetic of Biot-Savart Integrals for Reconnections of Vortex Filaments
复制标题
用于涡丝重联的 Biot-Savart 积分的多精度算法
DOI：
10.1007/978-3-030-86976-2_13
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Fujiwara Hiroshi
中科院分区：
文献类型：
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作者：
Lee Yu-Hsun;Fujiwara Hiroshi
在本文中，我们展示了一个有效的应用程序的多精度算法的数值计算的Biot-Savart积分，这是一个数学模型的运动的涡丝。由于它是一个非线性积分微分方程，数值方法在分析中起着重要的作用。因此，可靠的计划，即使他们的计算成本很高。多精度算法使我们能够定量地估计舍入误差，并比较各种精度算法。从而得出数值结果的可靠性结论。特别是，涡丝的重联进行了研究，我们满足由于奇异性的数值解的振荡。所提出的方法澄清，重新连接后立即发散仍然是可靠的舍入误差。
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.