High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-07-29 DOI:10.1016/j.cpc.2025.109770

O. Beznosov, J. Bonilla, X.-Z. Tang, G.A. Wimmer

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引用次数: 0

Abstract

We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides

C (m)

continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Finally, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.

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基于矢量势重构的粒子模拟高阶磁场插值

我们提出了一种利用Hermite插值的矢量位势重构来插值无发散连续磁场的方法，该方法确保了需要自适应高阶常微分方程（ODE）积分器（如Dormand-Prince方法）的应用的高阶连续性。该方法具有C(m)连续性和高阶精度，特别适用于最优积分阶数和时间步长调整下的粒子轨迹积分和庞卡罗剖面分析。通过数值实验，我们证明了Hermite插值方法保持了体积和连续性，这对于在导向中心模拟中，特别是在长期轨迹积分中，保持环面正则动量和磁矩是至关重要的。此外，我们分析了导数连续性不足对龙格-库塔格式的影响，并展示了它如何在低误差容限下降低精度，引入不连续诱导的截断误差。最后，我们在两种相关的现场数据设置中展示了高性能的poincarcars截面分析，这些数据来自有限元网格。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.