基于STVDRK积分和SENO插值的球面对角方程自适应光线追踪方法

IF 3.8 2区 物理与天体物理 Q2 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Wai Ming Chau, Shingyu Leung
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引用次数: 0

摘要

我们开发了一个有效的自适应框架,用于获得单位球上波前传播问题的高阶多值解,如表面对角方程所描述的那样。我们方法的一个关键发展是将传统的光线跟踪系统(通常跟踪S2×R3中的解)重新制定为相空间为S2×S2的微分方程系统。我们方法的核心是SLERP总变差递减龙格-库塔(STVDRK)方法和球面本质非振荡(SENO)插值技术。这些数值创新提供了一个强大的自适应策略来模拟波前的演变,而不依赖于任何投影步骤。通过在单位球上演化解时有效地保持精度和稳定性,我们的框架显著增强了演化曲线的表示,提高了数值解的整体鲁棒性。这种自适应方法明显优于传统方法,为更精确地模拟复杂几何结构中的波前传播提供了一种方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An adaptive ray-tracing method for eikonal equations on spheres using STVDRK integrators and SENO interpolations
We develop an efficient adaptive framework for obtaining high-order multivalued solutions to wavefront propagation problems on a unit sphere, as described by the surface eikonal equations. A key development in our approach is the reformulation of the conventional ray-tracing system, which typically tracks solutions in S2×R3, into a system of differential equations where the phase space is S2×S2. Central to our methodology are the SLERP Total Variation Diminishing Runge-Kutta (STVDRK) methods and Spherical Essentially Non-Oscillatory (SENO) interpolation techniques. These numerical innovations provide a robust adaptive strategy for modeling the evolution of the wavefront without relying on any projection steps. By effectively maintaining accuracy and stability while evolving solutions on the unit sphere, our framework significantly enhances the representation of evolving curves and improves the overall robustness of the numerical solutions. This adaptive approach significantly surpasses traditional methods, providing a way for more accurate modeling of wavefront propagation in complex geometries.
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来源期刊
Journal of Computational Physics
Journal of Computational Physics 物理-计算机:跨学科应用
CiteScore
7.60
自引率
14.60%
发文量
763
审稿时长
5.8 months
期刊介绍: Journal of Computational Physics thoroughly treats the computational aspects of physical problems, presenting techniques for the numerical solution of mathematical equations arising in all areas of physics. The journal seeks to emphasize methods that cross disciplinary boundaries. The Journal of Computational Physics also publishes short notes of 4 pages or less (including figures, tables, and references but excluding title pages). Letters to the Editor commenting on articles already published in this Journal will also be considered. Neither notes nor letters should have an abstract.
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