基于样条的 2D+t 时空方法求解转移

Logan Larose, Jude T. Anderson, David M. Williams
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引用次数: 0

摘要

本研究为基于板块的时空有限元方法引入了一种新的解转移过程。新的转移过程基于谢-克劳-托彻(HCT)样条,并满足以下要求:(i)保持高达 4 阶的高阶精度;(ii)保留离散最大原则;(iii)强制执行质量守恒;(iv)在时空板之间构建平滑、连续的代解。虽然现有的许多转移方法都能满足前三个要求,但第四个要求对于实现时空应用的可视化和边界条件强化至关重要。在本文中,我们推导出了基于 HCT 花键的转移过程的误差边界。此外,我们还进行了数值实验,量化了转移过程的保守性和精度等级。最后,我们对平滑代理解决方案的可视化特性进行了定性评估。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Spline-based solution transfer for space-time methods in 2D+t
This work introduces a new solution-transfer process for slab-based space-time finite element methods. The new transfer process is based on Hsieh-Clough-Tocher (HCT) splines and satisfies the following requirements: (i) it maintains high-order accuracy up to 4th order, (ii) it preserves a discrete maximum principle, (iii) it enforces mass conservation, and (iv) it constructs a smooth, continuous surrogate solution in between space-time slabs. While many existing transfer methods meet the first three requirements, the fourth requirement is crucial for enabling visualization and boundary condition enforcement for space-time applications. In this paper, we derive an error bound for our HCT spline-based transfer process. Additionally, we conduct numerical experiments quantifying the conservative nature and order of accuracy of the transfer process. Lastly, we present a qualitative evaluation of the visualization properties of the smooth surrogate solution.
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