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arXiv 2311.16699math.NAcs.NA
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一种扩展的不连续伽辽金激波跟踪方法

An extended discontinuous Galerkin shock tracking method

Jakob Vandergrift, Florian Kummer

AI总结:

本文提出一种结合隐式激波跟踪与扩展不连续伽辽金方法的高阶激波跟踪方法,通过约束优化将水平集零等值线拟合到间断位置,并在二维问题上验证了其能力。

摘要:

本文提出了一种新颖的高阶激波跟踪方法,并给出了概念验证。我们的方法借鉴了隐式激波跟踪和扩展不连续伽辽金方法中的概念,主要用于求解具有间断特征的偏微分方程。为应对这一挑战,我们求解一个约束优化问题,旨在将水平集函数的零等值线精确拟合到间断位置。此外,我们讨论了受数值实验和现有文献启发的多种鲁棒性措施。最后,我们通过一系列复杂度逐步增加的二维问题展示了该方法的能力。

英文摘要:

In this paper, we introduce a novel high-order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso-contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two-dimensional problems, progressively increasing in complexity.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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