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arXiv 1602.02124math.NAcs.NA
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一种用于高维传输方程的稀疏网格不连续伽辽金方法及其在动力学模拟中的应用

A sparse grid discontinuous Galerkin method for high-dimensional transport equations and its application to kinetic simulations

Michigan State University(密歇根州立大学)

Wei Guo, Yingda Cheng

AI总结:

本文提出一种稀疏网格不连续伽辽金方法用于高维传输方程,通过弱形式传统Runge-Kutta DG方案实现L²稳定性和收敛性,具有低计算和存储成本,应用于Vlasov和Boltzmann传输方程的模拟,数值测试验证了精度和守恒性。

摘要:

在本文中,我们开发了一种用于传输方程的稀疏网格不连续伽辽金(DG)方案,并将其应用于动力学模拟。该方法使用传统Runge-Kutta DG(RKDG)方案的弱形式来处理超几何问题,并被证明在L²稳定性和收敛性方面是成立的。该方案的主要优势在于其低计算和存储成本,这是由于采用了稀疏有限元近似空间。这一有吸引力的特性在模拟Vlasov和Boltzmann传输方程时得到了探索。通过在最高到四维的数值测试中验证了精度和守恒性的良好表现。

英文摘要:

In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic problems and is proven to be $L^2$ stable and convergent. A major advantage of the scheme lies in its low computational and storage cost due to the employed sparse finite element approximation space. This attractive feature is explored in simulating Vlasov and Boltzmann transport equations. Good performance in accuracy and conservation is verified by numerical tests in up to four dimensions.

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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