Dynamical low-rank approximation of the Vlasov–Poisson equation with piecewise linear spatial boundary

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-07 DOI:10.1007/s10543-024-01019-8

引用次数: 0

Abstract

Dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov–Poisson equations is based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. In this work, a variational formulation of the projector splitting is proposed which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach.

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具有片状线性空间边界的弗拉索夫-泊松方程的动态低阶近似

摘要用于 Vlasov-Poisson 方程数值模拟的动态低阶近似（DLRA）是基于空间和速度变量的分离，这在最近的一些著作中已经提出。DLRA 模型中时间积分的标准方法是根据分离变量分割低阶流形的切空间投影。这种方法也可以进行修改，以实现秩自洽性。研究较少的一个方面是在 DLRA 模型中加入边界条件。在这项工作中，提出了一种投影分割的变分公式，可以处理具有片断线性边界的空间域上的流入边界条件。数值实验证明了这种方法的原理可行性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.