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An h-Adaptive RKDG Method for the Vlasov–Poisson System

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Abstract

In this paper, we propose a new h-adaptive indicator for the Runge–Kutta discontinuous Galerkin (RKDG) scheme in simulations of the Vlasov–Poisson (VP) system. This adaptive indicator, tailored for the VP system, is based on the principle that each cell assumes solution variations as equally as possible. Under the framework of the RKDG method, such adaptive indicator is particularly simple and cheap for the computation. Its effectiveness is demonstrated by extensive numerical tests. The detailed adaptive algorithm as well as some important implementation issues, including the grid and data structure, adaptive criteria, data prolongation/projection and mesh projection, is presented.

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Author information

Authors and Affiliations

  1. School of Natural Sciences, Nanjing University of Posts and Telecommunications, Nanjing, 210023, Jiangsu, People’s Republic of China

    Hongqiang Zhu

  2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, People’s Republic of China

    Jianxian Qiu

  3. Department of Mathematics, University of Houston, Houston, TX, 77204-3008, USA

    Jing-Mei Qiu

Authors
  1. Hongqiang Zhu
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  2. Jianxian Qiu
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Correspondence to Jing-Mei Qiu.

Additional information

The research is partially supported by NSFC Grants 11201242, 91530107 and 11571290, NSF Grants NSF-DMS-1217008 and NSF-DMS-1522777, Jiangsu Government Scholarship for Overseas Studies, and Air Force Office of Scientific Computing FA9550-12-0318.

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Zhu, H., Qiu, J. & Qiu, JM. An h-Adaptive RKDG Method for the Vlasov–Poisson System. J Sci Comput 69, 1346–1365 (2016). https://doi.org/10.1007/s10915-016-0238-1

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  • DOI: https://doi.org/10.1007/s10915-016-0238-1

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