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Application of High Dimensional B-Spline Interpolation in Solving the Gyro-Kinetic Vlasov Equation Based on Semi-Lagrangian Method

Part of: Applications to specific types of physical systems Numerical approximation and computational geometry

Published online by Cambridge University Press:  06 July 2017

Xiaotao Xiao ,
Lei Ye ,
Yingfeng Xu  and
Shaojie Wang
Xiaotao Xiao*
Affiliation:
Institute of Plasma Physics, Chinese Academy of Science, Hefei, Anhui 230031, China
Lei Ye*
Affiliation:
Institute of Plasma Physics, Chinese Academy of Science, Hefei, Anhui 230031, China
Yingfeng Xu*
Affiliation:
Institute of Plasma Physics, Chinese Academy of Science, Hefei, Anhui 230031, China
Shaojie Wang*
Affiliation:
Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
*Corresponding author. Email addresses:xtxiao@ipp.ac.cn (X. Xiao), lye@ipp.ac.cn (L. Ye), xuyingfeng@ipp.ac.cn (Y. Xu), wangsj@ustc.edu.cn (S. Wang)
*Corresponding author. Email addresses:xtxiao@ipp.ac.cn (X. Xiao), lye@ipp.ac.cn (L. Ye), xuyingfeng@ipp.ac.cn (Y. Xu), wangsj@ustc.edu.cn (S. Wang)
*Corresponding author. Email addresses:xtxiao@ipp.ac.cn (X. Xiao), lye@ipp.ac.cn (L. Ye), xuyingfeng@ipp.ac.cn (Y. Xu), wangsj@ustc.edu.cn (S. Wang)
*Corresponding author. Email addresses:xtxiao@ipp.ac.cn (X. Xiao), lye@ipp.ac.cn (L. Ye), xuyingfeng@ipp.ac.cn (Y. Xu), wangsj@ustc.edu.cn (S. Wang)
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Abstract

The computation efficiency of high dimensional (3D and 4D) B-spline interpolation, constructed by classical tensor product method, is improved greatly by precomputing the B-spline function. This is due to the character of NLT code, i.e. only the linearised characteristics are needed so that the unperturbed orbit as well as values of the B-spline function at interpolation points can be precomputed at the beginning of the simulation. By integrating this fixed point interpolation algorithm into NLT code, the high dimensional gyro-kinetic Vlasov equation can be solved directly without operator splitting method which is applied in conventional semi-Lagrangian codes. In the Rosenbluth-Hinton test, NLT runs a few times faster for Vlasov solver part and converges at about one order larger time step than conventional splitting code.

Keywords

High dimensional interpolationsemi-Lagrangiangyro-kinetic simulationnumerical Lie transform

MSC classification

Secondary: 65D05: Interpolation 65Z05: Applications to physics 68U20: Simulation 82D10: Plasmas
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 789 - 802
Copyright
Copyright © Global-Science Press 2017 

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