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

  • Xiaotao Xiao (a1), Lei Ye (a1), Yingfeng Xu (a1) and Shaojie Wang (a2)

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.

Corresponding author
*Corresponding author. Email addresses: (X. Xiao), (L. Ye), (Y. Xu), (S. Wang)
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
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