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

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.