The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations

Abstract : The numerical resolution of kinetic equations and in particular of Vlasov type equations is most of the time performed using PIC (Particle In Cell) methods which consist in describing the time evolution of the equation through a finite number of particles which follow the characteristic curves of the equation, the interaction with the external and self consistent fields being resolved using a grid. Another approach consists in computing directly the distribution function on a grid by following the characteristics backward in time for one time step and interpolating the value at the feet of the characteristics using the grid points values of the distribution function at the previous time step. In this report we introduce this last method and its use for different types of Vlasov equations.
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Rapport
[Research Report] RR-3393, INRIA. 1998, pp.23
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Eric Sonnendrücker, Jean Roche, Pierre Bertrand, Alain Ghizzo. The Semi-Lagrangian Method for the Numerical Resolution of Vlasov Equations. [Research Report] RR-3393, INRIA. 1998, pp.23. 〈inria-00073296〉

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