A Direct and Accurate Adaptive Semi-Lagrangian Scheme for the Vlasov-Poisson Equation

Besse N. (2004): Convergence of a semi-Lagrangian scheme for the one-dimensional Vlasov-Poisson system.SIAM Journal on Numerical Analysis, Vol. 42, No. 1, pp. 350-382.10.1137/S0036142902410775Search in Google Scholar

Besse N., Filbet F., Gutnic M., Paun I. and Sonnendrücker E. (2001): An adaptive numerical method for the Vlasov equation based on a multiresolution analysis, In: Numerical Mathematics and Advanced Applications ENUMATH 2001 (F. Brezzi, A. Buffa, S. Escorsaro and A. Murli, Eds.). Ischia: Springer, pp. 437-446.Search in Google Scholar

Campos Pinto M. (2005): Développement et analyse de schémas adaptatifs pour les équations de transport. Ph.D. thesis (in French), Université Pierre et Marie Curie, Paris.Search in Google Scholar

Campos Pinto M. (2007): P₁ interpolation in the plane and functions of bounded total curvature. (in preparation).Search in Google Scholar

Campos Pinto M. and Mehrenberger M. (2005): Adaptive numerical resolution of the Vlasov equation, In: Numerical Methods for Hyperbolic and Kinetic Problems (S. Cordier, T. Goudon, M. Gutnic, E. Sonnendrücker, Eds.). Zürich: European Mathematical Society, Vol. 7, pp. 43-58.Search in Google Scholar

Campos Pinto M. and Mehrenberger M. (2007): Convergence of an adaptive semi-Lagrangian scheme for the Vlasov-Poisson system. (submitted).10.1007/s00211-007-0120-zSearch in Google Scholar

Cheng C.Z. and Knorr G. (1976): The integration of the Vlasov equation in configuration space.Journal of Computational Physics, Vol. 22, pp. 330-351.10.1016/0021-9991(76)90053-XSearch in Google Scholar

Cohen A., Kaber S.M., Müller S. and Postel M. (2003): Fully adaptive multiresolution finite volume schemes for conservation laws.Mathematics of Computation, Vol. 72, No. 241, pp. 183-225.Search in Google Scholar

Cooper J. and Klimas A. (1980): Boundary value problems for the Vlasov-Maxwell equation in one dimension.Journal of Mathematical Analysis and Applications, Vol. 75, No. 2, pp. 306-329.10.1016/0022-247X(80)90082-7Search in Google Scholar

Dahmen, W. (1982): Adaptive approximation by multivariate smooth splines.Journal of Approximation Theory, Vol. 36, No. 2, pp. 119-140.10.1016/0021-9045(82)90060-0Search in Google Scholar

DeVore, R. (1998): Nonlinear approximation.Acta Numerica, Vol. 7, pp. 51-150.10.1017/S0962492900002816Search in Google Scholar

Glassey R.T. (1996): The Cauchy Problem in Kinetic Theory. Philadelphia, PA: SIAM.10.1137/1.9781611971477Search in Google Scholar

Gutnic M., Haefele M., Paun I. and Sonnendrücker E. (2004): Vlasov simulations on an adaptive phase-space grid.Computer Physics Communications, Vol. 164, No. 1-3, pp. 214-219.10.1016/j.cpc.2004.06.073Search in Google Scholar

Iordanskii S.V. (1964): The Cauchy problem for the kinetic equation of plasma.American Mathematical Society Translations, Series 2, Vol. 35, pp. 351-363.10.1090/trans2/035/12Search in Google Scholar

Raviart P.-A. (1985): An analysis of particle methods.Lecture Notes in Mathematics, Vol. 1127, Springer, Berlin, pp. 243-324.Search in Google Scholar

Roussel O., Schneider K., Tsigulin, A. and Bockhorn H. (2003): A conservative fully adaptive multiresolution algorithm for parabolic PDEs.Journal of Computational Physics, Vol. 188, No. 2, pp. 493-523.10.1016/S0021-9991(03)00189-XSearch in Google Scholar

Sonnendrücker E., Filbet F., Friedman A., Oudet E. and Vay J.L. (2004): Vlasov simulation of beams with a moving grid.Computer Physics Communications, Vol. 164, pp. 390-395.10.1016/j.cpc.2004.06.077Search in Google Scholar

Sonnendrücker E., Roche J., Bertrand P. and Ghizzo A. (1999): The semi-Lagrangian method for the numerical resolution of the Vlasov equation.Journal of Computational Physics, Vol. 149, No. 2, pp. 201-220.10.1006/jcph.1998.6148Search in Google Scholar

Yserentant H. (1992): Hierarchical bases, In: ICIAM 91: Proceedings of the 2nd International Conference on Industrial and Applied Mathematics (R.E. O'Malley, Ed.). Philadelphia, PA: SIAM, pp. 256-276.Search in Google Scholar