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Two-Scale numerical simulation of sand transport problems
An exponential integrator for a highly oscillatory vlasov equation
1. | Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes |
2. | Inria Nancy-Grand Est, CALVI Project, & IRMA (UMR CNRS 7501), Université de Strasbourg, 7, rue René-Descartes, 67084, Strasbourg, France |
3. | Max Planck Institute for Plasma Physics, EURATOM Association, Boltzmannstr. 2, 85748 Garching, Germany |
References:
[1] |
C. K. Birdsall and A. B. Langdon, Plasma Physics Via Computer Simulation, Institute of Physics Publishing, Bristol and Philadelphia, 1991. |
[2] |
J. P. Boyd, Chebyshev and Fourier Spectral Methods, $2^{nd}$ edition, Dover, New York, 2001. |
[3] |
S. M. Cox and P. C. Matthews, Exponential time differencing for stiff systems, J. Comput. Phys., 176 (2002), 430-455.
doi: 10.1006/jcph.2002.6995. |
[4] |
N. Crouseilles, M. Lemou and F. Méhats, Asymptotic preserving schemes for highly oscillatory Vlasov-Poisson equations, J. Comput. Phys., 248 (2013), 287-308.
doi: 10.1016/j.jcp.2013.04.022. |
[5] |
F. Filbet and E. Sonnendrücker, Modeling and numerical simulation of space charge dominated beams in the paraxial approximation, Math. Models Methods Appl. Sci., 16 (2006), 763-791.
doi: 10.1142/S0218202506001340. |
[6] |
E. Frénod, Application of the averaging method to the gyrokinetic plasma, Asymptot. Anal., 46 (2006), 1-28. |
[7] |
E. Frénod, F. Salvarani and E. Sonnendrücker, Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method, Math. Models Methods Appl. Sci., 19 (2009), 175-197.
doi: 10.1142/S0218202509003395. |
[8] |
M. Hochbruck and A. Ostermann, Exponential integrators, Acta Numer., 19 (2010), 209-286.
doi: 10.1017/S0962492910000048. |
[9] |
A.-K. Kassam and L. N. Trefethen, Fourth-order time-stepping for stiff PDEs, SIAM J. Sci. Comput., 26 (2005), 1214-1233.
doi: 10.1137/S1064827502410633. |
[10] |
T. Tückmantel, A. Pukhov, J. Liljo and M. Hochbruck, Three-dimensional relativistic particle-in-cell hybrid code based on an exponential integrator, IEEE Trans. Plasma Sci., 38 (2010), 2383-2389. |
show all references
References:
[1] |
C. K. Birdsall and A. B. Langdon, Plasma Physics Via Computer Simulation, Institute of Physics Publishing, Bristol and Philadelphia, 1991. |
[2] |
J. P. Boyd, Chebyshev and Fourier Spectral Methods, $2^{nd}$ edition, Dover, New York, 2001. |
[3] |
S. M. Cox and P. C. Matthews, Exponential time differencing for stiff systems, J. Comput. Phys., 176 (2002), 430-455.
doi: 10.1006/jcph.2002.6995. |
[4] |
N. Crouseilles, M. Lemou and F. Méhats, Asymptotic preserving schemes for highly oscillatory Vlasov-Poisson equations, J. Comput. Phys., 248 (2013), 287-308.
doi: 10.1016/j.jcp.2013.04.022. |
[5] |
F. Filbet and E. Sonnendrücker, Modeling and numerical simulation of space charge dominated beams in the paraxial approximation, Math. Models Methods Appl. Sci., 16 (2006), 763-791.
doi: 10.1142/S0218202506001340. |
[6] |
E. Frénod, Application of the averaging method to the gyrokinetic plasma, Asymptot. Anal., 46 (2006), 1-28. |
[7] |
E. Frénod, F. Salvarani and E. Sonnendrücker, Long time simulation of a beam in a periodic focusing channel via a two-scale PIC-method, Math. Models Methods Appl. Sci., 19 (2009), 175-197.
doi: 10.1142/S0218202509003395. |
[8] |
M. Hochbruck and A. Ostermann, Exponential integrators, Acta Numer., 19 (2010), 209-286.
doi: 10.1017/S0962492910000048. |
[9] |
A.-K. Kassam and L. N. Trefethen, Fourth-order time-stepping for stiff PDEs, SIAM J. Sci. Comput., 26 (2005), 1214-1233.
doi: 10.1137/S1064827502410633. |
[10] |
T. Tückmantel, A. Pukhov, J. Liljo and M. Hochbruck, Three-dimensional relativistic particle-in-cell hybrid code based on an exponential integrator, IEEE Trans. Plasma Sci., 38 (2010), 2383-2389. |
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