Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation

• Autorzy: Crouseilles N. , Latu G. , Sonnendrücker E.
• Języki publikacji: EN

Abstrakty

EN

This work is devoted to the numerical simulation of the Vlasov equation using a phase space grid. In contrast to Particle- In-Cell (PIC) methods, which are known to be noisy, we propose a semi-Lagrangian-type method to discretize the Vlasov equation in the two-dimensional phase space. As this kind of method requires a huge computational effort, one has to carry out the simulations on parallel machines. For this purpose, we present a method using patches decomposing the phase domain, each patch being devoted to a processor. Some Hermite boundary conditions allow for the reconstruction of a good approximation of the global solution. Several numerical results demonstrate the accuracy and the good scalability of the method with up to 64 processors. This work is a part of the CALVI project.

Słowa kluczowe

EN

Vlasov-Poisson equation; semi-Lagrangian method; parallelism

PL

równanie Vlasova-Poissona; metoda Lagrangiana; równoległość

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2007
• Tom: Vol. 17, no 3
• Strony: 335--349
• Opis fizyczny: Bibliogr. 25 poz., tab., wykr.

Twórcy

autor

Crouseilles N.

• INRIA Lorraine, CALVI

autor

Latu G.

• INRIA Futurs, Scalapplix

autor

Sonnendrücker E.

• IRMA Strasbourg and INRIA Lorraine, CALVI

Bibliografia

• [1] Bermejo R. (1991): Analysis of an algorithm for the Galerkincharacteristic method. Numerische Mathematik, Vol. 60, pp. 163-194.
• [2] Besse N. and Sonnendrücker E. (2003): Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. Journal of Computational Physics, Vol. 191, pp. 341-376.
• [3] Birdsall C.K. and Langdon A.B.: Plasma Physics via Computer Simulation. Bristol: Institute of Physics Publishing.
• [4] Bouchut F., Golse F. and Pulvirenti M. (2000): Kinetic Equations and Asymptotic Theory. Paris: Gauthier-Villars.
• [5] DeBoor C. (1978): A Practical Guide to Splines. New-York: Springer.
• [6] Campos-Pinto M. and Merhenberger M. (2004): Adaptive Numerical Resolution of the Vlasov Equation.
• [7] Cheng C.Z. and Knorr G. (1976): The integration of the Vlasov equation in configuration space. Journal of Computational Physics, Vol. 22, p. 330.
• [8] Coulaud O., Sonnendrücker E., Dillon E., Bertrand P. and Ghizzo A. (1999): Parallelization of semi-Lagrangian Vlasov codes. Journal of Plasma Physics, Vol. 61, pp. 435-448.
• [9] Feix M.R., Bertrand P. and Ghizzo A. (1994): Title? In: Kinetic Theory and Computing, (B. Perthame, Ed.).
• [10] Filbet F., Sonnendrücker E. and Bertrand P. (2001): Conservative numerical schemes for the Vlasov equation. Journal of Computational Physics, Vol. 172, pp. 166-187.
• [11] Filbet F. and Sonnendrücker E. (2003): Comparison of Eulerian Vlasov solvers. Computer Physics Communications, Vol. 151, pp. 247-266.
• [12] Filbet F. and Violard E. (2002): Parallelization of a Vlasov Solver by Communication Overlapping. Proceedings PDPTA.
• [13] Glassey R.T. (1996): The Cauchy Problem in Kinetic Theory. Philadelphia, PA: SIAM.
• [14] Ghizzo A., Bertrand P., Begue M.L., Johnston T.W. and Shoucri M. (1996): A Hilbert-Vlasov code for the study of high frequency plasma beatwave accelerator. IEEE Transactions on Plasma Science, Vol. 24.
• [15] Ghizzo A., Bertrand P., Shoucri M., Johnston T.W., Filjakow E. and Feix M.R. (1990): A Vlasov code for the numerical simulation of stimulated Raman scattering. Journal of Computational Physis, Vol. 90, pp. 431-457.
• [16] Grandgirard V., Brunetti M., Bertrand P., Besse N., Garbet N., Ghendrih P., Manfredi G., Sarrazin Y., Sauter O., Sonnendrücker E., Vaclavik J. and Villard L. (2006): A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation. Journal of Computational Physics, Vol. 217, pp. 395-423.
• [17] Gutnic M., Haefele M., Paun I. and Sonnendrücker E. (2004): Vlasov simulation on an adaptive phase space grid. Computer Physical Communications, Vol. 164, pp. 214-219.
• [18] Hammerlin G. and Hoffmann K.H. (1991): Numerical Mathematics, New-York: Springer.
• [19] Kim C.C. and Parker S.E. (2000): Massively parallel threedimensional toroidal gyrokinetic flux-tube turbulence simulation. Journal of Computational Physics, Vol. 161, pp. 589-604.
• [20] McKinstrie C.J., Giacone R.E. and Startsev E.A. (1999): Accurate formulas for the Landau damping rates of electrostatic waves. Physics of Plasmas, Vol. 6, pp. 463-466.
• [21] Manfredi G. (1997): Long time behaviour of strong linear Landau damping. Physical Review Letters, Vol. 79.
• [22] Shoucri M. and Knorr G. (1974): Numerical integration of the Vlasov equation. Journal of Computational Physics, Vol. 14, pp. 84-92.
• [23] Sonnendrücker E., Filbet F., Friedman A., Oudet E. and Vay J.L. (2004): Vlasov simulation of beams on a moving phase space grid. Computer Physics Communications, Vol. 164, pp. 390-395.
• [24] Sonnendrücker E., Roche J., Bertrand P. and Ghizzo A. (1999): The semi-Lagrangian method for the numerical resolution of the Vlasov equations. Journal of Computational Physics, Vol. 149, pp. 201-220.
• [25] Staniforth A. and Coté J. (1991): Semi-Lagrangian integration schemes for atmospheric models - A review. Monthly Weather Review, Vol. 119, pp. 2206-2223.