A Hermite-type adaptive semi-Lagrangian scheme

Michel Mehrenberger; Eric Violard

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 3, page 329-334
  • ISSN: 1641-876X

Abstract

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We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.

How to cite

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Mehrenberger, Michel, and Violard, Eric. "A Hermite-type adaptive semi-Lagrangian scheme." International Journal of Applied Mathematics and Computer Science 17.3 (2007): 329-334. <http://eudml.org/doc/207840>.

@article{Mehrenberger2007,
abstract = {We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.},
author = {Mehrenberger, Michel, Violard, Eric},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Hermite operator; Vlasov equation; adaptive method; numerical simulation},
language = {eng},
number = {3},
pages = {329-334},
title = {A Hermite-type adaptive semi-Lagrangian scheme},
url = {http://eudml.org/doc/207840},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Mehrenberger, Michel
AU - Violard, Eric
TI - A Hermite-type adaptive semi-Lagrangian scheme
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 3
SP - 329
EP - 334
AB - We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.
LA - eng
KW - Hermite operator; Vlasov equation; adaptive method; numerical simulation
UR - http://eudml.org/doc/207840
ER -

References

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  1. Besse N. and Sonnendrucker E. (2003): Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space. Journal of Computational Physics, Vol.191, No.2, pp.341-376. Zbl1030.82011
  2. 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. Sonnendrucker, Eds.). Zurich: European Mathematical Society, pp.43-58. Zbl1210.65169
  3. Campos Pinto M. and Mehrenberger M. (2005): Convergence of an adaptive scheme for the one-dimensional Vlasov-Poissonsystem. Technical Report No. RR-5519, INRIA Lorraine. 
  4. Gutnic M., Haefele M., Paun I., Sonnendrucker E. (2004): Vlasov simulations on an adaptive phase-space grid. Computer Physics Communications, Vol.164, No.1-3, pp.214-219. Zbl1196.76098
  5. Gutnic M., Haefele M. and Latu G. (2005): A parallel Vlasov solver using a wavelet based adaptive mesh refinement. Proc. Int. Conf. Parallel Processing, ICPP'2005, 7th Workshop High Performance Scientific and Engineering Computing, Oo: IEEE Computer Society Press, pp.181-188. 
  6. Hoenen O., Mehrenberger M. and Violard E. (2004): Parallelization of an adaptive Vlasov solver,Proc. 11th European PVM/MPI Users' Group Conference, EuroPVM/MPI 2004, Berlin: Springer, pp.430-435. 
  7. Hoenen O. and Violard E. (2006): An efficient data structure for an adaptive Vlasov solver. Research Report RR 06-02, ICPS - LSIIT laboratory (CNRS UMR-7005). 
  8. Hong D., Schumaker L.L. (2004); Surface compression using a space of C1 cubic splines with a hierarchical basis. Geometric Modelling Computing, Vol.72, No.1-2, pp.79-92. Zbl1067.41005
  9. %Nakamura T. and Yabe T. (1999): Cubic interpolated propagation scheme for solving the hyperdimensional Vlasov-Poisson equation in phase space. Computer Physics Communications, Vol.120, No.2-3, pp.122-154. Zbl1001.82003
  10. Sonnendrucker E., Filbet F., Friedman A., Oudet E., Vay J. L. (2004): Vlasov simulation of beams on a moving phase-space grid.Computer Physics Communications, Vol.164, No.1-3, pp.390-395 

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