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

Nicolas Crouseilles; Guillaume Latu; Eric Sonnendrücker

International Journal of Applied Mathematics and Computer Science (2007)

  • Volume: 17, Issue: 3, page 335-349
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Crouseilles, Nicolas, Latu, Guillaume, and Sonnendrücker, Eric. "Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation." International Journal of Applied Mathematics and Computer Science 17.3 (2007): 335-349. <http://eudml.org/doc/207841>.

@article{Crouseilles2007,
abstract = {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.},
author = {Crouseilles, Nicolas, Latu, Guillaume, Sonnendrücker, Eric},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {parallelism; semi-Lagrangian method; Vlasov-Poisson equation; Vlasov equation},
language = {eng},
number = {3},
pages = {335-349},
title = {Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation},
url = {http://eudml.org/doc/207841},
volume = {17},
year = {2007},
}

TY - JOUR
AU - Crouseilles, Nicolas
AU - Latu, Guillaume
AU - Sonnendrücker, Eric
TI - Hermite spline interpolation on patches for parallelly solving the Vlasov-Poisson equation
JO - International Journal of Applied Mathematics and Computer Science
PY - 2007
VL - 17
IS - 3
SP - 335
EP - 349
AB - 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.
LA - eng
KW - parallelism; semi-Lagrangian method; Vlasov-Poisson equation; Vlasov equation
UR - http://eudml.org/doc/207841
ER -

References

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