<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation

IRMA Strasbourg and INRIA Lorraine, CALVI

International Journal of Applied Mathematics and Computer Science

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...

Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation

Published Online: Oct 11, 2007

Page range: 335 - 349

DOI: https://doi.org/10.2478/v10006-007-0028-x

Keywords
Vlasov-Poisson equation, semi-Lagrangian method, parallelism

This content is open access.

Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation

Published Online: Oct 11, 2007

Page range: 335 - 349

DOI: https://doi.org/10.2478/v10006-007-0028-x

KeywordsVlasov-Poisson equation, semi-Lagrangian method, parallelism

This content is open access.

Keywords
Vlasov-Poisson equation, semi-Lagrangian method, parallelism