Journal of Computational Physics
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Journal of Computational Physics
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
The semi-Lagrangian method for the numerical resolution of the Vlasov equation
Journal of Computational Physics
Outflow Boundary Conditions for the Fourier Transformed One-Dimensional Vlasov–Poisson System
Journal of Scientific Computing
Plasma Physics Via Computer
Introduction to Parallel Computing (Oxford Texts in Applied and Engineering Mathematics)
Introduction to Parallel Computing (Oxford Texts in Applied and Engineering Mathematics)
SIAM Journal on Scientific Computing
Multiplicative cascades applied to PDEs (two numerical examples)
Journal of Computational Physics
Probabilistically induced domain decomposition methods for elliptic boundary-value problems
Journal of Computational Physics
A parallel Vlasov solver based on local cubic spline interpolation on patches
Journal of Computational Physics
Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
A discontinuous Galerkin method for the Vlasov-Poisson system
Journal of Computational Physics
Smoothness and dimension reduction in Quasi-Monte Carlo methods
Mathematical and Computer Modelling: An International Journal
Journal of Computational Physics
Hi-index | 31.45 |
An efficient numerical method based on a probabilistic representation for the Vlasov-Poisson system of equations in the Fourier space has been derived. This has been done theoretically for arbitrary dimensional problems, and particularized to unidimensional problems for numerical purposes. Such a representation has been validated theoretically in the linear regime comparing the solution obtained with the classical results of the linear Landau damping. The numerical strategy followed requires generating suitable random trees combined with a Pade approximant for approximating accurately a given divergent series. Such series are obtained by summing the partial contributions to the solution coming from trees with arbitrary number of branches. These contributions, coming in general from multi-dimensional definite integrals, are efficiently computed by a quasi-Monte Carlo method. It is shown how the accuracy of the method can be effectively increased by considering more terms of the series. The new representation was used successfully to develop a Probabilistic Domain Decomposition method suited for massively parallel computers, which improves the scalability found in classical methods. Finally, a few numerical examples based on classical phenomena such as the non-linear Landau damping, and the two streaming instability are given, illustrating the remarkable performance of the algorithm, when compared the results with those obtained using a classical method.