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Title: Highly efficient numerical algorithm based on random trees for accelerating parallel Vlasov–Poisson simulations
Authors: Acebron, J. A.
Rodriguez-Rozas, A.
Keywords: Monte Carlo and quasi Monte-Carlo methods
Domain decomposition
Vlasov–Poisson system
Parallel computing
Scalable algorithms
Random trees
Issue Date: Oct-2013
Publisher: Elsevier
Abstract: 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 Padé 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.
Description: WOS:000321433800012 (Nº de Acesso Web of Science)
Peer reviewed: Sim
ISSN: 0021-9991
Publisher version: The definitive version is available at:
Appears in Collections:CTI-RI - Artigos em revistas científicas internacionais com arbitragem científica

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