**Topic/Type**:
2.2 Kinetic methods, Particle-In-Cell and Vlasov, Oral

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A probabilistic-based numerical method for solving efficiently
the three-dimensional Fourier transformed Vlasov-Poisson equation

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J.A. Acebron**^{1}, A. Rodriguez-Rozas^{1}, R. Spigler^{2}, R. Vilela Mendes^{3}

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*^{1} CEMAT, Instituto Superior Tecnico, Lisbon,Portugal

^{2} Dipartimento di Matematica, Universita di Roma Tre

^{3} CFN, Instituto Superior Tecnico,Lisbon, Portugal

An efficient numerical method for solving the three-dimensional Fourier transformed of the Vlasov-Poisson equation is developed. The method is based on a probabilistic representation of the solution, which requires generating a number of random trees, and averaging on suitable multiplicative functional. Others than the classical methods for solving the Vlasov-Poisson equation, the probabilistic approach allows to compute the solution at single points internal to the domain, without the need of generating first a computational grid and solving then the full problem. Moreover, the algorithm turns out to be

specially suited to massively parallel implementation, enjoying

arbitrary scalability properties. In order to assess the method, several numerical examples were investigated focusing mostly on the linear Landau damping.