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The authors are interested in solving the Vlasov equation used to describe collective effects in plasmas. This nonlinear partial differential equation coupled with Maxwell equation describes the time evolution of the particle distribution in phase space. The numerical solution of the full three-dimensional Vlasov-Maxwell system represents a considerable challenge due to the huge size of the problem. A numerical method based on wavelet transform enables to compute the distribution function on an adaptive mesh from a regular discretization of the phase space. In this paper, the costs of this recently developed adaptive scheme applied on a reduced one-dimensional model, and its parallelization was evaluated. The authors got a fine grain parallel application that achieves a good scalability up to 64 processors on a shared memory architecture.