“Parareal simulations of some oscillatory singularly perturbed ordinary differential equations”
The goal of this work is to develop a new strategy for solving by the parareal
algorithm highly oscillatory ordinary differential equations which are characteristics
of six-dimensional Vlasov equations. For the coarse solvers we
use reduced models, obtained from two-scale asymptotic expansions. Such
reduced models have a low computational cost since they are free of high
oscillations. The parareal method allows to improve their accuracy in a
few iterations through corrections by fine solvers of the full model. The accuracy
and the efficiency of the strategy is illustrated by numerical simulations of charged
particles submitted to a large magnetic field.
