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The simulation of problems in kinetic plasma physics are often challengingdue to strongly coupled phenomena across multiple scales. In this work, wepropose a wavelet-based coarse-grained numerical scheme, based on the frameworkof Equation-Free Projective Integration, for a kinetic plasma system modeled bythe Vlasov-Poisson equations. A kinetic particle-in-cell (PIC) code is used tosimulate the meso scale dynamics for short time intervals. This allows theextrapolation over long time-steps of the behavior of a coarse wavelet-baseddiscretization of the system. To validate the approach and the underlyingconcepts, we perform two 1D1V numerical experiments: nonlinear propagation andsteepening of an ion wave, and the expansion of a plasma slab in vacuum. Thedirect comparisons to resolved PIC simulations show good agreement. We showthat the speedup of the projective integration scheme over the full particlescheme scales linearly with the system size, demonstrating efficiency whiletaking into account fully kinetic, non-Maxwellian effects. This suggests thatthe approach is potentially interesting for kinetic plasma problems with alarge separation of scales, especially in higher dimensions.

Projective multiscale time-integration for electrostatic particle-in-cell methods