Numerical study demonstrates accelerated solutions for collisional Vlasov equations using a parareal algorithm, indicating substantial speedup for kinetic modeling.
We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of kinetic models, the cheap, coarse propagator consists of a fluid solver and the fine (expensive) propagation is achieved through a kinetic solver for a collisional Vlasov equation. To validate our approach, we present simulations in one dimension in space, three dimensions in velocity settings over a wide range of initial data and kinetic regimes, showcasing the accuracy, efficiency, and the speedup capabilities of our method.
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Laidin et al. (2026) studied this question.
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