Multilevel Asymptotic-Preserving Monte Carlo for Particle Simulations
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We develop a novel Multilevel Asymptotic-Preserving Monte Carlo (ML-APMC) method for simulating the kinetic Boltzmann transport equation with Bhatnagar-Gross-Krook (BGK) collision operator. This equation occurs, for instance, in mathematical models of the neutral particles in the plasma edge of nuclear fusion reactors. The main features of our method are a new and improved recipe for correlating particle trajectories with different time step sizes, and a new and more general level selection strategy. We illustrate the efficiency of our ML-APMC method by applying it to a one-dimensional fusion test case with nonhomogeneous and anisotropic plasma background. Our method yields significant speedups, both in the low and high collisional regime. In the high-collisional case, our ML-APMC outperforms the single-level APMC method by several orders of magnitude.
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