Multilevel Monte Carlo with Improved Correlation for Kinetic Equations in the Diffusive Scaling
| Autor: | Giovanni Samaey, Bert Mortier, Stefan Vandewalle, Emil Løvbak |
|---|---|
| Přispěvatelé: | Krzhizhanovskaya, Valeria V, Závodszky, Gábor, Lees, Michael H, Dongarra, Jack J, Sloot, Peter MA, Brissos, Sérgio, Teixeira, João |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
Work (thermodynamics) Monte Carlo method 010103 numerical & computational mathematics Collision 01 natural sciences Stability (probability) Article 010101 applied mathematics Phase space Multilevel Monte Carlo Kinetic equations Particle methods Particle Statistical physics 0101 mathematics Diffusive scaling Scaling Order of magnitude |
| Zdroj: | Computational Science – ICCS 2020 Lecture Notes in Computer Science ISBN: 9783030504328 ICCS (6) |
| Popis: | In many applications, it is necessary to compute the time-dependent distribution of an ensemble of particles subject to transport and collision phenomena. Kinetic equations are PDEs that model such particles in a position-velocity phase space. In the low collisional regime, explicit particle-based Monte Carlo methods simulate these high dimensional equations efficiently, but, as the collision rate increases, these methods suffer from severe time-step constraints. In the high collision regime, asymptotic-preserving particle schemes are able to produce stable results. However, this stability comes at the cost of a bias in the computed results. In earlier work, the multilevel Monte Carlo method was used to reduce this bias by combining simulations with large and small time steps. This multilevel scheme, however, still has large variances when correlating fine and coarse simulations, which leads to sub-optimal multilevel performance. In this work, we present an improved correlation approach that decreases the variance when bridging the gap from large time steps to time steps of the order of magnitude of the collision rate. We further demonstrate that this reduced variance results in a sharply reduced simulation cost at the expense of a small bias. ispartof: pages:374-388 ispartof: Lecture Notes in Computer Science (LNCS) vol:12142 pages:374-388 ispartof: International Conference on Computational Science (ICCS) 2020 location:Amsterdam, NL date:3 Jun - 5 Jun 2020 status: published |
| Databáze: | OpenAIRE |
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