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- Title
A STOCHASTIC ALGORITHM WITHOUT TIME DISCRETIZATION ERROR FOR THE WIGNER EQUATION.
- Authors
Muscato, Orazio; Wagner, Wolfgang
- Abstract
Stochastic particle methods for the numerical treatment of the Wigner equation are considered. The approximation properties of these meth- ods depend on several numerical parameters. Such parameters are the number of particles, a time step (if transport and other processes are treated sepa- rately) and the grid size (used for the discretization of the position and the wave-vector). A stochastic algorithm without time discretization error is intro- duced. Its derivation is based on the theory of piecewise deterministic Markov processes. Numerical experiments are performed in a one-dimensional test case. Approximation properties with respect to the grid size and the number of par- ticles are studied. Convergence of a time-splitting scheme to the no-splitting algorithm is demonstrated. The no-splitting algorithm is shown to be more efficient in terms of computational effort.
- Subjects
PARTICLE methods (Numerical analysis); STOCHASTIC processes; NUMERICAL analysis; APPROXIMATION theory; MARKOV processes
- Publication
Kinetic & Related Models, 2019, Vol 12, Issue 1, p59
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2019003