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Author: Wagner, Wolfgang × Subject: Wigner equation ×

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Now showing 1 - 3 of 3
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    A random cloud model for the Wigner equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Wagner, Wolfgang
    A probabilistic model for the Wigner equation is studied. The model is based on a particle system with the time evolution of a piecewise deterministic Markov process. Each particle is characterized by a real-valued weight, a position and a wave-vector. The particle position changes continuously, according to the velocity determined by the wave-vector. New particles are created randomly and added to the system. The main result is that appropriate functionals of the process satisfy a weak form of the Wigner equation.
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    A stochastic algorithm without time discretization error for the Wigner equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Muscato, Orazio; Wagner, Wolfgang
    Stochastic particle methods for the numerical treatment of the Wigner equation are considered. The approximation properties of these methods depend on several numerical parameters. Such parameters are the number of particles, a time step (if transport and other processes are treated separately) and the grid size (used for the discretization of the position and the wavevector). A stochastic algorithm without time discretization error is introduced. 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 particles 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.
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    A class of stochastic algorithms for the Wigner equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Muscato, Orazio; Wagner, Wolfgang
    A class of stochastic algorithms for the numerical treatment of the Wigner equation is introduced. The algorithms are derived using the theory of pure jump processes with a general state space. The class contains several new algorithms as well as some of the algorithms previously considered in the literature. The approximation error and the efficiency of the algorithms are analyzed. Numerical experiments are performed in a benchmark test case, where certain advantages of the new class of algorithms are demonstrated.