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Author: Wagner, Wolfgang × Subject: numerical experiments ×

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Now showing 1 - 3 of 3
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    A kinetic equation for the distribution of interaction clusters in rarefied gases
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Patterson, Robert I.A.; Simonella, Sergio; Wagner, Wolfgang
    We consider a stochastic particle model governed by an arbitrary binary interaction kernel. A kinetic equation for the distribution of interaction clusters is established. Under some additional assumptions a recursive representation of the solution is found. For particular choices of the interaction kernel (including the Boltzmann case) several explicit formulas are obtained. These formulas are confirmed by numerical experiments. The experiments are also used to illustrate various conjectures and open problems.
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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.