Stochastic Numerics for the Boltzmann Equation [electronic resource] /
Rjasanow, Sergej.author.
Wagner, Wolfgang.author.
Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.
Description based upon print version of record.
Includes bibliographical references (p. [243]-253) and index.
Kinetic theory -- Related Markov processes -- Stochastic weighted particle method -- Numerical experiments.
Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.
Numerical analysis.
Probabilities.
Mathematical physics.
Partial differential equations.
Numerical Analysis.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
Partial Differential Equations.
Springer series in computational mathematics