Description: Stochastic Numerics for the Boltzmann Equation by Sergej Rjasanow, Wolfgang Wagner 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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. Table of Contents Kinetic theory.- Related Markov processes.- Stochastic weighted particle method.- Numerical experiments. Review From the reviews:"The book under review deals with numerical methods for the resolution of the nonlinear Boltzmann equation for rarefied monoatomic gases in 1D and 2D. Because of the high dimensionality of standard kinetic models, the authors privilege the stochastic procedures, namely Direct Simulation Monte Carlo methods (DSMC). Such a method can be investigated mathematically relying on the theory of Markov processes; this in return allows for proposing an extension of DSMC, the so-called Stochastic Weighted Particle Method (SWPM). The outline of the book is classical: Chapter 1 recalls basic features of kinetic models and the Boltzmann equation. Chapter 2 introduces the reader to Markov processes in the context of various Boltzmann models. The main contribution is Chapter 3, where the authors convey the reader to the stochastic algorithms, for which precise convergence results are given in some generality. Finally, Chapter 4 presents numerical results: first for the spatially Boltzmann model, then 1D and 2D simulations are displayed." (Laurent E. Gosse, Mathematical Reviews)"The main part of the book is … where the stochastic algorithms for the Boltzmann equation are developed. The algorithms are based on the Monte Carlo Method introduced by the brilliant scientists J. von Neumann, Stanislaw Ulam and Nicholas Metropolis while working on the Manhattan project in Los Alamos. … The book is well written, clear and as much as possible self-contained." (Claudia Simionescu-Badea, Zentralblatt MATH, Vol. 1155, 2009) Long Description 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. Review Quote From the reviews:"The book under review deals with numerical methods for the resolution of the nonlinear Boltzmann equation for rarefied monoatomic gases in 1D and 2D. Because of the high dimensionality of standard kinetic models, the authors privilege the stochastic procedures, namely Direct Simulation Monte Carlo methods (DSMC). Such a method can be investigated mathematically relying on the theory of Markov processes; this in return allows for proposing an extension of DSMC, the so-called Stochastic Weighted Particle Method (SWPM). The outline of the book is classical: Chapter 1 recalls basic features of kinetic models and the Boltzmann equation. Chapter 2 introduces the reader to Markov processes in the context of various Boltzmann models. The main contribution is Chapter 3, where the authors convey the reader to the stochastic algorithms, for which precise convergence results are given in some generality. Finally, Chapter 4 presents numerical results: first for the spatially Boltzmann model, then 1D and 2D simulations are displayed." (Laurent E. Gosse, Mathematical Reviews)"The main part of the book is … where the stochastic algorithms for the Boltzmann equation are developed. The algorithms are based on the Monte Carlo Method introduced by the brilliant scientists J. von Neumann, Stanislaw Ulam and Nicholas Metropolis while working on the Manhattan project in Los Alamos. … The book is well written, clear and as much as possible self-contained." (Claudia Simionescu-Badea, Zentralblatt MATH, Vol. 1155, 2009) Details ISBN3642064434 Author Wolfgang Wagner Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Series Springer Series in Computational Mathematics Year 2010 ISBN-10 3642064434 ISBN-13 9783642064432 Format Paperback Publication Date 2010-10-19 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 510 Edition 1st Short Title STOCHASTIC NUMERICS FOR THE BO Language English Media Book Series Number 37 Pages 256 Edition Description Softcover reprint of hardcover 1st ed. 2005 Alternative 9783540252689 Audience Professional & Vocational Illustrations XIV, 256 p. We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96238022;
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ISBN-13: 9783642064432
Book Title: Stochastic Numerics for the Boltzmann Equation
Number of Pages: 256 Pages
Language: English
Publication Name: Stochastic Numerics for the Boltzmann Equation
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Publication Year: 2010
Subject: Mathematics, Physics
Item Height: 235 mm
Item Weight: 421 g
Type: Textbook
Author: Sergej Rjasanow, Wolfgang Wagner
Item Width: 155 mm
Format: Paperback
