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Stochastic Methods for Boundary Value Problems : Numerics for High-dimensional PDEs and Applications.

Author: Karl K Sabelfeld; N A Simonov
Publisher: Berlin/Boston, GERMANY : De Gruyter, 2016.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where the random walks live not only on the boundary, but also inside the domain. A variety of examples from capacitance calculations to electron dynamics in semiconductors are discussed to illustrate the viability of the  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 2016042706
(OCoLC)949750711
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Karl K Sabelfeld; N A Simonov
ISBN: 3110479451 9783110479454
OCLC Number: 960040322
Language Note: In English.
Description: 1 online resource (208)
Contents: 1 Introduction ; 2 Random walk algorithms for solving integral equations ; 2.1 Conventional Monte Carlo scheme ; 2.2 Biased estimators ; 2.3 Linear-fractional transformations and their relations to iterative processes. 2.4 Asymptotically unbiased estimators based on singular approximations 2.5 Integral equation of the first kind ; 3 Random walk-on-boundary algorithms for the Laplace equation ; 3.1 Newton potentials and boundary integral equations of the electrostatics. 3.2 The interior Dirichlet problem and isotropic random walk-on-boundary process 3.3 Solution of the Neumann problem ; 3.4 Random estimators for the exterior Dirichlet problem ; 3.5 Third BVP and alternative methods of solving the Dirichlet problem ; 3.6 Inhomogeneous problems. 3.7 Continuity BVP 3.7.1 Walk on boundary for the continuity problem ; 3.8 Calculation of the solution derivatives near the boundary ; 3.9 Normal derivative of a double-layer potential ; 4 Walk-on-boundary algorithms for the heat equation. 4.1 Heat potentials and Volterra boundary integral equations 4.2 Nonstationary walk-on-boundary process ; 4.3 The Dirichlet problem ; 4.4 The Neumann problem ; 4.5 Third BVP ; 4.6 Unbiasedness and variance of the walk-on-boundary algorithms.
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Abstract:

This monograph is devoted to random walk based stochastic algorithms for solving high-dimensional boundary value problems of mathematical physics and chemistry. It includes Monte Carlo methods where  Read more...

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