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

by Karl K. Sabelfeld, Nikolai A. Simonov

Overview

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 approach.
The book is written for mathematicians who work in the field of partial differential and integral equations, physicists and engineers dealing with computational methods and applied probability, for students and postgraduates studying mathematical physics and numerical mathematics.

Contents:
Introduction
Random walk algorithms for solving integral equations
Random walk-on-boundary algorithms for the Laplace equation
Walk-on-boundary algorithms for the heat equation
Spatial problems of elasticity
Variants of the random walk on boundary for solving stationary potential problems
Splitting and survival probabilities in random walk methods and applications
A random WOS-based KMC method for electron–hole recombinations
Monte Carlo methods for computing macromolecules properties and solving related problems
Bibliography

Product Details

ISBN-13:	9783110479164
Publisher:	De Gruyter
Publication date:	09/26/2016
Sold by:	Barnes & Noble
Format:	eBook
Pages:	208
File size:	37 MB
Note:	This product may take a few minutes to download.
Age Range:	18 Years

About the Author

Karl K. Sabelfeld, Novosibirsk State University, Russia;
Nikolai A. Simonov, Novosibirsk State University, Russia.

Editorial Reviews

"This book will be of great interest to any researcher who works in the eld of numerical solution of PDEs and integral equations."
Nikolaos Halidias in: Mathematical Review Clippings MR3676590 (2018)

From the Publisher