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Stochastic Methods for Boundary Value Problems: Numerics for High-Dimensional Pdes and Applications
Hardcover
General MathematicsPhysicsProbability & Statistics
ISBN13: 9783110479065
Publisher: De Gruyter
Published: Sep 26 2016
Pages: 208
Weight: 1.18
Height: 0.50 Width: 6.69 Depth: 9.61
Language: English
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.
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
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