An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation
Mathematical Physics
2009-10-31 v1 math.MP
Numerical Analysis
Abstract
A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) \cite{Rammile}. Here, we present a new and efficient grid-free random walk method. Based on a modified `` Walk On Spheres" (WOS) algorithm \cite{Elepov-Mihailov1973} for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. The new simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed.
Keywords
Cite
@article{arxiv.math-ph/0010032,
title = {An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation},
author = {Chi-Ok Hwang and Michael Mascagni},
journal= {arXiv preprint arXiv:math-ph/0010032},
year = {2009}
}
Comments
12 pages, 5 figures