An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

Details An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation An Efficient Modified "Walk On Spheres" Algorithm for the Linearized Poisson-Boltzmann Equation

2000-10-23

arxiv.org/abs/math-ph/0010032v1

Physics

Mathematical Physics

12 pages, 5 figures

Scientific paper

10.1063/1.1345817

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.

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