Efficient modified "walk on spheres" algorithm for the linearized Poisson-Bolzmann equation

Hwang, Chi-Ok; Mascagni, Michael
February 2001
Applied Physics Letters;2/5/2001, Vol. 78 Issue 6, p787
Academic Journal
A discrete random walk method on grids was proposed and used to solve the linearized Poisson-Boltzmann equation (LPBE) [R. Ettelaie, J. Chem. Phys. 103, 3657 (1995)]. Here, we present an efficient grid-free random walk method. Based on a modified "walk on spheres" algorithm [B. S. Elepov and G. A. Mihailov, Sov. Math. Dokl. 14, 1276 (1973)] for the LPBE, this Monte Carlo algorithm uses a survival probability distribution function for the random walker in a continuous and free diffusion region. This simulation method is illustrated by computing four analytically solvable problems. In all cases, excellent agreement is observed. © 2001 American Institute of Physics.


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