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.
Categories: math-ph math.MP math.NA