ELECTROSTATICS BY BROWNIAN DYNAMICS - SOLVING THE POISSON EQUATION NEAR DIELECTRIC INTERFACES

The isomorphism between electrostatics and diffusion is discussed and utilized to develop a Brownian dynamics algorithm for solving the Pois son equation near dielectric interfaces. The electrostatic potential b ehaves as if carried by noninteracting, randomly moving pseudo-particl es whose residence time in a given region of space is proportional to the electrostatic potential there. By applying random numbers from the exact solution for diffusion near a planar discontinuity, the Brownia n motion of these particles can be propagated for large time steps, in dependent of spatial grids or artificial boundary conditions. The appl icability of the Brownian algorithm is demonstrated in simple illustra tive calculations. (C) 1997 Elsevier Science B.V.