Infinite Parallel Plates Algorithm

Abstract

In a diffusion Monte Carlo simulation, when diffusion starts between two parallel planes, the "walks-on-spheres" (WOS) algorithm is usually used. In this case, an absorption epsilon-layer is used to terminate the diffusion. Here, based on isomorphism between the electrostatic Poisson problem and the corresponding diffusion motion expectation of the first passage, a new parallel-plates algorithm is developed without an absorption layer, which induces another diffusion error in addition to the intrinsic Monte Carlo error. As there is not an analytic closed solution for the induced charge density on the parallel plates by a charge at the center between them, a series solution is used, combined with the acceptance-rejection sampling method. Using this algorithm, even though a series solution is used, it is shown that an exact sampling can be performed, which means that the random walk jump can be performed to the parallel planes without using the detailed WOS random walk jumps. It is verified that the proposed parallel plates algorithm is significantly more efficient than the current WOS algorithm.