Off-centered last-passage Monte Carlo algorithm for the charge density on a flat conducting surface

Abstract

The last-passage (LP) Monte Carlo algorithm for the charge density on a flat conducting surface held at a constant potential is further developed by deriving a generalized last-passage Green's function on the flat surface. In the previous research, a centered Green's function on the flat surface was used. In the new last-passage algorithm, an off-centered point on the flat surface inside the Green's function hemisphere can also be used. To demonstrate the algorithm, the charge density on a circular disk is calculated and it is found that the result agrees very well with the analytic solution. Compared with the previous centered LP, the generalized algorithm is better in most cases and has an advantage that it can use the same potential distribution over the LP hemisphere for different locations inside of the lower flat surface including the center of the hemisphere for the charge density. © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim