Last-passage Monte Carlo Algorithm for Charge Density on a Conducting Spherical Surface

Abstract

For solving some elliptic boundary value problems, Monte Carlo diffusion algorithms are often the most efficient ones. Among them, last-passage algorithms are good for obtaining charge density at a specific point on a conducting surface. In our previous research, we developed the last-passage Monte Carlo algorithm for charge density on a flat conducting surface. In the research, we used the Laplace Green’s function only on a flat surface. In this paper, we further develop the lastpassage algorithm on a spherical surface. We demonstrate the last-passage algorithm by obtaining charge density on a sphere held at unit potential. In addition, using the last-passage algorithm we compute the mutual capacitance and charge distribution of two conducting spheres. We compare them with the analytic results of J. Lekner to find an excellent agreement.