Sphere Last-Passage Algorithm for Charge Density on a Smooth (Convex) Conducting Surface

Abstract

In a series of papers, the authors have been developing last-passage algorithms such as last-passage algorithm and off-centered last-passage algorithm on a flat conducting surface, quadrupole last-passage algorithm on an L-shaped conducting surface, and last-passage algorithm on a spherical conducting surface, held at (non)constant potentials. All the previous last-passage algorithms can compute charge density at a specific point on a flat or spherical conducting surface only. In this paper, the last-passage algorithms on any smooth (convex) surface for charge density at a specific point are further developed where a tangent plane can be constructed and a sphere can be put. The algorithm for charge density on a sphere, on a circular plate, and on the unit cube held at unit potential is demonstrated. The results show excellent agreements with theoretical or other simulation ones.