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

Abstract

AbstractIn 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.