Electrostatic Simulation in 2D With the Boundary Element Method: A tutorial

This article provides a detailed tutorial on the foundations of the boundary element method (BEM) by constructing a basic algorithm for 2D electrostatic systems. The geometry of a conductor is expressed as an N-sided polygon where each edge carries a surface charge density with linear continuity between nodes. The resulting basis functions are integrable using closed-form solutions, and the method of point matching yields a stable, invertible system matrix. We then expand the algorithm to include excitation by an impressed field as well as a simple method by which to model a floating conductor. The results are compared against analytic models, showing excellent precision with a relatively small amount of computational effort.