Mesh‐free Monte Carlo method for electrostatic problems with floating potentials

Abstract

Numerical simulation plays a crucial role in the analysis and design of power equipment, such as lightning protection devices, which may become inefficient using traditional grid‐based methods when handling complex geometries of large problems. The authors propose a grid‐free Monte Carlo method to handle electrostatic problems of complex geometry for both the interior and exterior domains, which is governed by the Poisson equation with a floating potential boundary condition that is neither a pure Dirichlet nor a Neumann condition. The potential and gradient at any given point can be expressed in terms of integral equations, which can be estimated recursively within the walk‐on‐sphere algorithm. Numerical examples have been demonstrated, including the evaluation of the mutual capacitance matrix of multi‐conductor structures and lighting striking near real fractal trees. The proposed method shows advantages in terms of geometric flexibility and robustness, output sensitivity, and parallelism, which may become a candidate for game‐changing numerical methods and exhibit great potential applications in high‐voltage engineering.