Distribution of electrical charge in a system of finite conductors

摘要

Numerical approximation of the distribution of electrical charge in systems of mutually electrically isolated conductors carrying different electric potential is in practice extremely difficult by means of standard FE schemes. The main obstacles are represented by lack of the boundary conditions and geometrical incommensurability of various elements present within the investigated domain. The paper reformulates the problem onto a system of the first-kind Fredholm integral equations with a weakly singular kernel that is discretized alternatively to the classical Nystrom method. Solvability and unambiguousness of the continuous mathematical model as well as convergence of the numerical scheme is shown. Quasi equilibrium approach for the simulation of moving conductors is also discussed. The methodology is illustrated on a typical example.