Asymptotic boundary conditions for the finite element modeling of axisymmetric electrical field problems

In this work, the general form of the solution to Laplace's equation is used to derive two formulations of asymptotic boundary conditions (ABC's) suitable for the finite element modeling of axisymmetric electrical field problems with open boundaries. The first formulation works for an arbitrary shape of the finite element region. However, it produces nonsymmetrical matrices. The second formulation works for rectangular outer boundaries and produces symmetric matrices. Both the formulations produce closed-form expressions for the elemental boundary matrices. A simple problem of electrostatic potential is solved as an example.