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 use d to derive two formulations of asymptotic boundary conditions (ABC's) suit able for the finite element modeling of axisymmetric electrical field probl ems with open boundaries. The first formulation works for an arbitrary shap e of the finite element region. However, it produces nonsymmetrical matrice s. The second formulation works for rectangular outer boundaries and produc es symmetric matrices. Both the formulations produce closed-form expression s for the elemental boundary matrices. A simple problem of electrostatic po tential is solved as an example.