Calculation of electrostatic field in 3-D unbounded non-uniform domains by FEM with kelvin transformation

Abstract

An approach for solving the electrostatic field in 3-D unbounded domains is introduced in this paper, which is the combination of the finite element method (FEM) and the Kelvin transformation. The principle of this method is dividing the whole infinite region into two parts by a spherical surface. In the inner part with a sphere as the boundary, the ordinary finite element method is employed. As for the outer open-boundary part, the approach first transforms it into a finite closed domain that is of the sphere as the boundary, in which the transmuted FEM is used. It is allowed that the exterior open-boundary part is of non-uniform medium, such as unlimited domains or different shapes with different materials whose interfaces might extend to infinity.