The scaled boundary finite element method applied to electromagnetic field problems

Computation electromagnetic is an important research field of electromagnetic fields and microwave technology subjects. In this paper, the scaled boundary finite element method (SBFEM) is extended to solve one type of electromagnetic field problems-electrostatic field problems. Based on Laplace equation of electrostatic field, the derivations and solutions of SBFEM equations for both bounded and unbounded domain problems are expressed in details, and the solution for the inclusion of prescribed potential along the side-faces of bounded domain is also presented in details, then the total charges on the side-faces can be semi-analytically solved. The accuracy and efficiency of the method are illustrated by numerical examples of electromagnetic field problems with complicated field domains, potential singularities, inhomogeneous media and open boundaries. In comparison with analytic solution method and other numerical methods, the results show that the present method has strong ability to resolve potential field singularities analytically by choosing the scaling centre at the singular point, has the inherent advantage of solving the open boundary problems without truncation boundary condition, has efficient application to the problems with inhomogeneous media by placing the scaling centre in the bi-material interfaces, and produces more accurate solution than conventional numerical methods with far less number of degrees of freedom. The method in electromagnetic field calculation can have broad application prospects.