Scaled boundary finite element method (SBFEM) was applied to solve the boundary value problems of the electrostatic field in coaxial-cable, i.e., ring-type domain. To avoid the singularity in eigenvalue method, Schur decomposition was employed to update the original method. With scaled boundary coordinate transformation, the governing Laplace equation was semi-discretized to set of a second-order ordinary differential equations (ODEs) by the weighted residual approach. Introducing auxiliary variables, the rank of ODEs was reduced to one, and the general solution of electric potential was obtained by Schur decomposition. Integral constants were determined by the boundary conditions. Numerical examples, including coaxial-cable with various types of cross-section, were calculated and the result showed that singularity is terminated by the proposed approach in respect to Schur decomposition.Wide adaptability, excellent results and less amount of computation consumption are reached beyond other methods.
