Scaled boundary finite element method for analysis of electrostatic field problems

The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique, which combines the advantages of the finite element method and the boundary element method with unique properties of its own. The solution in the radial direction is analytical, so the simulation precision of this method is high. This method can meet the boundary condition of the infinity automatically. Based on Laplace equation, a weighted residual approach and coordinate transformation between scaled and Cartesian coordinate are used to derive the scaled boundary finite element equations. The formulation for the calculation of electric potential and field is also addressed. Numerical examples are provided and compared with the results of analytical solution and other numerical methods. It has been shown that the proposed method yields quick convergence and less amount of computation time.