静电场分析的比例边界有限元法

比例边界有限元法（SBFEM）是一种半解析数值分析的新方法，集合了有限元法和边界元法的优点，又具有独特的优点．在其辐射坐标上保持了解析性，因此其模拟精度较高，另外可以自动满足无限远的边界条件．从拉普拉斯方程出发，利用加权余量法并通过比例坐标和笛卡儿坐标变换，推导出静电场分析的比例边界有限元方程、电位求解公式以及电场求解公式．算例计算结果与解析解和其他数值方法比较结果表明，此方法具有精度高、计算工作量小的优点．

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.