开域静电场全源积分人工边界法的GMRES迭代算法

GMRES Iteration Method of FEM-Actual Charge Method for Open Boundary Electrostatic Field Problems

全源积分人工边界法将媒质等效为源,通过对场源和媒质等效源的积分计算,确定人工边界条件。该方法的计算准确度高,可以将人工边界划在距媒质很近的位置,场域的计算区域小。全源积分人工边界法的方程是有限元和人工边界条件的耦合方程。直接迭代法求解该方程时收敛速度慢,并且对于复杂的区域分解问题不能收敛。本文在没有全源积分人工边界法方程的系数矩阵的情况下,基于人工边界条件与场源和媒质的物理关系,推导了全源积分人工边界法的广义极小残量(GMRES)迭代算法。通过与2D FEM对比,验证了GMRES迭代算法的正确性,并且用GMRES迭代算法计算了交流特高压绝缘子串的电场,计算结果与已有文献一致。算例表明GMRES迭代算法收敛速度快,并且能够求解复杂的区域分解问题,为解决复杂问题提供了一种新方法。

In finite element method(FEM)-actual charge method, the media are equivalent to sources. The artificial boundary conditions can be decided by integral calculation of sources and equivalent sources. The FEM-actual charge method can put artificial boundary closed to media. The equations of FEM-actual charge method are the coupling of FEM and artificial boundary conditions. The equations could be solved by direct iteration method, but it needed more time and could not converge for complicated domain decomposition problems. The GMRES iteration method of FEMactual charge method was proposed. The method is based the physical relationship between artificial boundary conditions and whole sources while the matrixes are unknowable. The GMRES iteration method was verified by 2D FEM problem and electric field problem of AC extra-high voltage insulator strings. The examples indicated that the GMRES iteration method could converge more quickly and could solve complicated domain decomposition problems. It is a new method for complicated electrostatic problems.