含集中电导和具有非线性、方向性电导率的介质中直流电场的有限元计算

DC Field Calculation by FEM in Dielctrics with Non-Linear and Directional Conductivity and Including Lumped Surface Conductance

对含非线性电导的介质中直流电场的非线性偏微分方程可以在假定每个试探解的附近电导率是常数的前提下用有限元法迭代求解。但当场强较高和非线性较强时,无论简单迭代法或牛顿——拉夫生法都极易振荡和发散。本文采用阻尼系数缩小迭代中每步的增量,使问题获得解决。文中还推导了介质电导具有方向性时以及场中存在集中电导(包括表面电导)时有限元方程系数应有的改变。

Non-linear differential equations of DC field potentials in dielctrics with non-linear conductivity can be solved by iterative calculation with FEM (Finite Element Method). But in case the field stress is high enough to drive the conductivity deeply into non-linear region, the iterative calculation, either by Simple Iteration or by Newton-Raphson Method, may easily be trapped in oscillation and divergence. This paper solved the problem by introducing a damping coefficient P_K to limit the potential increment at every step. Modifications of the coefficient matrices of the finite element equations were also presented by the author for field calculation in dielectrics with directional conductivity and/or lumped surface conductance.