基于JPCG算法的真空灭弧室三维电场有限元计算

建立了高压真空灭弧室三维电场有限元计算的模型及物理方程，分析了适用于大型稀疏矩阵求解的雅可比共轭梯度算法JPCG，给出JPCG算法的迭代流程。采用有限元法对高压真空灭弧室的三维电场分布进行了计算，同时应用JPCG算法来求解所得到的大型有限元方程组。最后采用不同的算法对真空灭弧室的自电容进行了对比计算，计算结果表明，采用JPCG算法可以明显减少有限元方程组求解的迭代次数，加快收敛速度，特别适合应用于三维电磁场有限元分析形成的大型稀疏方程组的求解，是用来计算大型有限元方程组的一种非常有效的方法。同时，真空灭弧室的自电容计算可以给真空灭弧室的优化设计提供参考。

APPLICATION OF JPCG ALGORITHM IN THE THREE DIMENSIONAL ELECTRIC FIELD CALCULATION OF VACUUM INTERRUPTERS

The finite-element calculation model and the physical equations of a high voltage vacuum interrupter were founded in this paper for optimized design. The jacobi preconditioned conjugate gradient (JPCG) algorithm applied to solve the large sparse matrix was also analyzed and the program diagram of JPCG algorithm was proposed. Based on the finite- element method, the three dimensional electrical field distributions including the potential distribution and the electri- cal field intensity distribution were calculated. The large sparse matrix was solved by using the JPCG algorithm. By means of applying different algorithms in computation in self-capacitance of vacuum interrupter, it shows that the JPCG algorithm is especially suitable for solving the large sparse matrix because of the less number of iteration and much more quickly convergent speed. The self-capacitance of the vacuum interrup- ter was also calculated to give a useful design parameter.