三维表面电荷法在位场计算中的几点改进

Some improvements for surface charge method in calculation of potential and field tensor

针对常规三维表面电荷法在位场计算中采用平面单元剖分、常值电荷估计致使计算效率低内存消耗大的缺点,对表面电荷法进行改进。采用曲面三角形单元对曲面进行剖分并通过二次多项式进行插值,利用线性或二次插值估计电荷密度以反映电极表面电荷密度的线性及非线性分布的特点,在奇异积分处理上通过切平面法解决格林函数基本解的奇异积分,并给出其具体实现。最后通过两个典型算例进行了验证,结果表明该方法精度较高,具有一定可行性。

Some improvements are made on traditional three-dimension surface charge method in view of the traditional one＇ s low operation efficiency and great memory requirements in calculation of potential and field tensor, which is caused by planar element plot on all kinds of electrode surface and constant approximation for charge density. That is, curved triangular element is introduced to approximate curved surface electrode and expressed by quadratic polynomial, linear or quadratic approximation is adopted to reflect linear or nonlinear distribution of charge and tangent plane method is used to solve singularity of fundamental solution of Green function. At the same time, complete implementation of these improvements is provided. At last, two typical examples of the concentric sphere and double cylinder system are calculated, and the results indicate that higher precision and higher efficiency can be achieved with these improvements. So the improved method is correct and feasible.