Green函数自作用单元积分奇异项的简洁闭式

Compact closed forms for integral singularity of self-reaction elements of Green′s functions

首先分析电磁场数值分析中经常遇到的二维交变场Green函数矩形自作用单元积分 ,导出了八阶解析近似公式 ,同时还给出了积分奇异项的等积圆变换简洁闭式。在此基础上 ,给出了三维Green函数中任意三角形单元和立方体自作用单元积分奇异项的等积变换简洁闭式。从计算结果可见 ,这些解析闭式简洁且精度较高 ,为电大尺寸目标的分析提供了理论基础 。

This paper begins with the integral of rectangular self-reaction elements of Green's functions in two-dimensional alternating fields, followed by a derivation of the eight-order analytic approximate formulations, and a compact closed-form for the integral singularity is also presented by using equal-area approximation. On this base, the compact closed forms for the integral singularities of the triangular and the cubic self-reaction elements of three-dimensional Green′s functions are derived by using equal-area circle and equal-volume sphere transformation, respectively. From the computational results, we see that these compact closed forms are of simplicity and high accuracy, which may be applied to the fast computation of the large electric dimension objects.