高阶矩量法求解MFIE 时近奇异性提取*

采用高阶矩量法求解磁场积分方程时,相邻面片之间的互阻抗是一个难以算准的奇异性四重积分,因为内层面积分和外层面积分中同时包含有奇异性.本文对于内层的近奇异积分采用sinh (x)函数作积分变换,而对于外层的弱奇异性积分采用Duffy变换进行处理,使得被积式变成能够直接数值积分的连续光滑函数.数值结果表明该方法计算近奇异积分时精度远高于直接高斯积分方法,求得的雷达散射截面与电场积分方程所得的结果完全一致,验证了方法的准确性和有效性.

Extracting the Near Singularity of the MFIE When Solved by the Higher Order Moment Method

When the higher order moment method is applied to solve the magnetic field integral equations(MFIE), it is very difficult to calculate the interactions between the two patches sharing a common edge accurately, since singularities a rise both in the inner integrals on the basis functions and in the outer integrals . This paper uses the integration transformation of sinh(x) function to handle the inner near singularity, and the Duffy transformation to deal with the outer weak singularity, thus leads to a continuous smooth integrand which can be calculated by the Gaussian quadrature easily. Numerical experi ments show that this singularity extraction method is much more accurate than the direct use of the Gaussian quadrature in computing these integrals, and that the RCS obtained is validated by the existing electric field integral equation (EFIE) code.