交变电磁场积分方程被积函数奇异性的消除

矢量的面积分方程因其被积函数具有高阶奇异性,不能直接应用于数值计算。利用分部积分将作用在标量Green函数上的Nabla算子转移到电磁场强上。在转移过程中出现的发散的线积分可以相互抵消,不会在最后结果中出现。剩下的部分是关于标量Green函数与场强值或与它们的一阶导数值乘积的面积分,这样积分方程的被积函数高阶奇异性被降到一阶,有利于计算机的程序实现。

Elimination of the singularity of integrands in the integral equation of harmonic electromagnetic field

The vector surface integral equation can't be applied to numerical computation directly because its integrands possess the high order singularity.Nabla operators applied on the scalar Green's function are applied on electric and magnetic fields using integration by parts.Divergent line integrals yielded in the process of integration by parts are eliminated mutually and don't occur in the final results.The residual parts are surface integrations whose integrands are the products of the scalar Green's function and fields or their derivatives.The high order singularity of integrands in the integral equation is reduced to one order,making for program implementation.