格林函数的奇异性处理

Treatment of the singularities in Green's functions

格林函数在解决电磁场和直流电场问题的积分方程法和边界单元法等方法中有着广泛的应用.在应用格林函数时会遇到格林函数奇异性的问题,即其在源区域的内部,当场点和源点重合时,会碰到对格林函数为无穷大,积分为奇异积分.对于不同问题中遇到的不同形式的格林函数奇异性问题的各种处理方法进行了分析和评述.对于标量格林函数奇异性问题处理方法有:挖去法、级数展开法、绕开法和解析法等.对于并矢格林函数奇异性问题处理方法有:分量处理法、源并矢法和拟源并矢法等处理方法.通过对实际工作中所遇到的新方法新问题中的不同形式的格林函数的研究,提供了奇异性问题的处理的方法和途径.

The Green＇s function is widely used in the integration equation method and boundary element method. They are used to solve the electromagnetic field and D.C. electrical field, When using the Green＇s function we will meet the problem of singularity. When the source point and the field point are at the same place, the Green＇s function is infinity. Which can lead to the singularity of the integral. We give an analysis and a critical review of the treatment of the singularity in the Green＇s function. For the scalar Green＇s function there are some treatments. Such as the excavating method, series expansion method, steer clear method and analytic method. For the dyadic Green＇s function, we have the constituent method, source dyadic method and the quasi source dyadic method. This provide some methods and approaches to solve singularities in Green＇s functions that are enciuntered in the new problems and the new numerical modelling methods.