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在利用边界元法分析平面电路问题时 ,常会遇到一些被积函数在积分区域内具有奇异性的积分。本文提出求解这类积分的新思路 ,即先采用适当的变量代换达到分离变量或改变奇异点在积分区域内位置的目的 ,然后采用奇异点去除法计算出简化后积分的值。该方法不仅能求解数值方法所无法求解的积分 ,而且由于尽可能地采用了解析方法 ,因而具有计算速度快 ,精度高等特点。该方法为奇异积分的计算提供了一种行之有效的手段。
When using the BEM to analyze the planar circuit, we often encounter some integrals whose integral function has singularity in the integral region. In this paper, we put forward a new idea to solve this kind of integral, that is, we use the appropriate variable substitution to achieve the purpose of separating variables or changing the position of singular points in the integral region. Then we use the singular point elimination method to calculate the value of the simplified integral. This method not only can solve the integral that the numerical method can not solve, but also has the advantages of fast computation speed and high accuracy because it uses the analytical method as much as possible. This method provides an effective means for the calculation of singular integrals.