轴对称位势问题边界元法中奇异积分的处理

Treatment of Singular Integral of Boundary Element Method in Axisymmetric Potential Problem

基于轴对称位势问题的边界积分方程,分别研究了系数矩阵计算中柯西积分的奇异性与对数积分的奇异性,并显式地消除了柯西积分的奇异性,将对数积分的奇异性进行了降阶处理。计算结果表明,数值解与解析解的最大相对误差不超过10-3数量级,表明对奇异积分的处理方法是正确合理的,而且可以非常方便地应用到任意轴对称位势问题的数值求解。

The singularities of Cauchy principal integral and logarithmic integral when calculating the elements of the coefficient matrix were studied respectively based on boundary integral equation of axisymmetric potential problem. The singularities of Cauchy integral were removed explicitly and the order of singularities in logarithmic integral was reduced. Comparison between the computed results and the analytical solutions shows the maximum relative errors are less than 10^-3, which indicates the treatment of singularities is correct and efficient. Meanwhile, it can be very conveniently applied to solution of random axisymmetric potential problem.