非连续边界元积分的精确表达式及相关问题

Discussion on Optimum Collocation Points of Discontinuous Boundary Elements

以二维位势问题边界元分析为例，给出了利用线性非连续边界元离散边界积分方程时系数矩阵积分计算的精确表达式，通过和利用Gauss积分方法计算系数矩阵所得数值结果的比较表明：配位点选择不同对数值计算结果精度影响的主要原因是积分计算的精度，尤其当配位因子选择较大时，存在的准奇异积分(Nearly Singular Integrals)很难利用常规Gauss积分方法准确求得。

In this paper, analytical integration scheme is presented to calculate both singular and nonsingular integrals associated with boundary integral equation of two-dimensional potential problems discretized by linear discontinuous elements. Both singular and nonsingular integrals are obtained in closed form. Numerical tests are performed to demonstrate the advantages of analytical approach. By comparison with the results obtained by Gauss quadrature rule, which is commonly employed to calculate nonsingular integrals, it is illustrated that the optimum collocation points of discontinuous boundary elements is greatly influenced by the accuracy of the integrals, especially the nearly singular integrals.