非线性变换在计算接近奇异积分中的应用

The Application of Nonlinear Transform in Calculating Nearly Singular Integrals

执行边界元方法的一个关键问题是接近奇异积分的快速精确计算.一般来说,经典的数值积分方法在执行边界元方法时是不能满足要求的.基于一类非线性变换,通过选择最优参数,提出了一种高效计算接近奇异积分的方法,数值试验证明这种算法是高效精确的.

One of the key problems in implementing the boundary element method is the rapid and accurate calculation of nearly singular integral. Generally speaking, classic numerical integration methods cannot meet the requirement in implementing the boundary ele- ment method. In this paper, we choose optimal parameters and promote a method which can calculate nearly singular integral with high efficiency. The test shows that the algorithm is efficient and accurate.