处理准奇异积分的自适应高斯积分法

A self-adaptive Gauss integral method for evaluation of nearly singular integrals

边界元法通常需要采用数值方法解决单元内的各种积分问题,而准奇异积分是各种积分中数值处理最为困难的部分.自适应高斯积分法通过指定条件下的局部单元细分,改变了整个计算区域上的积分点分布,提高了数值积分精度.对于三维水波对直立圆柱的绕射问题,采用此方法对求解过程中出现的准奇异积分进行了处理,计算结果表明本方法是一种高效实用的方法.

Different kinds of integrations have to be evaluated in boundary element methods. The nearly singular integral is the most proposed to divide the element into difficult one of them. A self-adaptive Gauss integral method is finer meshes under the specified conditions. The integral point distribution of the whole calculation domain is changed and the integral precision is promoted by this method. Applying the self adaptive method, an example of the wave diffraction from a uniform cylinder is examined. The examination results show that the present method is a fast and easily applicable one.