位势问题边界元法中几乎奇异积分的完全解析算法

导出了一种完全解析积分算法，用这种算法计算了平面位势问题边界元法中近边界点的几乎奇异积分。当内点离某单元较远时，保持常规高斯积分模式；而当内点离某单元较近时，因常规高斯积分结果失效，用本文的完全解析积分取代常规高斯积分．该算法适用于线性插值计算，对二次元，可将近边界点附近的二次元分解为两个线性元，该算法同样有效。算例证明了本法的有效性和精确性。二次元计算结果比线性元计算结果更精确。

Completely Analytical Algorithm of Nearly Singular Integrals in the Boundary Element Method of Potential Problems

The difficulty of calculating nearly singular integrals exists in BEM. In this paper, a new completely analytical integral algorithm is proposed and applied to the evaluation of the nearly singular integrals in the BEM of planar potential problems. When an internal point is far away from an element, the conventional Gaussian integral scheme is kept in use, but if the point is very close to the element, the conventional Gaussian integral is replaced by the new analytical integral algorithm because of the invalidation of the solution of the conventional Gaussian integral. The analytical algorithm is available for linear interpolation. For quadratic elements, the element near the internal point can be divided into two linear ones, so that the algorithm is still valid. Numerical examples demonstrate the effectiveness and accuracy of this algorithm. The results of quadratic elements are more accurate than the results of linear elements.