Neumann边值问题的小波边界元法

Wavelet Boundary Element Method of the Neumann boundary value problem

自然边界元法将上半平面的Laplace方程的Neumann边值问题归化为边界上的变分问题,总刚度矩阵对称正定,利于数值求解,然而存在着奇异积分的困难.通常的小波基用于边界元法不是很理想,本文采用拟小波基,这种小波基在时域中光滑性高且快速衰减,它是一种拟再生核函数,这一性质可以使奇异积分的计算和数值实现简便.这种小波边界元法不仅能保持自然边界元法的降维及计算便捷稳定的优点,而且还具有良好的逼近精度.

The Laplace equation with Neumann boundary on the upper half plane is reduced into the equivalent natural boundary integral equation. Total stiffness matrix is symmetrical and positive, and it is good for solving problem, but singular integral may exist. The general wavelet bases used in boundary element method is not ideal. In this paper, the authors use the quasi wavelet bases, and this kind of the base is smoother and weakens faster in the time domain. It is one kind of quasi nuclear function, and this character makes the computation of singular integral and the realization of numeral value more convenient. This wavelet boundary element method not only can maintain dimension reduction and computation stability, but also has desirable precision.