角形域上Neumann问题的拟小波自然边界元法

Quasi wavelet boundary element method of Neumann boundary value problem in angle domain

首先利用保角变换,通过自然边界元法将角形区域的调和方程的Neumann边值问题归化为边界上的变分问题。对于存在着奇异积分的困难,采用了拟小波基。这种小波基在时域中光滑性高且快速衰减,这一性质可以使奇异积分的计算简便。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。最后,给出数值算例,以示该方法的可行性。

Firstly, the conformal mapping is introduced in this paper, and the Neumann boundary value problem of Laplace equation in the angle domain is naturalized to the equivalent variational problem on the boundary with natural boundary element method. Because it probably has some difficulty of singular integral, the quasi wavelet bases is used in this paper. This kind of the bases is smoother and weakens faster in the time domain, the character makes the computation of singular integral more convenient. This wavelet boundary element method not only can maintain the advantages of reducing dimensions ofnatttral boundary element method and computation stability, but also has desirable precision. At the end, some numerical examples are presented to show the effectiveness.