Hermite三次样条多小波自然边界元法

针对应用自然边界元方法解上半平面的Laplace方程的Neumann边值问题时存在奇异积分的困难,本文提出了Hermite三次样条多小波自然边界元法.Hermite三次样条多小波具有较短的紧支集、很好的稳定性和显式表达式,而且它们在不同层上的导数还是相互正交的.因此,本文将它与自然边界元法相结合,利用小波伽辽金法离散自然边界积分方程,使自然边界积分方程中的强奇异积分化为弱奇异积分,从而降低了问题的复杂性.文中给出的算例表明了该方法的可行性和有效性.

HERMITE CUBIC SPLINE MULTI-WAVELET NATURAL BOUNDARY ELEMENT METHOD

The Neumann boundary value problem for the Laplacian equation on the upper half plane can be solved by natural boundary element method, but it is very difficult to solve its singular integral. In this paper, we propose a Hermite cubic spline multi-wavelet natural boundary element method. The Hermite cubic spline multi-wavelet has shorter tight collection, better stability and good explicit expression. Moreover, their derivatives on different levels are mutual orthogonal. Accordingly, taking advantage of Galerkin-wavelet method in discretizing the natural boundary integral equation and integral of the natural boundary element method with the above-mentioned, this paper makes the strongly singular integral of the natural boundary equations change into the weakly singular integral, so the problem is simplified. A numerical example is shown and the feasibility and validity of the method are proved.