自适应小波方法求解波传问题

本文提出了一种求解波传播问题的数值模拟方法——自适应小波时域积分法，即首先引入对偶变量，通过Hamilton变换将时间导数为二阶的波动方程改写为时间上的一阶方程，然后采用小波分析对波动方程的空间变量进行离散，并结合时域积分方法得到原方程递推形式的半解析解。利用小波分析的多尺度特性与消失矩特性，并结合阚值控制，可以自适应地控制计算精度；利用时域积分方法的半解析特性，可以有效地保证解在时间域上的稳定性。数值结果同解析解进行了对比，表明了本方法的有效性。

Using adaptive wavelet method to resolve issue of wave propagation

The paper presented a numeric modeling method--adaptive wavelet integration in time domain to resolve the issue of wave propagation. First, the dual variation was introduced and the wave equation in time derivatives of second order was reduced one-order equation by Hamilton transform, then, the wavelet analysis was used to digitize spatial variation of wave equation, the half-analytic solution in recursion form of original equation was obtained by combination with integration method in time domain. Using multi-scale property and vanishing moment property of wavelet analysis and in combination with threshold controlling, the calculating precision could be adaptively controlled; the stability of solution in time domain could be affectively guaranteed by using the half-analytic property of integration method in time domain. Comparison of numeric results with analytic solution showed the effectiveness of the method.