快速动态自适应小波配点法

A Fast Dynamically Adaptive Wavelet Collocation Method Based on the Precise Time-Integration

动态自适应多尺度小波配点法(AWCM)能有效地模拟具有间歇性的物理现象,此方法是近几年发展起来的非常新颖的数值计算方法。为了增强该方法识别与跟踪解的奇异性的能力,并提高数值计算稳定性与计算效率,将精细时程积分算法与之相结合形成了快速动态自适应多尺度小波配点法。为了实现这一算法,给出了构造动态自适应网格配点集的新方法,构建了以小波(或尺度函数)系数为变量的时程推进公式。通过求解一维Burgers方程,证明了方法具有更加良好的数值计算性质。

The dynamically adaptive wavelet collocation method（AWCM） is a new method developed recently for simulating the physical phenomenon with intermittency efficiently.In order to enhance the stability and efficiency of computation and the ability of identifying and tracking singularity,a new method is established combined the precise time-integration method with AWCM.In this method,a new way to generate dynamic adaptive grids is proposed and the time marching equations as functions of wavelet（or scale function） coefficients are set up.Validated by solving one- dimensional Burgers equation,it is found that the new method provided in this paper presents good performance of computation.