基于第二代小波自适应网格的二维声波方程波传模拟

本文利用第二代小波多尺度分解和快速变换的特点，构造自适应计算网格.对初始计算网格上的数值解进行第二代小波变换，得到数值解对应的小波系数空间.小波系数的大小表示相邻网格上数值变化率，小波系数大的区域网格点上的数值解变化梯度大.当小波系数大于等于预设的阈值时，在小波系数对应的网格点周围插入新的计算网格点，通过阈值可以实现网格的细化，得到多尺度下层层嵌套的细化自适应网格;由有限差分法得到相应网格点的空间导数.比较数值算例得到的波场快照和计算时间，验证了该方法的有效性.

Adaptive mesh based on second generation wavelet simulation wave propagation for 2D acoustic wave equation

In this paper, it takes second generation wavelet as a tool that structure adaptive mesh, because second generation wavelet has multilevel decomposition and the fast transformation of the characteristics. First, we make value of wave fields on coarse mesh processed second generation wavelet transform, which obtained wavelet coefficients corresponding to the space in which each wavelet coefficients with the real physical space on the discrete grid. These coefficients should decay quickly to zero in the smooth regions, and should be large only in the region where the gradient of u(x) is large. In order to better numerical simulation of the mutation of the region, we have set up a wavelet threshold to determine the grid for each point corresponding to the size of the wavelet coefficients, when the wavelet coefficients greater than or equal to the threshold, the wavelet coefficients corresponding to the grid together with the surrounding The new grid computing, the threshold to control to be multilevel under layers of nested adaptive mesh refinement, and to use adaptive mesh refinement algorithm to calculate the space derivative. By simulating the wave propagation in media, these results have proven the effectiveness of the method.