Abstract
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.