多尺度有限差分方法求解波动方程

小波分析是多尺度分析方法,本文利用具有紧支集的正交小波变换对有限差分方程进行空间多尺度近似,提出适合于层状介质波传问题数值计算的多尺度有限差分方法,将波动方程的求解转换到小波域中进行。利用小波基的自适应性与消失矩特性,有效减少了计算量、提高了稳定性,扩大了可求解的速度范围。地球物理勘探中的数值实例显示了算法具有良好效率。

A new method of multiresolution finite difference for wave equation

Wavelet transform is one kind of multi|resolution analytical methods. This paper is devoted to the resolution of wave function, using a spatial multi|resolution approximation to the finite differential scheme generated by the orthogonal compactly supported wavelet transform. A new method named Multi|resolution Finite Difference is proposed to solve the problem of wave propagation in the multi|layered medium. It is thus that the problem is solved in the wavelet domain rather than the traditional Euclidean space. Due to adaptive and vanishing moment property of the wavelet basis, it is a promising method because of some advantages such as large velocity range, little computational burden, and efficiency of convergence and robustness. The numerical results show effectiveness and potential of the method. A new solution procedure for the research of wave function is put forward.