A wavelet finite element method for the 2-D wave equation in fluid-saturated porous media

The wavelet finite element method is applied to forward simulation of the wave equation in fluid-saturated porous media. The 2-D scaling functions of Daubechies wavelet are used as the interpolation basis function to replace the polynomial functions, then the tensor wavelet element is constructed. In order to overcome the integral difficulty for lacking of the explicit expression of the Daubechies wavelet, a kind of character functions are introduced. The recursive expression of calculating the function value of Daubechies wavelet on the fraction node is deduced, and the rapid wavelet transform between the wavelet coefficient space and the wave field displacement space is constructed. The results of numerical simulation show that the method is effective.