A dynamic multiscale lifting computation method using Daubechies wavelet

An important property of wavelet multiresolution analysis is the capability to represent functions in a dynamic multiscale manner, so the solution in the wavelet domain enables a hierarchical approximation to the exact solution. The typical problem that arises when using Daubechies wavelets in numerical analysis, especially in finite element analysis, is how to calculate the connection coefficients, an integral of products of wavelet scaling functions or derivative operators associated with these. The method to calculate multiscale connection coefficients for stiffness matrices and load vectors is presented for the first time. And the algorithm of multiscale lifting computation is developed. The numerical examples are given to verify the effectiveness of such a method.