A numerical method based on Daubechies wavelet basis and B-spline patches for elasticity problems (Q1792862)

Summary: The Daubechies (DB) wavelets are used for solving 2D plane elasticity problems. In order to improve the accuracy and stability in computation, the DB wavelet scaling functions in \(\left[0, + \infty)\right.\) comprising boundary scaling functions are chosen as basis functions for approximation. The B-spline patches used in isogeometry analysis method are constructed to describe the problem domain. Through the isoparametric analysis approach, the function approximation and relevant computation based on DB wavelet functions are implemented on B-spline patches. This work makes an attempt to break the limitation that problems only can be discretized on uniform grids in the traditional wavelet numerical method. Numerical examples of 2D elasticity problems illustrate that this kind of analysis method is effective and stable.