Multi-scale B-spline method for 2-D elastic problems

In this paper, quadratic B-spline functions are used for solution of 2-D elastic problems. Because B-spline functions are directly used as basis function, there is no need to use meshes and nodes in function approximation. In order to improve the computational efficiency, different scales are used for sub-domains of entire problem domain in function approximation. The modified variational form and Lagrange multipliers method are used for coupling of different scale in function approximation. Compared with meshless methods and other wavelet based methods, this multi-scale B-spline-based method is simple and easy to work with for numerical analysis. Furthermore, the computational efficiency of the multi-scale method is much higher than that of single scale approach. The numerical examples of 2-D elastic problems indicate that the present method is effective and stable for solving complicated problems.