Construction of the Nested Approximation Interval B-Spline Wavelet Boundary Element Method to Solve Elasticity Problem

B-spline wavelet on the interval (BSWI) has the advantages of interval interpolation and nested approximation, which is suitable for numerical solution of partial differential equations (PDE) and integral equations. This method combines B-spline wavelet on the interval with the traditional boundary element method. By taking advantage of the nested approximation characteristics of B-spline wavelet on the interval, it provides a new numerical calculation method for the field of computational mechanics. In the present, interval B-spline wavelet boundary element method (BSWI-BEM) using the nested approximation has been presented to solve elasticity problems. First, the lifting scheme of BSWI basis functions is developed for nested approximation. Second, the boundary variables represented by the coefficients of wavelets expansion in wavelet space are transformed into the physical space via the corresponding multi-scale transformation matrices. Last, the BSWI-BEM computational schemes for 2D and 3D elasticity problems are derived using the fundamental solution of the elasticity problems in association with weighted residual techniques. Numerical simulations using typical examples of 2D and 3D elasticity problems are given and the corresponding accuracies are verified by comparison with closed-form solutions.