Applying wavelets to improve the boundary element method for elasticity problems

This paper describes application of fast wavelet transforms in the boundary element method to solve 2D elasticity problems. Daubechies compactly supported orthogonal wavelets have been applied to compress dense and fully populated matrices arising from BEM. GMRES solver is then used to solve linear algebraic systems. A comprehensive sensitivity study is presented to answer the questions like, which order and level of D-wavelets and thresholding parameters are efficient for elasticity problems. Numerical results include a precise study on effect of applying different wavelet orders (D4, D6, D8, D10 and D12), levels and thresholds on the solution accuracy for displacements and stresses and compression ratio of sparsified matrices. The suitable order, level and thresholding parameter as well as saving in computer time and memory are presented for practical engineering problems. The results show that the proposed method is efficient for large problems.