離散 wavelet 変換による選点法境界要素解析の効率化

Wavelets are employed in the boundary element analysis. A wavelet BEM provides a sparse coefficient matrix by truncating a small value in the matrix entries based on a specified threshold. In discretization process, the collocation method requires the wavelets as bases of an approximate solution, while the Galerkin method requires wavelets not only as bases of numerical solution but as weighting functions. The wavelet BEM is usually derived by the Galerkin method because of high sparsity and good condition of the matrix. However the Galerkin method requires double integration on the boundary. Therefore, in conventional BEMs, the discretized equations are derived based on the collocation method. In this study, improvement of the wavelet collocation BEM is attempted by applying the discrete wavelet transform to the system matrix. Through numerical examples, comparison of performance of the proposed method with the collocation and Galerkin methods is carried out and the validity of the method is investigated