An h-hierarchical Galerkin BEM using Haar wavelets

Application of Haar wavelet to h-hierarchical adaptive method is attempted to improve the performance. The wavelet boundary element method (BEM) is developed by means of the Galerkin method. In order to save memory requirement and computation time, sparse matrices are obtained by truncation of matrix coefficients. Error indicator and estimator are constructed based on the difference between the true solution and its projection onto the mesh. These values are effectively evaluated using the boundary element solution. The adaptive method is developed for 2D Laplace problems. Through numerical examples, performance of the present method is investigated concerning the sparseness of matrices and the computation time devoted to calculation of matrix coefficients and to equation solving process. (C) 2001 Elsevier Science Ltd. All rights reserved.