H-hierarchical adaptive BEM with Haar wavelet functions for two-dimensional Laplace problems

An h-hierarchical method is developed using Haar wavelets for two-dimensional Laplace problems and performance of the developed method is investigated. Haar wavelets provide complete hierarchical system for approximate solution and sparse coefficient matrix by truncation. The preconditioned GMRES(m), a kind of iterative solvers, is employed to solve equations. Through numerical example, it is found that the memory requirement is decreased, however, the CPU time is not shortened because of a large cost of preconditioning.