Wavelet Method for Boundary Integral Equations (Journal of Computational Mathematics, 2000)
In this paper, we show how to use wavelet to discretize the boundary integral equations which are both singular and ill-conditioned. By using an explicit diagonal preconditioning, the condition number of the corresponding matrix is bounded by a constant, while the sparse structure speeds up the iterative solving process. Using an iterative method, one thus obtains a fast numerical algorithm to solve the boundary integral equations.