Wavelet Method For Boundary Intergal Equations
Pin Wen Zhang 1, Yu Zhang 21 School of Mathematical Sciences, Peking University, Beijing 100871, China
2 Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China
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 speed up the iterative solving process. Using an iterative method, one thus obtains a fast numerical algorithm to solve the boundary integral equations.
Key words: Wavelet bases; Boundary integral equation; Preconditioning.