FAST SINGULARITY PRESERVING METHODS FOR INTEGRAL EQUATIONS WITH NON-SMOOTH SOLUTIONS

摘要

Fast singularity preserving multiscale Galerkin methods are developed in this paper for solving weakly sin-gular Fredholm integral equations of the second kind with non-smooth solutions. A truncation strategy for the coeffi-cient matrix obtained by using singularity preserving multi-scale Galerkin methods is proposed. The multilevel augmenta-tion method is developed for solving the discrete system with the truncated matrix. We prove that the methods preserve the singularities of the solutions and possess optimal order of convergence and linear computational complexity(up to a log-arithmic factor). Finally, numerical experiments are presented to confirm theoretical results and demonstrate the efficiency and accuracy of the methods.