A fast multipole method for Fredholm integral equations of the second kind with general kernel K(x, y)=K(x − y). (15th July 2022) - Liang, Jiangli; Xiang, Shuhuang
Abstract: This paper presents a fast multipole boundary element method (fast BEM) for solving the Fredholm integral equations of the second kind. The local expansion of the fast multipole method is based on polynomial approximation of the kernel, which is well defined and analytic in the far cells even for | x − y | α or log ⁡ | x − y | . The proposed algorithm has in efficiently extended the fast BEM to the integral equations with the more general kernels K ( x − y ) . The computational costs can be reduced significantly compared to the direct method in particular for the large-scale in the case that high accuracy is required. For the computation time, the proposed method always has a slight advantage in comparison with the analytic fast BEM.