Explicit error bound of the fast multipole method for scattering problems in 2-D

• Main Author: Meng, Wenhui
• Format: Journal Article
• Language: English
• Published: 22-06-2018
• Subjects: Computer Science - Numerical Analysis; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.1806.08512

This paper is concerned with the error estimation of the fast multipole
method (FMM) for scattering problems in 2-D. The FMM error is caused by
truncating Graf's addition theorem in each step of the algorithm, including two
expansions and three translations. We first give a novel bound on the
truncation error of Graf's addition theorem by the limiting forms of Bessel and
Neumann functions, and then estimate the error of the FMM. Explicit error bound
and its convergence order are derived. The method proposed in this paper can
also be used to the FMM for other problems, such as potential problems,
elastostatic problems, Stokes flow problems and so on.