Analysis of the truncation errors in the fast multipole method for scattering problems

Discretisation of the integral equations of acoustic scattering yields large dense systems of linear equations. Using the fast multipole method, an approximate solution to these systems can be computed with a low operation count. When implementing the method, various infinite sums must be truncated. In this paper, sharp computable bounds on the errors of these truncations are derived, which could form the basis for an automatic selection of truncation length. This choice will guarantee a given solution accuracy whilst minimising the operation count of the fast multipole algorithm.