Justification of the fast multipole method for the stokes system. Part II. Exterior domain problems

Abstract

This is the second part of the paper, which justifies the solution of the two-dimensional Stokes equations using the fast multipole method (FMM) of Greengard and Rokhlin. In addition to the interior Dirichlet problem, which was considered in the previous part, we are concerned with exterior domain problems of Dirichlet and Neumann kinds. For the solution of the boundary value problems, we choose a potential ansatz and show that for the reduction of the computational costs, FMM can be used. Therefor, we find a complex representation of the solution and provide the statements about the corresponding multipole and Taylor expansions, as well as the appropriate translation, rotation and conversion operators. Numerical experiments illustrate the performance of FMM for the proposed cases.