A fast multipole method for the Rotne–Prager–Yamakawa tensor and its applications

Abstract

We present a fast multipole method (FMM) for computing sums involving the Rotne–Prager–Yamakawa tensor. The method, similar to the approach in Tornberg and Greengard (2008) [26] for the Stokeslet, decomposes the tensor vector product into a sum of harmonic potentials and fields induced by four different charge and dipole distributions. Unlike the approach based on the kernel independent fast multipole method (Ying et al., 2004) [31], which requires nine scalar FMM calls, the method presented here requires only four. We discuss its applications to Brownian dynamics simulation with hydrodynamic interactions, and present some timing results.