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

  • Authors:

  • Zhi Liang;Zydrunas Gimbutas;Leslie Greengard;Jingfang Huang;Shidong Jiang

  • Affiliations:

  • Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, United States;Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States;Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, United States;Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States;Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, United States

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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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.