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

Zhi Liang, Zydrunas Gimbutas, Leslie Greengard, Jingfang Huang, Shidong Jiang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)133-139
Number of pages7
JournalJournal of Computational Physics
Issue number1
StatePublished - 2013


  • Brownian dynamics
  • Fast multipole method
  • Hydrodynamic interaction
  • Krylov subspace approximation
  • Lanzcos iteration
  • Rotne-prager-yamakawa tensor
  • Square root matrix

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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