A fast multipole method for the three-dimensional Stokes equations

Anna Karin Tornberg, Leslie Greengard

Research output: Contribution to journalArticle

Abstract

Many problems in Stokes flow (and linear elasticity) require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions. In the fluid mechanics setting, these are typically the Stokeslet (the kernel of the single layer potential) or the Stresslet (the kernel of the double layer potential). In this paper, we present a simple and efficient method for the rapid evaluation of such fields, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin [Y. Fu, G.J. Rodin, Fast solution methods for three-dimensional Stokesian many-particle problems, Commun. Numer. Meth. En. 16 (2000) 145-149]. While any fast summation algorithm for Coulombic interactions can be employed, we present numerical results from a scheme based on the most modern version of the fast multipole method [H. Cheng, L. Greengard, V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155 (1999) 468-498]. This approach should be of value in both the solution of boundary integral equations and multiparticle dynamics.

Original languageEnglish (US)
Pages (from-to)1613-1619
Number of pages7
JournalJournal of Computational Physics
Volume227
Issue number3
DOIs
StatePublished - Jan 10 2008

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Boundary integral equations
Fluid mechanics
Adaptive algorithms
multipoles
Elasticity
Decomposition
Stokes flow
many body problem
evaluation
fluid mechanics
integral equations
elastic properties
decomposition
interactions

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

A fast multipole method for the three-dimensional Stokes equations. / Tornberg, Anna Karin; Greengard, Leslie.

In: Journal of Computational Physics, Vol. 227, No. 3, 10.01.2008, p. 1613-1619.

Research output: Contribution to journalArticle

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