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

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

doi:10.1016/j.jcp.2012.09.021

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

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

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

34 Scopus citations

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.

Original language	English (US)
Pages (from-to)	133-139
Number of pages	7
Journal	Journal of Computational Physics
Volume	234
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2012.09.021
State	Published - 2013

All Science Journal Classification (ASJC) codes

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

Keywords

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

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10.1016/j.jcp.2012.09.021

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title = "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.",

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

author = "Zhi Liang and Zydrunas Gimbutas and Leslie Greengard and Jingfang Huang and Shidong Jiang",

note = "Funding Information: S.J. was supported in part by NSF under grant CCF-0905395 , J.H. was supported by NSF under grant CCF-0905473 . L.G. and Z.G. were supported in part by the Department of Energy under contract DEFG0288-ER-25053 and in part by the National Science Foundation under grant DMS-0934733 . Their support was thankfully acknowledged.",

year = "2013",

doi = "10.1016/j.jcp.2012.09.021",

language = "English (US)",

volume = "234",

pages = "133--139",

journal = "Journal of Computational Physics",

issn = "0021-9991",

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T1 - A fast multipole method for the Rotne-Prager-Yamakawa tensor and its applications

AU - Liang, Zhi

AU - Gimbutas, Zydrunas

AU - Greengard, Leslie

AU - Huang, Jingfang

AU - Jiang, Shidong

N1 - Funding Information: S.J. was supported in part by NSF under grant CCF-0905395 , J.H. was supported by NSF under grant CCF-0905473 . L.G. and Z.G. were supported in part by the Department of Energy under contract DEFG0288-ER-25053 and in part by the National Science Foundation under grant DMS-0934733 . Their support was thankfully acknowledged.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Brownian dynamics

KW - Fast multipole method

KW - Hydrodynamic interaction

KW - Krylov subspace approximation

KW - Lanzcos iteration

KW - Rotne-prager-yamakawa tensor

KW - Square root matrix

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DO - 10.1016/j.jcp.2012.09.021

M3 - Article

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SN - 0021-9991

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SP - 133

EP - 139

JO - Journal of Computational Physics

JF - Journal of Computational Physics

IS - 1

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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