The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets

Meurig Thomas Gallagher; David Smith

doi:10.1098/rsos.210108

The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets

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Abstract

The method of regularized stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly varying regularized stokeslet kernel. Here, we show how Richardson extrapolation with coarse values of the regularization parameter is ideally suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.

Original language	English
Article number	210108
Journal	Royal Society Open Science
Volume	8
Issue number	5
DOIs	https://doi.org/10.1098/rsos.210108
Publication status	Published - 26 May 2021

Bibliographical note

Funding Information:
Data accessibility. Data and relevant code for this research work are stored in GitLab: https://gitlab.com/ meuriggallagher/the-art-of-coarse-stokes (MATLAB code for Nyström and Richardson extrapolation) and https:// gitlab.com/meuriggallagher/NEAREST (MATLAB code for NEAREST and other dependencies); and have been archived within the Zenodo repository: https://doi.org/10.5281/zenodo.4632956. Competing interests. We declare we have no competing interests. Funding. This work was supported by Engineering and Physical Sciences Research Council (EPSRC) award no. EP/N021096/1. M.T.G. acknowledges support from EPSRC Centre grant no. EP/N014391/2. Acknowledgements. We thank Eamonn Gaffney and Kenta Ishimoto for valuable discussion.

Publisher Copyright:
© 2021 The Authors.

Keywords

regularized stokeslets
richardson extrapolation
Stokes flow

ASJC Scopus subject areas

Applied Mathematics
Modelling and Simulation

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10.1098/rsos.210108Licence: Creative Commons: Attribution (CC BY)

GallagherMT2021artFinal published version, 843 KBLicence: Creative Commons: Attribution (CC BY)

Passively parallel regularized stokeslets
Gallagher, M. T. & Smith, D., 4 Sept 2020, In: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 378, 2179, 18 p., 20190528.
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Regularized Stokeslet rings: an efficient method for axisymmetric Stokes flow with application to the growing pollen tube
Tyrrell, J., Smith, D. & Dyson, R., 6 Jun 2019, In: Physical Review Fluids. 4, 6, 39 p., 063102.
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Sharp quadrature error bounds for the nearest-neighbor discretization of the regularized stokeslet boundary integral equation
Gallagher, M. T., Choudhuri, D. & Smith, D., 19 Feb 2019, In: SIAM Journal on Scientific Computing. 41, 1, p. B139–B152 14 p.
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A nearest-neighbour discretisation of the regularized stokeslet boundary integral equation
Smith, D., 1 Apr 2018, In: Journal of Computational Physics. 358, p. 88-102 15 p.
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Meshfree and efficient modelling of swimming cells
Gallagher, M. T. & Smith, D., 31 May 2018, In: Physical Review Fluids. 3, 5, 27 p., 053101.
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EPSRC Centre for Predictive Modelling in Healthcare
Terry, J. (Principal Investigator)
Engineering & Physical Science Research Council
1/01/20 → 31/01/21
Project: Research Councils
Rapid sperm capture: integrating live imaging and machine learning to optimise fertility treatment
Kirkman-Brown, J. (Co-Investigator) & Smith, D. (Principal Investigator)
Engineering & Physical Science Research Council
1/07/16 → 30/06/22
Project: Research Councils

The art of coarse Stokes: Code for manuscript - Gallagher and Smith 2021, Roy. Soc. Open. Sci.
Gallagher, M. (Creator) & Smith, D. (Creator), The Royal Society, 26 May 2021
DOI: 10.5281/zenodo.4632956
Dataset

Cite this

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abstract = "The method of regularized stokeslets is widely used in microscale biological fluid dynamics due to its ease of implementation, natural treatment of complex moving geometries, and removal of singular functions to integrate. The standard implementation of the method is subject to high computational cost due to the coupling of the linear system size to the numerical resolution required to resolve the rapidly varying regularized stokeslet kernel. Here, we show how Richardson extrapolation with coarse values of the regularization parameter is ideally suited to reduce the quadrature error, hence dramatically reducing the storage and solution costs without loss of accuracy. Numerical experiments on the resistance and mobility problems in Stokes flow support the analysis, confirming several orders of magnitude improvement in accuracy and/or efficiency.",

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The art of coarse Stokes: Richardson extrapolation improves the accuracy and efficiency of the method of regularized stokeslets

Abstract

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Keywords

ASJC Scopus subject areas

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