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Fast Ewald summation for Green's functions of Stokes flow in a half-space
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0003-2629-3668
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2018 (English)In: RESEARCH IN THE MATHEMATICAL SCIENCES, ISSN 2197-9847, Vol. 5, article id 35Article in journal (Refereed) Published
Abstract [en]

Recently, Gimbutas et al. (J Fluid Mech, 2015. https://doi.org/10.1017/jfm.2015.302) derived an elegant representation for the Green's functions of Stokes flow in a half-space. We present a fast summation method for sums involving these half-space Green's functions (stokeslets, stresslets and rotlets) that consolidates and builds on the work by Klinteberg et al. (Res Math Sci 4(1): 1, 2017. https://doi.org/10.1186/s40687-016-0092-7) for the corresponding free-space Green's functions. The fast method is based on two main ingredients: The Ewald decomposition and subsequent use of FFTs. The Ewald decomposition recasts the sum into a sum of two exponentially decaying series: one in real space (short-range interactions) and one in Fourier space (long-range interactions) with the convergence of each series controlled by a common parameter. The evaluation of short-range interactions is accelerated by restricting computations to neighbours within a specified distance, while the use of FFTs accelerates the computations in Fourier space thus accelerating the overall sum. We demonstrate that while the method incurs extra costs for the half-space in comparison with the free-space evaluation, greater computational savings is also achieved when compared to their respective direct sums.

Place, publisher, year, edition, pages
Springer, 2018. Vol. 5, article id 35
Keywords [en]
Ewald summation, Stokes flow, Green's function, Stokeslet, Rotlet, Stresslet, Half-space
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-234613DOI: 10.1007/s40687-018-0153-1ISI: 000442336600002Scopus ID: 2-s2.0-85080875939OAI: oai:DiVA.org:kth-234613DiVA, id: diva2:1248169
Note

QC 20180914

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2020-05-11Bibliographically approved

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Srinivasan, ShriramTornberg, Anna-Karin

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