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Srinivasan, S. & Tornberg, A.-K. (2018). Fast Ewald summation for Green's functions of Stokes flow in a half-space. RESEARCH IN THE MATHEMATICAL SCIENCES, 5, Article ID 35.
Open this publication in new window or tab >>Fast Ewald summation for Green's functions of Stokes flow in a half-space
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
Keywords
Ewald summation, Stokes flow, Green's function, Stokeslet, Rotlet, Stresslet, Half-space
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-234613 (URN)10.1007/s40687-018-0153-1 (DOI)000442336600002 ()
Note

QC 20180914

Available from: 2018-09-14 Created: 2018-09-14 Last updated: 2018-09-14Bibliographically approved
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-2629-3668

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