Spectrally accurate fast summation for periodic Stokes potentials
2010 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, no 23, 8994-9010 p.Article in journal (Refereed) Published
A spectrally accurate method for the fast evaluation of N-particle sums of the periodic Stokeslet is presented. Two different decomposition methods, leading to one sum in real space and one in reciprocal space, are considered. An FFT based method is applied to the reciprocal part of the sum, invoking the equivalence of multiplications in reciprocal space to convolutions in real space, thus using convolutions with a Gaussian function to place the point sources on a grid. Due to the spectral accuracy of the method, the grid size needed is low and also in practice, for a fixed domain size, independent of N. The leading cost, which is linear in N, arises from the to-grid and from-grid operations. Combining this FFT based method for the reciprocal sum with the direct evaluation of the real space sum, a spectrally accurate algorithm with a total complexity of 0(N log N) is obtained. This has been shown numerically as the system is scaled up at constant density. (C) 2010 Elsevier Inc. All rights reserved.
Place, publisher, year, edition, pages
2010. Vol. 229, no 23, 8994-9010 p.
Viscous flow, Stokes equations, Potential theory, Ewald summation, FFT, Spectral accuracy
IdentifiersURN: urn:nbn:se:kth:diva-26264DOI: 10.1016/j.jcp.2010.08.026ISI: 000283405700019ScopusID: 2-s2.0-77956947285OAI: oai:DiVA.org:kth-26264DiVA: diva2:387717
QC 201101142011-01-142010-11-212011-11-25Bibliographically approved