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Abstract and Applied Analysis
Volume 2014, Article ID 563603, 12 pages
Research Article

The FMM-BEM Method for the 3D Particulate Stokes Flow

1Technical and Vocational Training Corporation, Riyadh 11523, Saudi Arabia
2Laboratory of Engineering Mathematics, Polytechnic School of Tunisia, 2078 La Marsa, Tunisia
3Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia

Received 8 April 2014; Accepted 13 May 2014; Published 3 June 2014

Academic Editor: Hassan Eltayeb

Copyright © 2014 Hassib Selmi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work introduces new functions based on the spherical harmonics and the solid harmonics which have been used to construct a multipole development for the 3D Stokes problem in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serve to calculate the multipole moments and the transfer functions that are necessary for the schemes of order . Moreover, new translation formulas are introduced to obtain an scheme. The error truncation of the resulting scheme is discussed. In comparison to the BEM that attains a limit storage at , we present here a method based on FMM-BEM that attains a storage at a limit of . The implementation of the method achieves a high accuracy level at a reasonable cost.