Fast Multipole Method for the 3D Stokes Flow: Truncation Error Analysis and Asymptotic Complexity

Journal Article · Thu Sep 06 00:00:00 EDT 2007 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.2790189· OSTI ID:21035862

Selmi, Hassib; Hamda, Hatem; El Asmi, Lassaad ^[1]

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1. Laboratory of Engineering Mathematics, Polytechnic School of Tunisia, BP 743, La Marsa 2078 (Tunisia)

This work introduces new functions based on the spherical harmonic and the solid harmonic which be 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 serves to calculate the multipole moments and the transfer functions that are necessar for the schemes of order O(NlogN). Moreover, new translations formulas were introduced to obtain O(N) scheme. The error truncation of the resulting scheme is discussed.

• OSTI ID: 21035862
• Journal Information: AIP Conference Proceedings, Vol. 936, Issue 1; Conference: International conference on numerical analysis and applied mathematics, Corfu (Greece), 16-20 Sep 2007; Other Information: DOI: 10.1063/1.2790189; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
ERRORS
FINITE DIFFERENCE METHOD
HARMONICS
MULTIPOLES
SPHERICAL CONFIGURATION
TRANSFER FUNCTIONS