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

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 t...

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Bibliographic Details
Main Authors: Selmi, Hassib, Hamda, Hatem, El Asmi, Lassaad
Format: Conference Proceeding
Language:English
Subjects:
ASYMPTOTIC SOLUTIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
ERRORS
FINITE DIFFERENCE METHOD
HARMONICS
MULTIPOLES
SPHERICAL CONFIGURATION
TRANSFER FUNCTIONS
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Summary: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.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.2790189