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Wavelet BEM for large‐scale Stokes flows based on the direct integral formulation
Author(s) -
Xiao Jinyou,
Ye Wenjing
Publication year - 2011
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3198
Subject(s) - discretization , wavelet , galerkin method , matrix (chemical analysis) , stokes flow , boundary element method , integral equation , mathematics , cantilever , compressed sensing , compression (physics) , mathematical analysis , computer science , finite element method , flow (mathematics) , algorithm , physics , geometry , materials science , engineering , structural engineering , artificial intelligence , composite material , thermodynamics
This paper describes a new wavelet boundary element method (WBEM) for large‐scale simulations of three‐dimensional Stokes problems. It is based on a Galerkin formulation and uses only one set of wavelet basis. A method for the efficient discretization and compression of the double‐layer integral operator of Stokes equation is proposed. In addition, a compression strategy for further reducing the setting‐up time for the sparse system matrix is also developed. With these new developments, the method has demonstrated a high matrix compression rate for problems with complicated geometries. Applications of the method are illustrated through several examples concerning the modeling of damping forces acting on MEMS resonators including a cantilever resonator oscillating in an unbounded air and a perforated plate resonator oscillating next to a fixed substrate. The numerical results clearly illustrate the efficiency and accuracy of the developed WBEM in these large‐scale Stokes flow simulations. Copyright © 2011 John Wiley & Sons, Ltd.