Wavelet BEM for large-scale Stokes flows based on the direct integral formulation

摘要

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.