A parallel fast multipole accelerated integral equation scheme for 3D Stokes equations

• Published in: International journal for numerical methods in engineering Vol. 70; no. 7; pp. 812 - 839
• Main Authors: Wang, Haitao, Lei, Ting, Li, Jin, Huang, Jingfang, Yao, Zhenhan
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 14.05.2007; Wiley
• Subjects: Applied sciences; Computational techniques; Computer science; control theory; systems; Computer systems and distributed systems. User interface; diagonal translation; Exact sciences and technology; fast multipole method; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; integral equation method; Mathematical methods in physics; parallel computing; Physics; preconditioner; Software; Stokes equations; Stokes equation; Reynolds number; diagonal translation; fast multipole method; Parallel algorithms; Distributed computing; Stokes equations; Integral method; integral equation method; Multipole field; Integral equations; Diagonal matrix; Parallel computation; Modelling; preconditioner; Preconditioning; parallel computing; Stokes flow; Navier-Stokes equations
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1910

In this paper, we discuss a numerical scheme for the Stokes equations in three dimensions. It uses an integral equation formulation and is accelerated by the new version of fast multipole method first introduced by Greengard and Rokhlin in 1997 (Acta Numerica 1997; 6:229–269). The code is parallelized to solve problems of extremely large size. The resulting numerical solver can be applied to Stokes flows in complex geometry and also serves as a building block for solving the Navier–Stokes equations of low to moderate Reynold's numbers. Copyright © 2006 John Wiley & Sons, Ltd.