A new fast multipole boundary element method for solving 2-D Stokes flow problems based on a dual BIE formulation

Engineering Analysis with Boundary Elements

Volumn 32, Issue 2, 2008, Pages 139-151

  Liu, Y J ^a  

^a University of Cincinnati   (United States)

Author keywords

2 D Stokes flows; Boundary element method; Fast multipole method

Indexed keywords

BOUNDARY INTEGRAL EQUATIONS; LINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING;

2-D STOKES FLOWS; FAST MULTIPOLE METHOD; MULTIPOLE BOUNDARY ELEMENT METHOD;

BOUNDARY ELEMENT METHOD;

EID: 36749053415     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2007.07.005     Document Type: Article

References (44)

1. Pozrikidis C. Boundary integral and singularity methods for linearized viscous flow (1992), Cambridge University Press, New York
2. Power H., and Wrobel L.C. Boundary integral methods in fluid mechanics (1995), Computational Mechanics Publications, Southampton
3. Rokhlin V. Rapid solution of integral equations of classical potential theory. J Comp Phys 60 (1985) 187-207
4. Greengard L.F., and Rokhlin V. A fast algorithm for particle simulations. J Comput Phys 73 2 (1987) 325-348
5. Greengard L.F. The rapid evaluation of potential fields in particle systems (1988), The MIT Press, Cambridge
6. Peirce A.P., and Napier J.A.L. A spectral multipole method for efficient solution of large-scale boundary element models in elastostatics. Int J Numer Methods Eng 38 (1995) 4009-4034
7. Greengard L.F., Kropinski M.C., and Mayo A. Integral equation methods for Stokes flow and isotropic elasticity in the plane. J Comput Phys 125 (1996) 403-414
8. Greengard L.F., and Helsing J. On the numerical evaluation of elastostatic fields in locally isotropic two-dimensional composites. J Mech Phys Solids 46 8 (1998) 1441-1462
9. Fu Y., Klimkowski K.J., Rodin G.J., Berger E., Browne J.C., Singer J.K., et al. A fast solution method for three-dimensional many-particle problems of linear elasticity. Int J Numer Methods Eng 42 (1998) 1215-1229
10. Yoshida K., Nishimura N., and Kobayashi S. Application of fast multipole Galerkin boundary integral equation method to crack problems in 3D. Int J Numer Methods Eng 50 (2001) 525-547
11. Yoshida K., Nishimura N., and Kobayashi S. Application of new fast multipole boundary integral equation method to elastostatic crack problems in three dimensions. J Struct Eng 47A March (2001) 169-179
12. Richardson J.D., Gray L.J., Kaplan T., and Napier J.A. Regularized spectral multipole BEM for plane elasticity. Eng Anal Bound Elem 25 (2001) 297-311
13. Popov V., and Power H. An O(N) Taylor series multipole boundary element method for three-dimensional elasticity problems. Eng Anal Boundary Elem 25 1 (2001) 7-18
14. Popov V., Power H., and Walker S.P. Numerical comparison between two possible multipole alternatives for the BEM solution of 3D elasticity problems based upon Taylor series expansions. Eng Anal Boundary Elem 27 5 (2003) 521-531
15. Lai Y.-S., and Rodin G.J. Fast boundary element method for three-dimensional solids containing many cracks. Eng Anal Boundary Elem 27 8 (2003) 845-852
16. Masters N., and Ye W. Fast BEM solution for coupled 3D electrostatic and linear elastic problems. Eng Anal Boundary Elem 28 9 (2004) 1175-1186
17. Yao Z., Kong F., Wang H., and Wang P. 2D simulation of composite materials using BEM. Eng Anal Boundary Elem 28 8 (2004) 927-935
18. Liu Y.J. A new fast multipole boundary element method for solving large-scale two-dimensional elastostatic problems. Int J Numer Methods Eng 65 6 (2005) 863-881
19. Nishimura N. Fast multipole accelerated boundary integral equation methods. Appl Mech Rev 55 4 (July) (2002) 299-324
20. Liu Y.J., and Nishimura N. The fast multipole boundary element method for potential problems: a tutorial. Eng Anal Boundary Elem 30 5 (2006) 371-381
21. Gomez J.E., and Power H. A multipole direct and indirect BEM for 2D cavity flow at low Reynolds number. Eng Anal Boundary Elem 19 (1997) 17-31
22. Mammoli A.A., and Ingber M.S. Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods. Int J Numer Methods Eng 44 (1999) 897-917
23. Ding J., and Ye W. A fast integral approach for drag force calculation due to oscillatory slip stokes flows. Int J Numer Methods Eng 60 9 (2004) 1535-1567
24. Frangi A. A fast multipole implementation of the qualocation mixed-velocity-traction approach for exterior Stokes flows. Eng Anal Boundary Elem 29 11 (2005) 1039-1046
25. Frangi A., and Gioia A.d. Multipole BEM for the evaluation of damping forces on MEMS. Comput Mech 37 1 (2005) 24-31
26. Frangi A., and Tausch J. A qualocation enhanced approach for Stokes flow problems with rigid-body boundary conditions. Eng Anal Boundary Elem 29 9 (2005) 886
27. Frangi A., Spinola G., and Vigna B. On the evaluation of damping in MEMS in the slip-flow regime. Int J Numer Methods Eng 68 (2006) 1031-1051
28. Krishnasamy G., Rizzo F.J., and Rudolphi T.J. Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation. In: Banerjee P.K., et al. (Ed). Developments in boundary element methods (1991), Elsevier Applied Science Publishers, London [Chapter 7]
29. Mukherjee S. CPV and HFP integrals and their applications in the boundary element method. Int J Solids Struct 37 45 (2000) 6623-6634
30. Mukherjee S. Finite parts of singular and hypersingular integrals with irregular boundary source points. Eng Anal Boundary Elem 24 (2000) 767-776
31. Liu Y.J., and Rudolphi T.J. Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations. Eng Anal Boundary Elem 8 6 (1991) 301-311
32. Frangi A., and Novati G. Symmetric BE method in two-dimensional elasticity: evaluation of double integrals for curved elements. Comput Mech 19 (1996) 58-68
33. Perez-Gavilan J.J., and Aliabadi M.H. Symmetric Galerkin BEM for multi-connected bodies. Commun Numer Methods Eng 17 (2001) 761-770
34. Liu Y.J. Dual BIE approaches for modeling electrostatic MEMS problems with thin beams and accelerated by the fast multipole method. Eng Anal Boundary Elem 30 11 (2006) 940-948
35. Liu Y.J., and Shen L. A dual BIE approach for large-scale modeling of 3-D electrostatic problems with the fast multipole boundary element method. Int J Numer Methods Eng 71 (2007) 837-855
36. Liu Y.J., and Rizzo F.J. A weakly-singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems. Comput Methods Appl Mech Eng 96 (1992) 271-287
37. Liu Y.J., and Rizzo F.J. Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions. Comput Methods Appl Mech Eng 107 (1993) 131-144
38. Liu Y.J., and Rizzo F.J. Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation. J Acoust Soc Am 102 2 (Part 1, August) (1997) 926-932
39. Shen L., and Liu Y.J. An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation. Comput Mech 40 3 (2007) 461-472
40. Pozrikidis C. Fluid dynamics-theory, computation and numerical simulation (2001), Kluwer Academic Publishers, Boston
41. Gomez J.E., and Power H. A parallel multipolar indirect boundary element method for the Neumann interior Stokes flow problem. Int J Numer Methods Eng 48 4 (2000) 523-543
42. Mukherjee S., Telukunta S., and Mukherjee Y.X. BEM modeling of damping forces on MEMS with thin plates. Eng Anal Boundary Elem 29 (2005) 1000-1007
43. Power H. The interaction of a deformable bubble with a rigid wall at small Reynolds number: a general approach via integral equations. Eng Anal Boundary Elem 19 4 (1997) 291
44. Zhu G., Mammoli A.A., and Power H. A 3-D indirect boundary element method for bounded creeping flow of drops. Eng Anal Boundary Elem 30 10 (2006) 856