A dual BIE approach for large-scale modelling of 3-D electrostatic problems with the fast multipole boundary element method

International Journal for Numerical Methods in Engineering

Volumn 71, Issue 7, 2007, Pages 837-855

  Liu, Yi Jun ^a   Shen, L ^a  

^a University of Cincinnati   (United States)

Author keywords

3 D electrostatic problems; Boundary element method; Fast multipole method

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTER SIMULATION; CRACKS; ELASTICITY; INTEGRAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS);

FAST MULTIPOLE METHOD; FINITE DOMAIN PROBLEMS; LARGE-SCALE MODELLING;

ELECTROSTATICS;

BOUNDARY ELEMENT METHOD; COMPUTER SIMULATION; CRACKS; ELASTICITY; ELECTROSTATICS; INTEGRAL EQUATIONS; PLATES (STRUCTURAL COMPONENTS);

EID: 34547922006     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2000     Document Type: Article

References (48)

1. Mukherjee S. Boundary Element Methods in Creep and Fracture. Applied Science Publishers: New York, 1982.
2. Cruse TA. Boundary Element Analysis in Computational Fracture Mechanics. Kluwer Academic Publishers: Dordrecht, The Netherlands, 1988.
3. Brebbia CA, Dominguez J. Boundary Elements - An Introductory Course. McGraw-Hill: New York, 1989.
4. Banerjee PK. The Boundary Element Methods in Engineering (2nd edn). McGraw-Hill: New York, 1994.
5. Kane JH. Boundary Element Analysis in Engineering Continuum Mechanics. Prentice-Hall: Englewood Cliffs, NJ, 1994.
6. Shi F, Ramesh P, Mukherjee S. Simulation methods for micro-electro-mecbanical structures (MEMS) with application to a microtweezer. Computers and Structures 1995; 56:769-783.
7. Ye W, Mukherjee S. Optimal shape design of three-dimensional MEMS with applications to electrostatic comb drives. International Journal for Numerical Methods in Engineering 1999; 45:175-194.
8. Ye W, Mukherjee S. Design and fabrication of an electrostatic variable gap comb drive in micro-electro-mechanical systems. Computer Modeling in Engineering and Sciences 2000; 1:111-120.
9. Bao Z, Mukherjee S. Electrostatic BEM for MEMS with thin conducting plates and shells. Engineering Analysis with Boundary Elements 2004; 28:1427-1435.
10. Bao Z, Mukherjee S. Electrostatic BEM for MEMS with thin beams. Communications in Numerical Methods in Engineering 2005; 21:297-312.
11. De SK, Aluru NR. Full-Lagrangian schemes for dynamic analysis of electrostatic MEMS. Journal of Microelectromechanical Systems 2004; 13:737.
12. Chyuan S-W, Liao Y-S, Chen J-T. Computational study of the effect of finger width and aspect ratios for the electrostatic levitating force of MEMS combdrive. Journal of Microelectromechanical Systems 2005; 14:305-312.
13. Liu YJ. Dual BIE approaches for modeling electrostatic MEMS problems with thin beams and accelerated by the fast multipole method. Engineering Analysis with Boundary Elements 2006; 30:940-948.
14. Frangi A. A fast multipole implementation of the qualocation mixed-velocity-traction approach for exterior Stokes flows. Engineering Analysis with Boundary Elements 2005; 29:1039-1046.
15. Frangi A, Tausch J. A qualocation enhanced approach for Stokes flow problems with rigid-body boundary conditions. Engineering Analysis with Boundary Elements 2005; 29:886.
16. Mukherjee S, Telukunta S, Mukherjee YX. BEM modeling of damping forces on MEMS with thin plates. Engineering Analysis with Boundary Elements 2005; 29:1000-1007.
17. Rokhlin V. Rapid solution of integral equations of classical potential theory. Journal of Computational Physics 1985; 60:187-207.
18. Greengard LF, Rokhlin V. A fast algorithm for particle simulations. Journal of Computational Physics 1987; 73:325-348.
19. Greengard LF. The Rapid Evaluation of Potential Fields in Particle Systems. The MIT Press: Cambridge, 1988.
20. Nishimura N. Fast multipole accelerated boundary integral equation methods. Applied Mechanics Reviews 2002; 55:299-324.
21. Liu YJ, Nishimura N. The fast multipole boundary element method for potential problems: a tutorial. Engineering Analysis with Boundary Elements 2006; 30:371-381.
22. Nabors K, White J. FastCap: a multipole accelerated 3-D capacitance extraction program. IEEE Transactions on Computer-Aided Design 1991; 10: 1447-1459.
23. Ljung P, Bachtold M, Spasojevic M. Analysis of realistic large MEMS devices. Computer Modeling in Engineering and Sciences 2000; 1:21-30.
24. Frangi A, Gioia Ad. Multipole BEM for the evaluation of damping forces on MEMS. Computational Mechanics 2005; 37:24-31.
25. Urago M, Koyama T, Takahashi K, Saito S, Mochimaru Y. Fast multipole boundary element method using the binary tree structure with tight bounds: application to a calculation of an electrostatic force for the manipulation of a metal micro particle. Engineering Analysis with Boundary Elements 2003; 27:835-844.
26. Masters N, Ye W. Fast BEM solution for coupled 3D electrostatic and linear elastic problems. Engineering Analysis with Boundary Elements 2004; 28:1175-1186.
27. Ding J, Ye W. A fast integral approach for drag force calculation due to oscillatory slip Stokes flows. International Journal for Numerical Methods in Engineering 2004; 60:1535-1567.
28. Krishnasamy G, Rizzo FJ, Liu YJ. Boundary integral equations for thin bodies. International Journal for Numerical Methods in Engineering 1994; 37:107-121.
29. Liu YJ, Rizzo FJ. Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation. Journal of the Acoustical Society of America 1997; 102(2):926-932.
30. Shen L, Liu YJ. An adaptive fast multipole boundary element method for three-dimensional potential problems. Computational Mechanics, in press (Published online 15 March 2006).
31. Krishnasamy G, Rizzo FJ, Rudolphi TJ. Hypersingular boundary integral equations: their occurrence, interpretation, regularization and computation. In Developments in Boundary Element Methods (Chapter 7), Banerjee PK et al. (eds). Elsevier Applied Science Publishers: London, 1991.
32. Sladek V, Sladek J (eds). In Singular Integrals in Boundary Element Methods, Advances in Boundary Element Series, Brebbia CA, Aliabadi MH (eds). Computational Mechanics Publications: Boston, 1998.
33. Mukherjee S. CPV and HFP integrals and their applications in the boundary element method. International Journal of Solids and Structures 2000; 37:6623-6634.
34. Liu YJ, Rudolphi TJ. Some identities for fundamental solutions and their applications to weakly-singular boundary element formulations. Engineering Analysis with Boundary Elements 1991; 8:301-311.
35. Perez-Gavilan JJ, Aliabadi MH. A symmetric Galerkin BEM for multi-connected bodies: a new approach. Engineering Analysis with Boundary Elements 2001; 25:633-638.
36. Perez-Gavilan A Aliabadi MH. Symmetric Galerkin BEM for multi-connected bodies. Communications in Numerical Methods in Engineering 2001; 17:761-770.
37. Frangi A, Novati G. Symmetric BE method in two-dimensional elasticity: evaluation of double integrals for curved elements. Computational Mechanics 1996; 19:58-68.
38. Liu YJ. Analysis of shell-like structures by the boundary element method based on 3-D elasticity: formulation and verification. International Journal for Numerical Methods in Engineering 1998; 41:541-558.
39. Mukherjee S. On boundary integral equations for cracked and for thin bodies. Mathematics and Mechanics of Solids 2001; 6:47-64.
40. Burton AJ, Miller GF. The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proceedings of the Royal Society of London, Series A 1971; 323:201-210.
41. Liu YJ, Rizzo FJ. A weakly-singular form of the hypersingular boundary integral equation applied to 3-D acoustic wave problems. Computer Methods in Applied Mechanics and Engineering 1992; 96:271-287.
42. Yoshida K. Applications of fast multipole method to boundary integral equation method. Ph.D. Dissertation, Department of Global Environment Engineering, Kyoto University, 2001.
43. Yoshida K, Nishimura N, Kobayashi S. Application of new fast multipole boundary integral equation method to crack problems in 3D. Engineering Analysis with Boundary Elements 2001; 25:239-247.
44. Fukui T. Research on the boundary element method-development and applications of fast and accurate computations. Ph.D. Dissertation, Department of Global Environment Engineering, Kyoto University, 1998 (in Japanese).
45. Mukherjee S. Finite parts of singular and hypersingular integrals with irregular boundary source points. Engineering Analysis with Boundary Elements 2000; 24:767-776.
46. Hayt WH, Buck JA. Engineering Electromagnetics. McGraw-Hill: London, 2001.
47. Liu YJ, Nishimura N, Otani Y, Takahashi T, Chen XL, Munakata H. A fast boundary element method for the analysis of fiber-reinforced composites based on a rigid-inclusion model. Journal of Applied Mechanics 2005; 72:115-128.
48. Liu YJ, Nishimura N, Otani Y. Large-scale modeling of carbon-nanotube composites by the boundary element method based on a rigid-inclusion model. Computational Materials Science 2005; 34:173-187.