An accelerated surface discretization-based BEM approach for non-homogeneous linear problems in 3-D complex domains

International Journal for Numerical Methods in Engineering

Volumn 63, Issue 12, 2005, Pages 1775-1795

  Ding, Jian ^a   Ye, Wenjing ^a   Gray, L J ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

BEM; Fast algorithm; Poisson equation; Precorrected FFT technique; Volume integral

Indexed keywords

BOUNDARY ELEMENT METHOD; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; POISSON RATIO; PROBLEM SOLVING;

ANALYTICAL SOLUTIONS; UNIFORM GRIDS; VOLUME INTEGRALS;

SURFACE STRUCTURE;

MATHEMATICAL METHOD;

EID: 22444445617     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1346     Document Type: Article

References (30)

1. Greengard L. The Rapid Evaluation of Potential Fields in Particle Systems. MIT Press: Cambridge, MA, 1988.
2. Greengard L, Rokhlin V. New version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 1997; 229-269.
3. Phillips JR, White J. A precorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Transactions on Computer-Aided Design of Integrated Circuits and System 1997; 16 (10):1059-1072.
4. Bruno OP, Kunyansky LA. A fast, high-order algorithm for the solution of surface scattering problems: basic implementation, tests and applications. Journal of Computational Physics 2001; 169 (1):80-110.
5. Pierce AP, Napier JAL. A spectral multipole method for efficient solution of large-scale boundary element models in electrostatics. International Journal for Numerical Methods in Engineering 1995; 38:4009-4034.
6. Nabors K, White J. Fastcap: a multipole accelerated 3-D capacitance extraction program. IEEE Transactions on Computer-Aided Design of Integrated Circuits and System 1991; 10(11):1447-1459.
7. Aluru NR, White J. A fast integral equation technique for analysis of microflow sensors based on drag force calculation. International Conference on Modeling and Simulation of Microsystems 1998; 283-286. (Available at http://www.cr.org/publications/index.html).
8. Ye W, Kanapka J, Wang X, White J. Efficiency and accuracy improvements for faststokes, a precorrected-FFT accelerated 3-D Stokes solver. International Conference on Modeling and Simulation of Microsystems 1998; 502-505. (Available at http://www.cr.org/ publications/index.html).
9. Ye W, Wang X, White J. A fast 3D solver for unsteady flow with applications to micro-electro-mechanical systems. International Conference on Modeling and Simulation of Microsystems 1999; 518-521. (Available at http://www.cr.org/publications/index.html).
10. Ye W, Wang X, White J. Fast stokes solver for generalized flow problems. International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators 2000; 524-527.
11. Silveira LM, Elfadel IM, White JK, Chilukuri M, Kundert KS. Efficient frequency-domain modeling and circuit simulation of transmission lines. IEEE Transactions on Components, Hybrids, and Manufacturing Technology - Part B: Advanced Packaging, Special issue on Electrical Performance of Electrical Packaging 1994; 17(4):505-513.
12. Ye W, Wang X, Hemmert W, Freeman D, White J. Air damping in lateral oscillating micro resonators: a numerical and experimental study. Journal of Microelectromechanical Systems 2003; 12(5):1-10.
13. Nardini D, Brebbia CA. A new approach to free vibration analysis using boundary elements. Applied Mathematical Modelling 1983; 7 (3):157-162.
14. Ahmed S, Banerjee PK. Free vibration analysis of BEM using particular integrals. Journal of Engineering Mechanics 1986; 112: 682-695.
15. Ingber MS. An efficient boundary element method for a class of parabolic differential equations using discretization in time. Numerical Methods for Partial Differential Equations 1987; 3(3):187-197.
16. Herry D, Banerjee PK. A new boundary element formulation for two- and three-dimensional thermoelasticity using particular integrals. International Journal for Numerical Methods in Engineering 1988; 26:2061-2077.
17. Nowak AJ, Brebbia CA. The multiple-reciprocity method. A new approach for transforming BEM domain integrals to the boundary. Engineering Analysis with Boundary Elements 1989; 6(3):164-167.
18. Ingber MS, Phan-Thien N. A boundary element approach for parabolic differential equations using a class of particular solutions. Applied Mathematical Modelling 1992; 16(3):124-132.
19. Partridge PW, Brebbia CA, Wrobel LC. The Dual Reciprocity Boundary Element Method. Elsevier: London, 1992.
20. Ingber MS. A triple reciprocity boundary element method for transient heat conduction analysis. International Conference on Boundary Element Technology 1994; 41-49.
21. Zhang JJ, Afagh FF, Tan CL. Boundary integral transformation of body-force volume integral in BEM for 2D anisotropic elasticity. Mechanics Research Communications 1996; 23(2):227-232.
22. Goldberg MA, Chen CS, Bowman H, Power H. Some comments on the use of radial basis functions in the dual reciprocity method. Computational Mechanics 1998; 21(2):141-148.
23. Katsikadelis JT, Nerantzaki MS. The boundary element methods for nonlinear problems. Engineering Analysis with Boundary Elements 1999; 23:365-373.
24. Ingber MS, Mammoli A, Brown M. A comparison of domain integral evaluation techniques for boundary element methods. International Journal for Numerical Methods in Engineering 2001; 52 (4):417-432.
25. Gao XW. The radial integration methods for evaluation of domain integrals with boundary-only discretization. Engineering Analysis with Boundary Elements 2002; 26:905-916.
26. Mammoli AA. Solution of non-linear integral equations in complex geometries with auxiliary integral subtraction. International Journal for Numerical Methods in Engineering 2002; 55:1115-1128.
27. Gao XW. Boundary element analysis in thermoelasticity with and without internal cells. International Journal for Numerical Methods in Engineering 2003; 57(7):975-990.
28. Hsiao SC, Mammoli AA, Ingber MS. The evaluation of domain integrals in complex multiply-connected three-dimensional geometries for boundary element methods. Computational Mechanics 2003; 32:226-233.
29. Nagarajan A, Mukherjee S. Mapping method for numerical evaluation of two-dimensional integrals with 1/r singularity. Computational Mechanics 1993; 12:19-26.
30. Saad Y, Schultz M. GMRES: a generalized minimal residual algorithm for solving symmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1986; 7:856-869.