Definition
The boundary element method is a numerical method for solving integral equations. These integral equations are the integral representations of the governing equations of the underlying physical problems, often formulated based on the fundamental solutions of the problems.
Overview
The boundary element method (BEM) has been established as a powerful numerical method for solving engineering problems. Applications include, but are not limited to, electromagnetics, elasticity, acoustics, potential, and viscous flow. In contrast to other numerical techniques, the governing equations are cast into a set of integral equations that are solved by collocation or Galerkin discretization. A detailed description of this method can be found in [1]. One major advantage of the BEM is that it reduces the dimensionality of the problem by one. Thus, for the majority of practical cases, the simple boundary discretization leads to a...
References
Banerjee PK (1994) The boundary element methods in engineering. McGraw-Hill, London
Greengard L, Rokhlin V (1997) A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numer 6:229–269
Phillips JR, White JA (1997) Precorrected-FFT method for electrostatic analysis of complicated 3D structures. IEEE Trans Comput Aided Des Integr Circ Syst 16(10):1059–1072
Ye W, Wang X, Hemmert W, Freeman D, White J (2003) Air damping in lateral oscillating micro resonators: a numerical and experimental study. J Microelectromech Syst 12(5):557–566
Cho YH, Pisano AP, Howe RT (1994) Viscous damping model for laterally oscillating microstructures. J Microelectromech Syst 3(2):81–87
Aluru NR, White J (1998) A fast integral equation technique for analysis of microflow sensors based on drag force calculations. In: Proceedings of the international conference on modeling and simulation of microsystems, semiconductors, sensors and actuators, Santa Clara, pp 283–286
Ye W, Wang X, White J (1999) A fast 3D solver for unsteady Stokes flow with applications to Micro-Electro-Mechanical Systems. In: Proceedings of the international conference on modeling and simulation of microsystems, semiconductors, sensors and actuators, Puerto Rico, pp 518–521
Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving symmetric linear systems, SIAM. J Sci Stat Comput 7:856–869
Partridge PW, Brebbia CA, Wrobel LC (1992) The dual reciprocity boundary element method. Elsevier, London
Ding J, Ye W (2006) A grid based integral approach for quasilinear problems. Comput Mech 38(2):114–118
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this entry
Cite this entry
Ye, W. (2014). Boundary Element Method and Its Applications to the Modeling of MEMS Devices. In: Li, D. (eds) Encyclopedia of Microfluidics and Nanofluidics. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27758-0_122-2
Download citation
DOI: https://doi.org/10.1007/978-3-642-27758-0_122-2
Received:
Accepted:
Published:
Publisher Name: Springer, Boston, MA
Online ISBN: 978-3-642-27758-0
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering