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Fast multipole boundary element method for electrostatic field computations

Fast multipole boundary element method for electrostatic field computations Purpose – A wide range of micro‐electro‐mechanical‐systems are based on the electrostatic principle, and for their design the computation of the electric capacities is of great importance. The purpose of this paper is to efficiently compute the capacities as a function of all possible positions of the two electrode structures within the transducer by an enhanced boundary element method (BEM). Design/methodology/approach – A Galerkin BEM is developed and the arising algebraic system of equations is efficiently solved by a CG‐method with a multilevel preconditioner and an appropriate fast multipole algorithm for the matrix‐vector operations within the CG‐iterations. Findings – It can be demonstrated that the piecewise linear and discontinuous trial functions give an approximation, which is almost as good as the one of the piecewise constant trial functions on the refined mesh, at lower computational costs and at about the same memory requirements. Originality/value – The paper can proof mathematically and demonstrate in practice, that a higher order of convergence is achieved by using piecewise linear, globally discontinuous basis functions instead of piecewise constant basis functions. In addition, an appropriate preconditioner (artificial multilevel boundary element preconditioner, which is based on the Bramble Pasciak Xu like preconditioner) has been developed for the fast iterative solution of the algebraic system of equations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

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References (29)

Publisher
Emerald Publishing
Copyright
Copyright © 2009 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640910929236
Publisher site
See Article on Publisher Site

Abstract

Purpose – A wide range of micro‐electro‐mechanical‐systems are based on the electrostatic principle, and for their design the computation of the electric capacities is of great importance. The purpose of this paper is to efficiently compute the capacities as a function of all possible positions of the two electrode structures within the transducer by an enhanced boundary element method (BEM). Design/methodology/approach – A Galerkin BEM is developed and the arising algebraic system of equations is efficiently solved by a CG‐method with a multilevel preconditioner and an appropriate fast multipole algorithm for the matrix‐vector operations within the CG‐iterations. Findings – It can be demonstrated that the piecewise linear and discontinuous trial functions give an approximation, which is almost as good as the one of the piecewise constant trial functions on the refined mesh, at lower computational costs and at about the same memory requirements. Originality/value – The paper can proof mathematically and demonstrate in practice, that a higher order of convergence is achieved by using piecewise linear, globally discontinuous basis functions instead of piecewise constant basis functions. In addition, an appropriate preconditioner (artificial multilevel boundary element preconditioner, which is based on the Bramble Pasciak Xu like preconditioner) has been developed for the fast iterative solution of the algebraic system of equations.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Mar 6, 2009

Keywords: Electrostatics; Galerkin method; Mathematics; Transducers

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