Fast multipole boundary element method for electrostatic field computations

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.

Citation

Of, G., Kaltenbacher, M. and Steinbach, O. (2009), "Fast multipole boundary element method for electrostatic field computations", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 2, pp. 304-319. https://doi.org/10.1108/03321640910929236