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On the numerical evaluation of electrostatic fields in composite materials

Published online by Cambridge University Press:  07 November 2008

Leslie Greengard  and
Monique Moura
Leslie Greengard
Affiliation:
Courant Institute of Mathematical SciencesNew York University, New York 10012, USA E-mail: [email protected]
Monique Moura
Affiliation:
Courant Institute of Mathematical SciencesNew York University, New York 10012, USA E-mail: [email protected]
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Abstract

A classical problem in electrostatics is the determination of the effective electrical conductivity in a composite material consisting of a collection of piecewise homogeneous inclusions embedded in a uniform background. We discuss recently developed fast algorithms for the evaluation of the potential and electrostatic fields induced in multiphase composites by an applied potential, from which the desired effective properties may be easily obtained. The schemes are based on combining a suitable boundary integral equation with the Fast Multipole Method and the GMRES iterative method; the CPU time required grows linearly with the number of points in the discretization of the interface between the inclusions and the background material.

A variety of other questions in electrostatics, magnetostatics and diffusion can be formulated in terms of interface problems. These include the evaluation of electrostatic fields in the presence of dielectric inclusions, the determination of magnetostatic fields in media with variable magnetic permeability, and the calculation of the effective thermal conductivity of a composite material. The methods presented here apply with minor modification to these other situations as well.

Type
Research Article
Information
Acta Numerica , Volume 3 , January 1994 , pp. 379 - 410
Copyright
Copyright © Cambridge University Press 1994

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