On the numerical evaluation of electrostatic fields in composite materials

Leslie Greengard, Monique Moura

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)379-410
Number of pages32
JournalActa Numerica
Volume3
Issue number9
DOIs
StatePublished - 1994

Fingerprint

Electrostatic Field
Composite Materials
Effective Conductivity
Magnetostatics
Inclusion
Electric fields
Electrostatics
Composite materials
Evaluation
GMRES Method
Fast multipole Method
Magnetic permeability
Interface Problems
Effective Properties
Boundary integral equations
Potential Field
Electrical Conductivity
Boundary Integral Equations
CPU Time
Thermal Conductivity

ASJC Scopus subject areas

  • Mathematics(all)
  • Numerical Analysis

Cite this

On the numerical evaluation of electrostatic fields in composite materials. / Greengard, Leslie; Moura, Monique.

In: Acta Numerica, Vol. 3, No. 9, 1994, p. 379-410.

Research output: Contribution to journalArticle

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