A method of images for the evaluation of electrostatic fields in systems of closely spaced conducting cylinders

Hongwei Cheng, Leslie Greengard

Research output: Contribution to journalArticle

Abstract

A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composites with densely packed inclusions whose material properties differ markedly from that of the background. While powerful tools exist for dilute suspensions, accurate calculations in the close-to-touching case have been carried out largely by asymptotic methods and only for simple geometries such as regular arrays of cylinders or spheres. In this paper, we develop a hybrid numerical method for the evaluation of electrostatic fields in composites consisting of arbitrary dispersions of cylinders. Our approach is based on an integral equation formulation of the governing interface problem combined with a new method of images. High accuracy is achieved using only a small number of degrees of freedom for each inclusion.

Original languageEnglish (US)
Pages (from-to)122-141
Number of pages20
JournalSIAM Journal on Applied Mathematics
Volume58
Issue number1
StatePublished - Feb 1998

Fingerprint

Electrostatic Field
Method of Images
Inclusion
Composite
Electric fields
Interface Problems
Materials Science
Composite materials
Evaluation
Asymptotic Methods
Materials science
Hybrid Method
Dispersions
Electrostatics
Material Properties
Integral equations
Numerical methods
Materials properties
Integral Equations
High Accuracy

Keywords

  • Composite materials
  • Electrostatics
  • Method of images

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A method of images for the evaluation of electrostatic fields in systems of closely spaced conducting cylinders. / Cheng, Hongwei; Greengard, Leslie.

In: SIAM Journal on Applied Mathematics, Vol. 58, No. 1, 02.1998, p. 122-141.

Research output: Contribution to journalArticle

@article{a87a6848832b41b9ad871a2bb10b6b96,
title = "A method of images for the evaluation of electrostatic fields in systems of closely spaced conducting cylinders",
abstract = "A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composites with densely packed inclusions whose material properties differ markedly from that of the background. While powerful tools exist for dilute suspensions, accurate calculations in the close-to-touching case have been carried out largely by asymptotic methods and only for simple geometries such as regular arrays of cylinders or spheres. In this paper, we develop a hybrid numerical method for the evaluation of electrostatic fields in composites consisting of arbitrary dispersions of cylinders. Our approach is based on an integral equation formulation of the governing interface problem combined with a new method of images. High accuracy is achieved using only a small number of degrees of freedom for each inclusion.",
keywords = "Composite materials, Electrostatics, Method of images",
author = "Hongwei Cheng and Leslie Greengard",
year = "1998",
month = "2",
language = "English (US)",
volume = "58",
pages = "122--141",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - A method of images for the evaluation of electrostatic fields in systems of closely spaced conducting cylinders

AU - Cheng, Hongwei

AU - Greengard, Leslie

PY - 1998/2

Y1 - 1998/2

N2 - A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composites with densely packed inclusions whose material properties differ markedly from that of the background. While powerful tools exist for dilute suspensions, accurate calculations in the close-to-touching case have been carried out largely by asymptotic methods and only for simple geometries such as regular arrays of cylinders or spheres. In this paper, we develop a hybrid numerical method for the evaluation of electrostatic fields in composites consisting of arbitrary dispersions of cylinders. Our approach is based on an integral equation formulation of the governing interface problem combined with a new method of images. High accuracy is achieved using only a small number of degrees of freedom for each inclusion.

AB - A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composites with densely packed inclusions whose material properties differ markedly from that of the background. While powerful tools exist for dilute suspensions, accurate calculations in the close-to-touching case have been carried out largely by asymptotic methods and only for simple geometries such as regular arrays of cylinders or spheres. In this paper, we develop a hybrid numerical method for the evaluation of electrostatic fields in composites consisting of arbitrary dispersions of cylinders. Our approach is based on an integral equation formulation of the governing interface problem combined with a new method of images. High accuracy is achieved using only a small number of degrees of freedom for each inclusion.

KW - Composite materials

KW - Electrostatics

KW - Method of images

UR - http://www.scopus.com/inward/record.url?scp=0032002322&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032002322&partnerID=8YFLogxK

M3 - Article

VL - 58

SP - 122

EP - 141

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 1

ER -