Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

The effective conductivity of random checkerboards

Helsing, Johan LU orcid (2011) In Journal of Computational Physics 230(4). p.1171-1181
Abstract
An algorithm is presented for the fast and accurate solution of the electrostatic equation on multi-component random checkerboards. It relies on a particular choice of integral equation, extended as to separate ill-conditioning due to singular fields in corners from ill-conditioning due to interaction of clusters of well-conducting squares at large distances. Two separate preconditioners take care of the two separate phenomena. In a series of numerical examples, effective conductivities are computed for random checkerboards containing up to 10^4 squares with conductivity ratios of up to 10^6. The achievable relative precision in these examples is on the order of 10^{−11}.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Fast solver, Integral equation, Corner singularity, Effective conductivity, Checkerboard
in
Journal of Computational Physics
volume
230
issue
4
pages
1171 - 1181
publisher
Academic Press
external identifiers
  • wos:000286782300018
  • scopus:78650568507
ISSN
0021-9991
DOI
10.1016/j.jcp.2010.10.033
language
English
LU publication?
yes
additional info
The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
id
0629fcc9-4203-4912-b93d-ff40653673a0 (old id 1758266)
alternative location
http://www.maths.lth.se/na/staff/helsing/JCP10.pdf
date added to LUP
2016-04-01 09:57:04
date last changed
2025-10-14 09:56:07
@article{0629fcc9-4203-4912-b93d-ff40653673a0,
  abstract     = {{An algorithm is presented for the fast and accurate solution of the electrostatic equation on multi-component random checkerboards. It relies on a particular choice of integral equation, extended as to separate ill-conditioning due to singular fields in corners from ill-conditioning due to interaction of clusters of well-conducting squares at large distances. Two separate preconditioners take care of the two separate phenomena. In a series of numerical examples, effective conductivities are computed for random checkerboards containing up to 10^4 squares with conductivity ratios of up to 10^6. The achievable relative precision in these examples is on the order of 10^{−11}.}},
  author       = {{Helsing, Johan}},
  issn         = {{0021-9991}},
  keywords     = {{Fast solver; Integral equation; Corner singularity; Effective conductivity; Checkerboard}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1171--1181}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Computational Physics}},
  title        = {{The effective conductivity of random checkerboards}},
  url          = {{https://lup.lub.lu.se/search/files/1416915/3878568.pdf}},
  doi          = {{10.1016/j.jcp.2010.10.033}},
  volume       = {{230}},
  year         = {{2011}},
}