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The effective conductivity of random checkerboards

Helsing, Johan LU (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
Elsevier
external identifiers
  • wos:000286782300018
  • scopus:78650568507
ISSN
0021-9991
DOI
10.1016/j.jcp.2010.10.033
language
English
LU publication?
yes
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
2011-07-14 11:03:51
date last changed
2017-11-19 03:02:48
@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},
  keyword      = {Fast solver,Integral equation,Corner singularity,Effective conductivity,Checkerboard},
  language     = {eng},
  number       = {4},
  pages        = {1171--1181},
  publisher    = {Elsevier},
  series       = {Journal of Computational Physics},
  title        = {The effective conductivity of random checkerboards},
  url          = {http://dx.doi.org/10.1016/j.jcp.2010.10.033},
  volume       = {230},
  year         = {2011},
}