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:
https://lup.lub.lu.se/record/1758266
- author
- Helsing, Johan
LU
- organization
- publishing date
- 2011
- 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
- project
- Harmonic Analysis and Applications
- 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
- 2026-02-02 11:01:00
@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}},
}