The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios
(2011) In Journal of Computational Physics 230(20). p.7533-7547- Abstract
- An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends recent work on multi-component checkerboards at medium contrast ratios. General improvement include the simplification of a long-range preconditioner, the use of a banded solver, and a more efficient placement of quadrature points. This, together with a reduction in the number of unknowns, allows for a substantial increase in achievable accuracy as well as in tractable system size. Results, accurate to at least nine digits, are obtained for random checkerboards with over a million squares in the unit cell at... (More)
- An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends recent work on multi-component checkerboards at medium contrast ratios. General improvement include the simplification of a long-range preconditioner, the use of a banded solver, and a more efficient placement of quadrature points. This, together with a reduction in the number of unknowns, allows for a substantial increase in achievable accuracy as well as in tractable system size. Results, accurate to at least nine digits, are obtained for random checkerboards with over a million squares in the unit cell at contrast ratio 106. Furthermore, the scheme is flexible enough to handle complex valued conductivities and, using a homotopy method, purely negative contrast ratios. Examples of the accurate computation of resonant spectra are given. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2061863
- author
- Helsing, Johan LU
- organization
- publishing date
- 2011
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Random checkerboard, Homogenization, Integral equation, Fast solver, Metamaterial
- in
- Journal of Computational Physics
- volume
- 230
- issue
- 20
- pages
- 7533 - 7547
- publisher
- Elsevier
- external identifiers
-
- wos:000294517900001
- scopus:79961020934
- ISSN
- 0021-9991
- DOI
- 10.1016/j.jcp.2011.05.032
- 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
- e1ba195e-fddb-4e27-b728-4250b4257daf (old id 2061863)
- alternative location
- http://www.maths.lth.se/na/staff/helsing/JCP11.pdf
- date added to LUP
- 2016-04-01 10:58:17
- date last changed
- 2022-04-12 19:20:04
@article{e1ba195e-fddb-4e27-b728-4250b4257daf,
abstract = {{An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends recent work on multi-component checkerboards at medium contrast ratios. General improvement include the simplification of a long-range preconditioner, the use of a banded solver, and a more efficient placement of quadrature points. This, together with a reduction in the number of unknowns, allows for a substantial increase in achievable accuracy as well as in tractable system size. Results, accurate to at least nine digits, are obtained for random checkerboards with over a million squares in the unit cell at contrast ratio 106. Furthermore, the scheme is flexible enough to handle complex valued conductivities and, using a homotopy method, purely negative contrast ratios. Examples of the accurate computation of resonant spectra are given.}},
author = {{Helsing, Johan}},
issn = {{0021-9991}},
keywords = {{Random checkerboard; Homogenization; Integral equation; Fast solver; Metamaterial}},
language = {{eng}},
number = {{20}},
pages = {{7533--7547}},
publisher = {{Elsevier}},
series = {{Journal of Computational Physics}},
title = {{The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios}},
url = {{https://lup.lub.lu.se/search/files/2276694/3878567.pdf}},
doi = {{10.1016/j.jcp.2011.05.032}},
volume = {{230}},
year = {{2011}},
}