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The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios

Helsing, Johan LU (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:
author
organization
publishing date
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
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
2011-08-23 14:30:55
date last changed
2017-08-13 03:22:04
@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},
  keyword      = {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          = {http://dx.doi.org/10.1016/j.jcp.2011.05.032},
  volume       = {230},
  year         = {2011},
}