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

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Author

Summary, in English

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.

Department/s

Publishing year

2011

Language

English

Pages

7533-7547

Publication/Series

Journal of Computational Physics

Volume

230

Issue

20

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Random checkerboard
  • Homogenization
  • Integral equation
  • Fast solver
  • Metamaterial

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 0021-9991