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

Research output: Contribution to journalArticle


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.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Random checkerboard, Homogenization, Integral equation, Fast solver, Metamaterial
Original languageEnglish
Pages (from-to)7533-7547
JournalJournal of Computational Physics
Issue number20
Publication statusPublished - 2011
Publication categoryResearch

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)

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