| Title | The effective conductivity of arrays of squares: Large random unit cells and extreme contrast ratios |
| Authors | Johan Helsing |
| Alternative Location | http://www.maths.lth.se/na/... |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Computational Physics |
| Year | 2011 |
| Volume | 230 |
| Issue | 20 |
| Pages | 7533 - 7547 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier Science |
| Abstract 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. |
| Keywords | Random checkerboard, Homogenization, Integral equation, Fast solver, Metamaterial, |
| ISBN/ISSN/Other | ISSN: 0021-9991 (print) |
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