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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:230

Article

Helsing, Johan

关键词: Random checkerboard;    Homogenization;    Integral equation;    Fast solver;    Metamaterial;   

DOI  :  10.1016/j.jcp.2011.05.032

来源: Elsevier

【 摘 要 】

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 10(6). 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. (C) 2011 Elsevier Inc. All rights reserved..

【 授权许可】

Free