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

摘要: An integral equation based scheme is presented for the fast and accurate computation of effective conductivities two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The extends recent work on multi-component checkerboards medium General improvement include simplification a long-range preconditioner, use banded solver, more efficient placement quadrature points. This, together reduction in number unknowns, allows substantial increase achievable accuracy as well tractable system size. Results, to least nine digits, are obtained random over million squares cell ratio 106. Furthermore, flexible enough handle complex valued and, using homotopy method, purely negative Examples resonant spectra given.