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

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.

• Författare: Johan Helsing
• Avdelning/ar: Matematik LTH; Harmonic Analysis and Applications; eSSENCE: The e-Science Collaboration
• Publiceringsår: 2011
• Språk: Engelska
• Sidor: 7533-7547
• Publikation/Tidskrift/Serie: Journal of Computational Physics
• Volym: 230
• Issue: 20
• Fulltext: - 589 kB; Download statistics
• Länkar: http://www.maths.lth.se/na/staff/helsing/JCP11.pdf; http://dx.doi.org/10.1016/j.jcp.2011.05.032
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: Random checkerboard; Homogenization; Integral equation; Fast solver; Metamaterial
• Status: Published
• Forskningsgrupp: Harmonic Analysis and Applications; Harmonic Analysis and Applications
• ISBN/ISSN/Övrigt: ISSN: 0021-9991