The effective conductivity of random checkerboards

Summary, in English

An algorithm is presented for the fast and accurate solution of the electrostatic equation on multi-component random checkerboards. It relies on a particular choice of integral equation, extended as to separate ill-conditioning due to singular fields in corners from ill-conditioning due to interaction of clusters of well-conducting squares at large distances. Two separate preconditioners take care of the two separate phenomena. In a series of numerical examples, effective conductivities are computed for random checkerboards containing up to 10^4 squares with conductivity ratios of up to 10^6. The achievable relative precision in these examples is on the order of 10^{−11}.

• Författare: Johan Helsing
• Avdelning/ar: Matematik LTH; Harmonic Analysis and Applications; eSSENCE: The e-Science Collaboration
• Publiceringsår: 2011
• Språk: Engelska
• Sidor: 1171-1181
• Publikation/Tidskrift/Serie: Journal of Computational Physics
• Volym: 230
• Issue: 4
• Fulltext: - 258 kB; Download statistics
• Länkar: http://www.maths.lth.se/na/staff/helsing/JCP10.pdf; http://dx.doi.org/10.1016/j.jcp.2010.10.033
• Dokumenttyp: Artikel i tidskrift
• Förlag: Elsevier
• Ämne: Mathematics
• Nyckelord: Fast solver; Integral equation; Corner singularity; Effective conductivity; Checkerboard
• Status: Published
• Forskningsgrupp: Harmonic Analysis and Applications; Harmonic Analysis and Applications
• ISBN/ISSN/Övrigt: ISSN: 0021-9991