The effective conductivity of random checkerboards

Research output: Contribution to journalArticle


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}.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics


  • Fast solver, Integral equation, Corner singularity, Effective conductivity, Checkerboard
Original languageEnglish
Pages (from-to)1171-1181
JournalJournal of Computational Physics
Issue number4
Publication statusPublished - 2011
Publication categoryResearch

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)

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