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The effective conductivity of random checkerboards

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Author

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}.

Department/s

Publishing year

2011

Language

English

Pages

1171-1181

Publication/Series

Journal of Computational Physics

Volume

230

Issue

4

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Fast solver
  • Integral equation
  • Corner singularity
  • Effective conductivity
  • Checkerboard

Status

Published

Research group

  • Harmonic Analysis and Applications
  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 0021-9991