| Title | The effective conductivity of random checkerboards |
| Authors | Johan Helsing |
| Alternative Location | http://www.maths.lth.se/na/... |
| Alternative Location | http://dx.doi.org/10.1016/j..., Restricted Access |
| Publication | Journal of Computational Physics |
| Year | 2011 |
| Volume | 230 |
| Issue | 4 |
| Pages | 1171 - 1181 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Elsevier Inc. |
| Abstract 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}. |
| Keywords | Fast solver, Integral equation, Corner singularity, Effective conductivity, Checkerboard, |
| ISBN/ISSN/Other | ISSN: 0021-9991 |
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