Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 230, Issue 4, Pages 1171-1181Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2010.10.033
Keywords
Integral equation; Corner singularity; Fast solver; Effective conductivity; Checkerboard
Funding
- Swedish Research Council [621-2007-6234]
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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). (C) 2010 Elsevier Inc. All rights reserved.
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