期刊论文详细信息
JOURNAL OF COMPUTATIONAL PHYSICS 卷:230
The effective conductivity of random checkerboards
Article
Helsing, Johan
关键词: Integral equation;    Corner singularity;    Fast solver;    Effective conductivity;    Checkerboard;   
DOI  :  10.1016/j.jcp.2010.10.033
来源: Elsevier
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【 摘 要 】

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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