The effective conductivity of random checkerboards

被引：15

作者：

Helsing, Johan ^{[1
]}

机构：

[1] Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2011年 / 230卷 / 04期

基金：

瑞典研究理事会;

关键词：

Integral equation; Corner singularity; Fast solver; Effective conductivity; Checkerboard; ALGORITHM; EQUATIONS; INVERSE; THEOREM;

D O I：

10.1016/j.jcp.2010.10.033

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

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.

引用

页码：1171 / 1181

页数：11

共 22 条

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