Journal of Applied Mathematics
Volume 2012 (2012), Article ID 874239, 7 pages
http://dx.doi.org/10.1155/2012/874239
Research Article

Generalized Chessboard Structures Whose Effective Conductivities Are Integer Valued

Dag Lukkassen1,2 and Annette Meidell1,2

1Narvik University College, P.O. Box 385, 8505 Narvik, Norway
2Norut Narvik, P.O. Box 250, 8504 Narvik, Norway

Received 28 September 2011; Accepted 18 November 2011

Academic Editor: Srinivasan Natesan

Copyright © 2012 Dag Lukkassen and Annette Meidell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider generalized chessboard structures where the local conductivity takes two values 𝑎 and 𝑏 . All integer combinations of 𝑎 and 𝑏 which make the components of effective conductivity matrix integer valued are found. Moreover, we discuss the problem of estimating the effective conductivity matrix by using the finite-element method.