Automatic generation of cuts on large-sized meshes for the T-Ω geometric eddy-current formulation

In this paper a Geometric T-Omega formulation to solve eddy-current problems oil a tetrahedral mesh is presented. When non-simply-connected conducting regions are considered, the formulation requires the so-called thick cuts, while, in the literature, more attention is usually given to the so-called thin cuts. While the automatic construction of thin cuts has been theoretically solved many years ago, no implementation of all algorithm to compute the thick cuts which can be used in practice exists so far. In this paper, we propose how to fill this gap by introducing ail algorithm to automatically compute the thick cuts oil real-sized meshes, based oil a belted tree and a tree-cotree decomposition. The belted tree is constructed by means of a homology computation by exploiting efficient reduction methods. A number of benchmarks are presented to demonstrate the generality and the robustness of the algorithm. A rigorous definition of thick cuts, which necessarily has to rely on cohomology, is presented in addition. (C) 2009 Elsevier B.V. All rights reserved.