Fast Computation of Cuts With Reduced Support by Solving Maximum Circulation Problems
| Autor: | Bernard Kapidani, Pawel Dlotko, Ruben Specogna |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Mathematical optimization
Computer science Computation eddy currents Scalar potential thin and thick cuts Homology (mathematics) Flow network Terms-(Co)homology Homology (biology) Graph Electronic Optical and Magnetic Materials maximum circulation network flow problem Electronic Optical and Magnetic Materials Electrical and Electronic Engineering Time complexity Sparse matrix |
| Zdroj: | IEEE Transactions on Magnetics. 51:1-4 |
| ISSN: | 1941-0069 0018-9464 |
| DOI: | 10.1109/tmag.2014.2359976 |
| Popis: | We present a technique to efficiently compute optimal cuts required to solve 3-D eddy current problems by magnetic scalar potential formulations. By optimal cuts, we mean the representatives of (co)homology generators with minimum support among the ones with a prescribed boundary. In this paper, we obtain them by starting from the minimal (co)homology generators of the combinatorial two-manifold representing the interface between conducting and insulating regions. Optimal generators are useful because they reduce the fill-in of the sparse matrix and ease human-guided basis selection. In addition, provided that the mesh is refined enough to allow it, they are not self-intersecting. The proposed technique is based on a novel graph-theoretic algorithm to solve a maximum circulation network flow problem in unweighted graphs that typically runs in linear time. |
| Databáze: | OpenAIRE |
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