Critical Analysis of the Spanning Tree Techniques

Two algorithms based upon a tree-cotree decomposition, called in this paper spanning tree technique (STT) and generalized spanning tree technique (GSTT), have been shown to be useful in computational electromagnetics. The aim of this paper is to give a rigorous description of the GSTT in terms of homology and cohomology theories, together with an analysis of its termination. In particular, the authors aim to show, by concrete counterexamples, that various problems related with both STT and GSTT algorithms exist. The counterexamples clearly demonstrate that the failure of STT and GSTT is not an exceptional event, but something that routinely occurs in practical applications. Key words. algebraic topology, scalar potential in multiply connected regions, tree-cotree decomposition, belted tree, computational topology, homology theory, cohomology theory, homology and cohomology generators, homology-cohomology duality AMS subject classifications. 65N30, 78M10, 78M25, 55N99, 55M05, 55N33 DOI....

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Pawel Dlotko, Ruben Specogna
• Keywords: GSTT, SIAMNUM 2010, Tree Technique, Tree-cotree Decomposition