Cohomology in 3D Magneto-Quasistatics Modeling
作者机构：Institute of Computer ScienceJagiellonian Universityul.St.Łojasiewicza 630-348 KrakowPoland Universita di UdineDipartimento di Ingegneria ElettricaGestionale e MeccanicaVia delle Scienze 20833100 UdineItaly
出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)
年 卷 期：2013年第14卷第6期
页 面：48-76页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：partially supported by MNiSW grant N N206625439
主 题：Algebraic topology (co)homology computational electromagnetics cuts
摘 要：Electromagnetic modeling provides an interesting context to present a link between physical phenomena and homology and cohomology *** the past twenty-five years,a considerable effort has been invested by the computational electromagnetics community to develop fast and general techniques for defining *** magneto-quasi-static discrete formulations based on magnetic scalar potential are employed in problems which involve conductive regions with holes,cuts are needed to make the boundary value problem well *** an intimate connection with homology theory has been quickly recognized,heuristic definitions of cuts are surprisingly still dominant in the *** aim of this paper is first to survey several definitions of cuts together with their ***,cuts are defined as generators of the first cohomology group over integers of a finite *** provably general definition has also the virtue of providing an automatic,general and efficient algorithm for the computation of *** counter-examples show that heuristic definitions of cuts should be *** use of cohomology theory is not an option but the invaluable tool expressly needed to solve this problem.
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