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Formulation of the eddy current problem in multiply connected regions in terms of h
Author(s) -
Kettunen Lauri,
Forsman Kimmo,
Bossavit Alain
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19980315)41:5<935::aid-nme321>3.0.co;2-f
Subject(s) - eddy current , current (fluid) , bounded function , electromagnetic field , mathematics , field (mathematics) , boundary value problem , integrable system , mathematical problem , decomposition , consistency (knowledge bases) , space (punctuation) , square integrable function , magnetic field , mathematical analysis , computer science , physics , pure mathematics , geometry , ecology , quantum mechanics , biology , thermodynamics , operating system
In this paper various formulations for the eddy current problem are presented. The formulations are based on solving directly for the magnetic field h , and they differ from each other mainly by how the field on the boundary is treated. The electromagnetic problem is studied in connection with the fivefold decomposition of the space of square integrable vector fields within a bounded region. This provides us with numerical approaches with clear signposts about how to solve the eddy current problem in multiply connected domains. Besides the fivefold decomposition, another essential tool in our approach is Whitney elements, as they provide the structure needed to retain consistency between the continuous and discrete problems. The paper demonstrates the usefulness of these mathematical tools in solving electromagnetic field problems. © 1998 John Wiley & Sons, Ltd.