Formulation of the eddy current problem in multiply connected regions in terms of h

✍ Scribed by Lauri Kettunen; Kimmo Forsman; Alain Bossavit

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 227 KB
• Volume: 41
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19980315)41:5<935::aid-nme321>3.0.co;2-f

✦ Synopsis

In this paper various formulations for the eddy current problem are presented. The formulations are based on solving directly for the magnetic ÿeld h, and they di er from each other mainly by how the ÿeld on the boundary is treated. The electromagnetic problem is studied in connection with the ÿvefold decomposition of the space of square integrable vector ÿelds 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 ÿvefold 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 ÿeld problems.