Formulation of the eddy current problem in multiply connected regions in terms of h. Kettunen, L., Forsman, K., & Bossavit, A. International Journal for Numerical Methods in Engineering, 41(5):935–954, Wiley, 1998.
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.
@Article{         Kettunen_1998aa,
abstract      = {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.},
author        = {Kettunen, Lauri and Forsman, Kimmo and Bossavit, Alain},
doi           = {10.1002/(SICI)1097-0207(19980315)41:5<935::AID-NME321>3.0.CO;2-F},
file          = {Kettunen_1998aa.pdf},
issn          = {0029-5981},
journal       = {International Journal for Numerical Methods in Engineering},
keywords      = {field,physics},
langid        = {english},
number        = {5},
pages         = {935--954},
publisher     = {Wiley},
title         = {Formulation of the eddy current problem in multiply connected regions in terms of h},
volume        = {41},
year          = {1998},
shortjournal  = {Int. J. Numer. Meth. Eng.}
}