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

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