FORMULATION OF THE EDDY-CURRENT PROBLEM IN MULTIPLY CONNECTED REGIONSIN TERMS OF H

In this paper various formulations for the eddy current problem are pr esented. The formulations are based on solving directly for the magnet ic field h, and they differ from each other mainly by how the field on the boundary is treated. The electromagnetic problem is studied in co nnection with the fivefold decomposition of the space of square integr able vector fields within a bounded region. This provides us with nume rical approaches with clear signposts about how to solve the eddy curr ent problem in multiply connected domains. Besides the fivefold decomp osition, another essential tool in our approach is Whitney elements, a s they provide the structure needed to retain consistency between the continuous and discrete problems. The paper demonstrates the usefulnes s of these mathematical tools in solving electromagnetic field problem s. (C) 1998 John Wiley & Sons, Ltd.