The development of a structure linking the various potentials and field vectors of the electric and magnetic fields is presented. The approach shows that it is usually possible to find alternative formulations, for a given problem, in a relatively simple manner. These alternative formulations, when correctly chosen, pose problems in dual or complementary form such that bounded solutions are possible. Such properties are particularly attractive when numerical solutions are being considered. The proposed structure is general, incorporating both electrostatic and magnetostatic systems as well as time varying field quantities.
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Penman et al. (1984) studied this question.