Abstract
Publisher Summary This chapter discusses the dual and complementary variational formulations of the electromagnetic field equations and explores the usefulness of these techniques, particularly when they are used in conjunction with the finite element method. Dual and complementary variational formulations also allow local solutions to be exploited so that a more efficient use can be made of the finite element technique. This, in turn, releases the user of such methods from many of the time consuming tasks associated with data entry and mesh design. This chapter outlines a short historical perspective of the relevant work in the dual and complementary variational formulations of the electromagnetic field, as it relates to the needs. This chapter also examines the extension of complementary variational principles to complementary finite element principles and the globally bounded nature of the two complementary finite element solutions verified. Finally, this allowed the application of these techniques to magnetostatic, electrostatic, and steady state eddy current systems.
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