boundary-value problems; calculus; electromagnetic field theory
A new representation for electromagnetic boundary conditions involving a boundary projection operator defined using the interior and exterior products of the calculus of differential forms is developed. This operator expresses boundary conditions for fields represented by differential forms of arbitrary degree. With vector analysis, the field intensity boundary conditions require the cross product, whereas the flux boundary conditions use the inner product. With differential forms, the field intensity and flux density boundary conditions are expressed using a single operator. This boundary projection operator is readily applied in practice, so that this work extends the utility of the calculus of differential forms in applied electromagnetics.
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