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A general finite element method is applied to compute the skin currents flowing on a perfectly conducting surface when it is illuminated by a time-harmonic incident electromagnetic wave. In this paper, we introduce and study the framework in which the continuous problem can be stated in order to make possible the numerical analysis which will follow in a second part.

mathematics of computation

Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. I. The continuous problem