Variational expressions and saddle-point (or "mini-max") principles for linear problems in electromagnetism are proposed. When conservative conditions are considered, well-known variational expressions for the resonant frequencies of a cavity and the propagation constant of a waveguide are revised directly in terms of electric and magnetic field vectors. In both cases the unknown constants are typefied as stationary (but not extremum) points of some energy-like functionals. On the contrary, if dissipation is involved then variational expressions achieve the extremum property. Indeed, we point out that a saddle-point characterizes the unique solution of Maxwell equations subject to impedance-like dissipative boundary conditions. In particular, we deal with the quasi-static problem and the time-harmonic case.

Extremum principles in electromagnetic systems

GIORGI, Claudio;VUK, Elena
1999-01-01

Abstract

Variational expressions and saddle-point (or "mini-max") principles for linear problems in electromagnetism are proposed. When conservative conditions are considered, well-known variational expressions for the resonant frequencies of a cavity and the propagation constant of a waveguide are revised directly in terms of electric and magnetic field vectors. In both cases the unknown constants are typefied as stationary (but not extremum) points of some energy-like functionals. On the contrary, if dissipation is involved then variational expressions achieve the extremum property. Indeed, we point out that a saddle-point characterizes the unique solution of Maxwell equations subject to impedance-like dissipative boundary conditions. In particular, we deal with the quasi-static problem and the time-harmonic case.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/27441
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