Analysis of time-harmonic electromagnetic problems with elliptic material coefficients

TL;DR

This paper investigates electromagnetic problems involving elliptic material coefficients, analyzing their properties, establishing well-posedness of variational formulations, and applying the framework to various media types.

Contribution

It provides a comprehensive analysis of elliptic material coefficients in electromagnetic problems, including well-posedness results and applications to different media.

Findings

Well-posedness of variational formulations established

Conditions for coercivity of sesquilinear forms identified

Framework successfully applied to isotropic, geometric, and gyrotropic media

Abstract

We consider time-harmonic electromagnetic problems with material coefficients represented by elliptic fields, covering a wide range of complex and anisotropic material media. The properties of elliptic fields are analyzed, with particular emphasis on scalar fields and normal tensor fields. Time-harmonic electromagnetic problems with general elliptic material fields are then studied. Well-posedness results for classical variational formulations with different boundary conditions are reviewed, and hypotheses for the coercivity of the corresponding sesquilinear forms are investigated. Finally, the proposed framework is applied to examples of media used in the literature: isotropic lossy media, geometric media, and gyrotropic media.