Abstract
A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.
Highlights
The presence of rotating objects in electromagnetic problems is of interest in several applications, ranging from the detection of helicopters to the tachometry of celestial bodies [1,2]
Of the motion, bianisotropic media have been considered in several recent investigations, in particular in the context of metamaterials, with frequencies belonging to the microwave band or to the photonic one [5,6,7,8], for their huge potentialities or for their practical applications
The well posedness and finite element approximability guaranteed by our theory allow us to obtain reliable solutions from numerical simulations for rotating axisymmetric objects
Summary
The presence of rotating objects in electromagnetic problems is of interest in several applications, ranging from the detection of helicopters to the tachometry of celestial bodies [1,2]. As an immediate consequence of the presence of materials in motion, all these electromagnetic problems are difficult to solve This is a consequence of the fact that all moving media are perceived as bianisotropic [3,4]. The complexity of electromagnetic problems involving media in motion or bianisotropic materials prevents any chance of getting results without the use of numerical simulators. The well posedness and finite element approximability guaranteed by our theory allow us to obtain reliable solutions from numerical simulations for rotating axisymmetric objects.
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