A General Formulation for Time-Harmonic Maxwell Equations in 3D Cavities and Approximation by a Spectral Method (original) (raw)

The first purpose of this paper is to investigate time-harmonic Maxwell's equations in Lipschitz and multiply connected cavities of R 3 . We prove the wellposedness of the current source problem by means of a new formulation. Our starting point is the curl second order equation satisfied by the magnetic field. The use of an appropriate compact operator is at the heart of the proof. Secondly, we propose a discretization relying on spectral elements and numerical integration. Then we prove the convergence of the discrete solutions to the exact one and we derive error estimates. Examples of numerical solutions are given and compared with those obtained by a finite element method in the case of a simple geometry.