Eigenvalue enclosures and applications to the Maxwell operator
Résumé
In this work we discuss the numerical estimation of the eigenfrequencies and field phasors of the resonant cavity problem on a bounded region filled with a possibly anisotropic medium. We present a general framework which allows finding lower and upper bounds for the eigenfrequencies, hence providing a computable residual and multiplicity counting. We establish precise rates of convergence of the method in general, and show that this rate is optimal for trial spaces of standard nodal finite elements. In the final part of the paper we include a reproducible computational procedure and then report on various numerical experiments performed on two and three-dimensional benchmark geometries, with and without symmetries.
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