Stability of the Scattering from a Large Electromagnetic Cavity in Two Dimensions

This work is concerned with a time harmonic scattering problem of electromagnetic waves from a two-dimensional open cavity embedded in the infinite ground plane. Because of the highly oscillatory nature of the solution for large or deep cavity, the model scattering problem is challenging both mathematically and computationally. A variational formulation reduces the scattering problem into a bounded domain (the cavity) problem. The stability of the solution is established for the bounded domain problem in the energy space. Moreover, our stability estimates provide the explicit dependence on the high wave number and the depth of the cavity.