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In this paper, we consider the scattering of a time-dependent electromagneticwave by an elastic body immersed in the lower half-space of a two-layeredbackground medium which is separated by an unbounded rough surface. Byproposing two exact transparent boundary conditions (TBCs) on the artificialplanes, we reformulate the unbounded scattering problem into an equivalentinitial-boundary value problem in a strip domain with the well-posedness andstability proved using the Laplace transform, variational method and energymethod. A perfectly matched layer (PML) is then introduced to truncate theinteraction problem with two finite layers containing the elastic body, leadingto a PML problem in a finite strip domain. We further verify the existence,uniqueness and stability estimate of solution for the PML problem. Finally, weestablish the exponential convergence in terms of the thickness and parametersof the PML layers via an error estimate on the electric-to-magnetic (EtM)capacity operators between the original problem and the PML problem.

Time domain analysis for electromagnetic scattering by an elastic obstacle in a two-layered medium