## A PML finite element method for electromagnetic scattering problems in a two-layer medium.(English)Zbl 1479.35842

Summary: The paper concerns the numerical solution for three-dimensional electromagnetic scattering problems in a two-layer medium. The Cartesian perfectly matched layer (PML) method is adopted to truncate the unbounded physical domain into a bounded computational domain. Although the PML method has been used widely to solve electromagnetic scattering problems, rigorous finite element error analyses are still rare in the literature, particularly, for electromagnetic scattering problems in layered media. This paper presents a thorough error analysis for finite element approximation to the scattering problems in a two-layer medium with PML boundary condition. Numerical experiments are presented to demonstrate the efficiency of the PML method and the optimal convergence of the finite element solution.

### MSC:

 35Q60 PDEs in connection with optics and electromagnetic theory 78A45 Diffraction, scattering 78A48 Composite media; random media in optics and electromagnetic theory 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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