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The perfectly matched layer in curvilinear coordinates. (English) Zbl 0940.78011
A Maxwell system in two space dimensions is considered. Change of variable technique is used to construct Berenger’s perfectly matched layer (PML) model in curvilinear coordinates. For the time harmonic scattering problem the existence of a unique solution is proved for the obtained model with infinite layer. Then two truncation procedures are considered using, respectively Dirichlet condition and Sommerfeld radiation condition on the outer boundary. Except for a finite set of exceptional frequencies the existence of a unique solution of the truncated problems is proved. The models obtained are suitable to be solved numerically by the finite element method. Berenger’s PML for a time dependent Maxwell system is developed as well. Several test problems are considered. The numerical results show high accuracy of the developed approach.

78M10Finite element methods (optics)
78A45Diffraction, scattering (optics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35Q60PDEs in connection with optics and electromagnetic theory
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