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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.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A45 Diffraction, scattering
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
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