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Mathematical analysis of Ziolkowski’s PML model with application for wave propagation in metamaterials. (English) Zbl 1431.78010
Summary: In this paper, we investigate one perfectly matched layer (PML) model proposed by R. W. Ziolkowski [Comput. Methods Appl. Mech. Eng. 169, No. 3–4, 237–262 (1999; Zbl 0960.78018)]. Various schemes for solving this PML model have been developed and have been shown to be effective in absorbing outgoing waves when the wave propagation in unbounded domain problem is reduced to a bounded domain problem. However, a rigorous analysis of this model is lacking. In this paper we establish the stability of this PML model and propose a fully-discrete finite element scheme to solve this model with edge elements. Discrete stability and optimal error estimate of this scheme are proved. Numerical results justifying the analysis and demonstrating the effectiveness of this PML model are presented.
MSC:
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
35L15 Initial value problems for second-order hyperbolic equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
78A25 Electromagnetic theory, general
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
Software:
FEniCS; SyFi
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References:
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