Development and analysis of a new finite element method for the Cohen-Monk PML model

DOI10.1007/S00211-020-01166-4zbMath1459.65181OpenAlexW3120302522MaRDI QIDQ1996222

Yanyan Li

Publication date: 3 March 2021

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-020-01166-4

zbMATH Keywords

finite element methodCohen-Monk perfectly matched layer (PML) modelRaviart-Thomas-Nédélec

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Stability in context of PDEs (35B35) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite difference methods applied to problems in optics and electromagnetic theory (78M20) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (10)

Developing and analyzing an explicit unconditionally stable finite element scheme for an equivalent Bérenger’s PML model ⋮ Analysis and application of a time-domain finite element method for the Drude metamaterial perfectly matched layer model ⋮ Analysis and Application of Two Novel Finite Element Methods for Solving Ziolkowski’s PML Model in the Integro-Differential Form ⋮ Efficient energy structure-preserving schemes for three-dimensional Maxwell's equations ⋮ A FETD scheme and analysis for photonic crystal waveguides comprising third-order nonlinear and linear materials ⋮ Numerical analysis of the direct method for 3D Maxwell's equation in Kerr-type nonlinear media ⋮ High order locally conservative finite element solutions for anisotropic diffusion problems in two dimensions ⋮ A PML finite element method for electromagnetic scattering problems in a two-layer medium ⋮ Discontinuous Galerkin discretizations and analysis for the Cohen-Monk PML model ⋮ Analysis and FDTD Simulation of a Perfectly Matched Layer for the Drude Metamaterial

Cites Work

• Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials
• Energy-dissipation splitting finite-difference time-domain method for Maxwell equations with perfectly matched layers
• Finite element study of the Lorentz model in metamaterials
• Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
• On the use of perfectly matched layers at corners for scattering problems with sign-changing coefficients
• Studies on some perfectly matched layers for one-dimensional time-dependent systems
• A perfectly matched layer for the absorption of electromagnetic waves
• Mur-Nédélec finite element schemes for Maxwell's equations
• Stable and efficient numerical schemes for two-dimensional Maxwell equations in lossy medium
• Perfectly matched layers in negative index metamaterials and plasmas
• Perfectly Matched Layers for Hyperbolic Systems: General Formulation, Well‐posedness, and Stability
• An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures
• Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials
• Finite Element Methods for Maxwell's Equations
• Mathematical analysis of a PML model obtained with stretched coordinates and its application to backward wave propagation in metamaterials

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