Studies on some perfectly matched layers for one-dimensional time-dependent systems

DOI10.1007/s10444-007-9055-2zbMath1166.65042OpenAlexW2056710801MaRDI QIDQ1014870

J. Martínez

Publication date: 29 April 2009

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-007-9055-2

zbMATH Keywords

stabilityconvergencefinite difference schemesMaxwell systemhyperbolic systemperfectly matched layersacoustic equation

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Finite difference methods applied to problems in fluid mechanics (76M20) 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) Hydro- and aero-acoustics (76Q05) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (13)

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 ⋮ Development and analysis of both finite element and fourth-order in space finite difference methods for an equivalent Berenger's PML model ⋮ Finite element method and discontinuous Galerkin method for stochastic scattering problem of Helmholtz type in \(\mathbb R^{d} (d =2, 3)\) ⋮ Analysis and application of an equivalent Berenger's PML model ⋮ Development and analysis of a new finite element method for the Cohen-Monk PML model ⋮ Weak Galerkin finite element method for valuation of American options ⋮ Mathematical analysis of a PML model obtained with stretched coordinates and its application to backward wave propagation in metamaterials ⋮ Discontinuous Galerkin discretizations and analysis for the Cohen-Monk PML model ⋮ Mathematical analysis of Ziolkowski's PML model with application for wave propagation in metamaterials ⋮ Front-fixing FEMs for the pricing of American options based on a PML technique ⋮ Analysis and FDTD Simulation of a Perfectly Matched Layer for the Drude Metamaterial

Cites Work

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• Absorbing PML boundary layers for wave-like equations
• A perfectly matched layer for the absorption of electromagnetic waves
• A mathematical analysis of the PML method
• A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell's equations with high-order staggered finite difference schemes
• Long time behavior of the perfectly matched layer equations in computational electromagnetics
• Three-dimensional perfectly matched layer for the absorption of electromagnetic waves
• Well-posed perfectly matched layers for advective acoustics
• On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• The Perfectly Matched Layer in Curvilinear Coordinates
• An Adaptive Finite Element Method with Perfectly Matched Absorbing Layers for the Wave Scattering by Periodic Structures
• Reflectionless Sponge Layers as Absorbing Boundary Conditions for the Numerical Solution of Maxwell Equations in Rectangular, Cylindrical, and Spherical Coordinates

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