GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids

Zhao, Lanhao; Cangellaris, A.C.

doi:10.1109/mwsym.1996.510998

Cited by 38 publications

(51 citation statements)

References 4 publications

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“…This technique has been initially introduced by Be erenger [10] for MaxwellÕs equations, and has been widely used for the simulation of time dependent electromagnetic waves as well as Helmholtz-like equations (e.g. [11,12,28,37,39]). The method has been extended to various propagation models (the paraxial wave equations [15], the linearized Euler equations [22,24,32], etc.…”

Section: Introductionmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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Perfectly matched layers (PML) are a recent technique for simulating the absorption of waves in open domains. They have been introduced for electromagnetic waves and extended, since then, to other models of wave propagation, including waves in elastic anisotropic media. In this last case, some numerical experiments have shown that the PMLs are not always stable. In this paper, we investigate this question from a theoretical point of view. In the first part, we derive a necessary condition for the stability of the PML model for a general hyperbolic system. This condition can be interpreted in terms of geometrical properties of the slowness diagrams and used for explaining instabilities observed with elastic waves but also with other propagation models (anisotropic MaxwellÕs equations, linearized Euler equations). In the second part, we specialize our analysis to orthotropic elastic waves and obtain separately a necessary stability condition and a sufficient stability condition that can be expressed in terms of inequalities on the elasticity coefficients of the model.

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Section: Introductionmentioning

confidence: 99%

Stability of perfectly matched layers, group velocities and anisotropic waves

Bécache

Fauqueux

Joly

2003

Journal of Computational Physics

306

355

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“…This can be shown to be equivalent to an analytic continuation of Maxwell's equations to a complex coordinate spatial domain [11], hence the name complex-space. In the second class of formulations, Maxwell's equations retain their form and the PML is obtained through the insertion of artificial anisotropic tensors for the permittivity and permeability within the PML layer [5]- [7], [10].…”

Section: Discussionmentioning

confidence: 99%

Conformal PML-FDTD schemes for electromagnetic field simulations: a dynamic stability study

Teixeira

Hwang

Chew

et al. 2001

IEEE Trans. Antennas Propagat.

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Abstract-We present a study on the dynamic stability of the perfectly matched layer (PML) absorbing boundary condition for finite-difference time-domain (FDTD) simulations of electromagnetic radiation and scattering problems in body-conformal orthogonal grids. This work extends a previous dynamic stability analysis of Cartesian, cylindrical and spherical PMLs to the case of a conformal PML. It is shown that the conformal PML defined over surface terminations with positive local radii of curvature (concave surfaces as viewed from inside the computational domain) is dynamically stable, while the conformal PML defined over surface terminations with a negative local radius (convex surfaces as viewed from inside the computational domain) is dynamically unstable. Numerical results illustrate the analysis.

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“…It has been adapted to open problems though with the development of fictitious boundaries avoiding the reflections at the region frontiers. 111 In particular, the usage of Periodic Boundary Conditions 112 can provide an efficient numerical approach for analyzing the impact of the PS microstructure (porosity, etc. ), assuming translational invariance, on the electromagnetic properties of the material (effective refractive index, etc.).…”

Section: A the Finite Difference Methodsmentioning

confidence: 99%