×

zbMATH — the first resource for mathematics

A mathematical analysis of the PML method. (English) Zbl 0887.65122
The perfectly matched layer (PML) method for the electromagnetic computations on a finite numerical domain consists of the splitting of the usual Maxwell equations acting in different layers, creating the absorbing layer where waves decay in all directions. A detailed analysis of this formulation applied to two-dimensional transvers-electric mode of Maxwell’s equations shows that the PML method is only “weakly well-posed”. It means that its solution can diverge under some small perturbations.

MSC:
65Z05 Applications to the sciences
78A25 Electromagnetic theory, general
35Q60 PDEs in connection with optics and electromagnetic theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abarbanel, S.; Gottlieb, D., Optimal time splitting methods for the navier – stokes equations in two and three space variables, J. comput. phys., 41, 1, (1981)
[2] Berenger, J.-P., A perfectly matched layer for the absorption of electromagnetic waves, J. comput. phys., 114, 185, (1994) · Zbl 0814.65129
[3] Gustafsson, B.; Kreiss, H.O.; Oliger, J., Time dependent problems and difference methods, (1995), Wiley New York
[4] Taflov, A., Computational electrodynamics, the finite difference time domain approach, (1995), Artech House Norwood
[5] Hu, F.Q., On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer, J. comput. phys., 129, 201, (1996) · Zbl 0879.76084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.