Abarbanel, Saul; Gottlieb, David A mathematical analysis of the PML method. (English) Zbl 0887.65122 J. Comput. Phys. 134, No. 2, 357-363 (1997). 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. Reviewer: J.Gilewicz (Marseille) Cited in 1 ReviewCited in 75 Documents MSC: 65Z05 Applications to the sciences 78A25 Electromagnetic theory (general) 35Q60 PDEs in connection with optics and electromagnetic theory Keywords:weakly well-posed problem; perfectly matched layer method; electromagnetic computations; Maxwell equations PDFBibTeX XMLCite \textit{S. Abarbanel} and \textit{D. Gottlieb}, J. Comput. Phys. 134, No. 2, 357--363 (1997; Zbl 0887.65122) 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: Wiley New York [4] Taflov, A., Computational Electrodynamics, The Finite Difference Time Domain Approach (1995), Artech House: 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.