Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 2, March-April 2023
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Page(s) | 621 - 644 | |
DOI | https://doi.org/10.1051/m2an/2022086 | |
Published online | 27 March 2023 |
- S. Abarbanel, D. Gottlieb and J.S. Hesthaven, Non-linear PML equations for time dependent electromagnetics in three dimensions. J. Sci. Comput. 28 (2006) 125–137. [CrossRef] [MathSciNet] [Google Scholar]
- D. Appelö, T. Hagstrom and G. Kreiss, Perfectly matched layers for hyperbolic systems: general formulation, well-posedness, and stability. SIAM J. Appl. Math. 67 (2006) 1–23. [CrossRef] [MathSciNet] [Google Scholar]
- G. Bao, P. Li and H. Wu, An adaptive edge element method with perfectly matched absorbing layers for wave scattering by biperiodic structures. Math. Comp. 79 (2010) 1–34. [CrossRef] [MathSciNet] [Google Scholar]
- E. Bécache and P. Joly, On the analysis of Bérenger’s perfectly matched layers for maxwell’s equations. ESAIM: M2AN 36 (2002) 87–119. [CrossRef] [EDP Sciences] [Google Scholar]
- E. Bécache, P. Joly, M. Kachanovska and V. Vinoles, Perfectly matched layers in negative index metamaterials and plasmas. ESAIM: Proc. Surv. 50 (2015) 113–132. [CrossRef] [EDP Sciences] [Google Scholar]
- E. Bécache and M. Kachanovska, Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: necessary and sufficient conditions of stability. ESAIM: M2AN 51 (2017) 2399–2434. [CrossRef] [EDP Sciences] [Google Scholar]
- J.P. Bérenger, A perfectly matched layer for the absorbing EM waves. J. Comput. Phys. 114 (1994) 185–200. [CrossRef] [Google Scholar]
- A.-S. Bonnet-Ben Dhia, L. Chesnel and P. Ciarlet, T-coercivity for scalar interface problems between dielectrics and metamaterials. ESAIM: M2AN 46 (2012) 1363–1387. [CrossRef] [EDP Sciences] [Google Scholar]
- J.H. Bramble and J.E. Pasciak, Analysis of a finite element PML approximation for the three dimensional time-harmonic Maxwell problem. Math. Comp. 77 (2008) 1–10. [CrossRef] [MathSciNet] [Google Scholar]
- M. Chen, Y. Huang and J. Li, Development and analysis of a new finite element method for the Cohen-Monk PML model. Numer. Math. 147 (2021) 127–155. [CrossRef] [MathSciNet] [Google Scholar]
- G.C. Cohen and P. Monk, Mur-Nédélec finite element schemes for Maxwell’s equations. Comput. Methods Appl. Mech. Eng. 169 (1999) 197–217. [CrossRef] [Google Scholar]
- D. Correia and J.-M. Jin, 3D-FDTD-PML analysis of left-handed metamaterials. Microwave Opt. Technol. Lett. 40 (2004) 201–205. [CrossRef] [Google Scholar]
- S.A. Cummer, Perfectly matched layer behavior in negative refractive index materials. IEEE Antennas Wireless Propag. Lett. 3 (2004) 172–175. [CrossRef] [Google Scholar]
- K. Duru, L. Rannabauer, A.-A. Gabriel, G. Kreiss and M. Bader, A stable discontinuous Galerkin method for the perfectly matched layer for elastodynamics in first order form. Numer. Math. 146 (2020) 729–782. [CrossRef] [MathSciNet] [Google Scholar]
- J.L. Hong, L.H. Ji and L.H. Kong, Energy-dissipation splitting finite-difference time- domain method for Maxwell equations with perfectly matched layers. J. Comput. Phys. 269 (2014) 201–214. [CrossRef] [MathSciNet] [Google Scholar]
- Q. Hu, C. Liu, S. Shu and J. Zou, An effective preconditioner for a PML system for electromagnetic scattering problem. ESAIM: M2AN 49 (2015) 839–854. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
- Y. Huang, H. Jia and J. Li, Analysis and application of an equivalent Berenger’s PML model. J. Comp. Appl. Math. 333 (2018) 157–169. [CrossRef] [Google Scholar]
- Y. Huang, M. Chen and J. Li, Development and analysis of both finite element and fourth-order in space finite difference methods for an equivalent Berenger’s PML model. J. Comput. Phys. 405 (2020) 109154. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Huang, M. Chen and J. Li, Developing and analyzing new unconditionally stable leapfrog schemes for Maxwell’s equations in complex media. J. Sci. Comput. 86 (2021) 35. [CrossRef] [Google Scholar]
- X. Jiang, P. Li, J. Lv and W. Zheng, An adaptive finite element PML method for the elastic wave scattering problem in periodic structures. ESAIM: M2AN 51 (2016) 2017–2047. [CrossRef] [EDP Sciences] [Google Scholar]
- J. Li and J.S. Hesthaven, Analysis and application of the nodal discontinuous Galerkin method for wave propagation in metamaterials. J. Comput. Phys. 258 (2014) 915–930. [CrossRef] [MathSciNet] [Google Scholar]
- J. Li and Y. Huang, Time-domain finite element methods for Maxwell’s equations in metamaterials, in Springer Series in Computational Mathematics. Vol. 43. Springer (2013). [Google Scholar]
- J. Li, C. Shi and C.-W. Shu, Optimal non-dissipative discontinuous Galerkin methods for Maxwell’s equations in Drude metamaterials. Comput. Math. Appl. 73 (2017) 1768–1780. [Google Scholar]
- J. Li, C.-W. Shu and W. Yang, Development and analysis of two new finite element schemes for a time-domain carpet cloak model. Adv. Comput. Math. 48 (2022) 1–30. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Lin, K. Zhang and J. Zou, Studies on some perfectly matched layers for one-dimensional time-dependent systems. Adv. Comput. Math. 30 (2009) 1–35. [CrossRef] [MathSciNet] [Google Scholar]
- T. Lu, P. Zhang and W. Cai, Discontinuous Galerkin methods for dispersive and lossy Maxwell’s equations and PML boundary conditions. J. Comput. Phys. 200 (2004) 549–580. [CrossRef] [MathSciNet] [Google Scholar]
- P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [Google Scholar]
- J.-C. Nédélec, Mixed finite elements in R3. Numer. Math. 35 (1980) 315–341. [Google Scholar]
- P.A. Raviart and J.M. Thomas, A mixed finite element method for 2nd order elliptic problems, in Mathematical Aspects of the Finite Element Method. Lecture Notes in Mathematics, edited by I. Galligani and E. Magenes. Vol. 606. Springer, Berlin-Heidelberg-New York (1977) 292–315. [CrossRef] [Google Scholar]
- A. Taflove and S.C. Haguess, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd edition. Artech House, Norwood (2005). [Google Scholar]
- F.L. Teixeira and W.C. Chew, Advances in the theory of perfectly matched layers, in Fast and Efficient Algorithms in Computational Electromagnetics edited by W.C. Chew et al. Artech House, Boston (2001) 283–346. [Google Scholar]
- C. Wei, J. Yang and B. Zhang, Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems. ESAIM: M2AN 55 (2021) 2421–2443. [CrossRef] [EDP Sciences] [Google Scholar]
- Z. Xie, J. Wang, B. Wang and C. Chen, Solving Maxwell’s equation in meta-materials by a CG-DG method. Commun. Comput. Phys. 19 (2016) 1242–1264. [CrossRef] [MathSciNet] [Google Scholar]
- L. Zhao and A.C. Cangellaris, A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation. IEEE Microwave Guided Wave Lett. 6 (1996) 209–211. [CrossRef] [Google Scholar]
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