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All issues Volume 55 / No 5 (September-October 2021) ESAIM: M2AN, 55 5 (2021) 2421-2443 References
Open Access
Issue
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
Page(s) 2421 - 2443
DOI https://doi.org/10.1051/m2an/2021064
Published online 26 October 2021
  1. G. Bao and H. Wu, Convergence analysis of the perfectly matched layer problems for time-harmonic Maxwell’s equations. SIAM. J. Numer. Anal. 43 (2005) 2121–2143. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Bao, Y. Gao and P. Li, Time-domain analysis of an acoustic-elastic interaction problem. Arch. Ration. Mech. Anal. 229 (2018) 835–884. [CrossRef] [MathSciNet] [Google Scholar]
  3. J.P. Bérenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185–200. [Google Scholar]
  4. J.H. Bramble and J.E. Pasciak, Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems. Math. Comp. 76 (2007) 597–614. [Google Scholar]
  5. J.H. Bramble and J.E. Pasciak, Analysis of a finite element PML approximation for the three dimensional time-harmonic Maxwell problem. Math. Comput. 77 (2008) 1–10. [CrossRef] [Google Scholar]
  6. J.H. Bramble and J.E. Pasciak, Analysis of a Cartesian PML approximation to the three dimensional electromagnetic wave scattering problem. Int. J. Numer. Anal. Model. 9 (2012) 543–561. [MathSciNet] [Google Scholar]
  7. J.H. Bramble and J.E. Pasciak, Analysis of a Cartesian PML approximation to acoustic scattering problems in ℝ2 and ℝ3. J. Comput. Appl. Math. 247 (2013) 209–230. [Google Scholar]
  8. J.H. Bramble, J.E. Pasciak and D. Trenev, Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem. Math. Comput. 79 (2010) 2079–2101. [Google Scholar]
  9. A. Buffa, M. Costabel and D. Sheen, On traces for H(curl, Ω) in Lipschitz domains. J. Math. Anal. Appl. 276 (2002) 845–867. [Google Scholar]
  10. Z. Chen, Convergence of the time-domain perfectly matched layer method for acoustic scattering problems. Int. J. Numer. Anal. Model. 6 (2009) 124–146. [Google Scholar]
  11. J. Chen and Z. Chen, An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems. Math. Comput. 77 (2007) 673–698. [CrossRef] [Google Scholar]
  12. Z. Chen and X. Liu, An adaptive perfectly matched layer technique for time-harmonic scattering problems. SIAM J. Numer. Anal. 43 (2005) 645–671. [Google Scholar]
  13. Q. Chen and P. Monk, Discretization of the time domain CFIE for acoustic scattering problems using convolution quadrature. SIAM J. Math. Anal. 46 (2014) 3107–3130. [CrossRef] [MathSciNet] [Google Scholar]
  14. Z. Chen and J.C. Nédélec, On Maxwell equations with the transparent boundary condition. J. Comput. Math. 26 (2008) 284–296. [MathSciNet] [Google Scholar]
  15. Z. Chen and X. Wu, An adaptive uniaxial perfectly matched layer method for time-harmonic scattering problems. Numer. Math. TMA 1 (2008) 113–137. [CrossRef] [Google Scholar]
  16. Z. Chen and X. Wu, Long-time stability and convergence of the uniaxial perfectly matched layer method for time-domain acoustic scattering problems. SIAM J. Numer. Anal. 50 (2012) 2632–2655. [Google Scholar]
  17. Z. Chen and W. Zheng, Convergence of the uniaxial perfectly matched layer method for time-harmonic scattering problems in two-layered media. SIAM J. Numer. Anal. 48 (2010) 2158–2185. [Google Scholar]
  18. Z. Chen and W. Zheng, PML method for electromagnetic scattering problem in a two-layer medium. SIAM. J. Numer. Anal. 55 (2017) 2050–2084. [CrossRef] [MathSciNet] [Google Scholar]
  19. Z. Chen, T. Cui and L. Zhang, An adaptive anisotropic perfectly matched layer method for 3-D time harmonic electromagnetic scattering problems. Numer. Math. 125 (2013) 639–677. [CrossRef] [MathSciNet] [Google Scholar]
  20. Z. Chen, X. Xiang and X. Zhang, Convergence of the PML method for elastic wave scattering problems. Math. Comp. 85 (2016) 2687–2714. [CrossRef] [MathSciNet] [Google Scholar]
  21. W.C. Chew and W.H. Weedon, A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. Microw. Opt. Technol. Lett. 7 (1994) 599–604. [CrossRef] [Google Scholar]
  22. A.M. Cohen, Numerical Methods for Laplace Transform Inversion. Springer (2007). [Google Scholar]
  23. F. Collino and P. Monk, The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19 (1998) 2061–2090. [Google Scholar]
  24. A.T. DeHoop, P.M. van den Berg and R.F. Remis, Absorbing boundary conditions and perfectly matched layers: an analytic time-domain performance analysis. IEEE Trans. Magn. 38 (2002) 657–660. [CrossRef] [Google Scholar]
  25. J. Diaz and P. Joly, A time domain analysis of PML models in acoustics. Comput. Methods Appl. Mech. Eng. 195 (2006) 3820–3853. [CrossRef] [Google Scholar]
  26. Y. Gao and P. Li, Analysis of time-domain scattering by periodic structures. J. Differ. Equ. 261 (2016) 5094–5118. [CrossRef] [Google Scholar]
  27. Y. Gao and P. Li, Electromagnetic scattering for time-domain Maxwell’s equations in an unbounded structure. Math. Models Methods Appl. Sci. 27 (2017) 1843–1870. [CrossRef] [MathSciNet] [Google Scholar]
  28. Y. Gao, P. Li and B. Zhang, Analysis of transient acoustic-elastic interaction in an unbounded structure. SIAM J. Math. Anal. 49 (2017) 3951–3972. [CrossRef] [MathSciNet] [Google Scholar]
  29. T. Hagstrom, Radiation boundary conditions for the numerical simulation of waves. Acta Numer. 8 (1999) 47–106. [CrossRef] [Google Scholar]
  30. T. Hohage, F. Schmidt and L. Zschiedrich, Solving time-harmonic scattering problems based on the pole condition II: convergence of the PML method. SIAM J. Math. Anal. 35 (2003) 547–560. [CrossRef] [MathSciNet] [Google Scholar]
  31. G.C. Hsiao, F.J. Sayas and R.J. Weinacht, Time-dependent fluid-structure interaction. Math. Method. Appl. Sci. 40 (2017) 486–500. [CrossRef] [Google Scholar]
  32. M. Lassas and E. Somersalo, On the existence and convergence of the solution of PML equations. Computing 60 (1998) 229–241. [CrossRef] [MathSciNet] [Google Scholar]
  33. P. Li, L. Wang and A. Wood, Analysis of transient electromagnetic scattering from a three-dimensional open cavity. SIAM J. Appl. Math. 75 (2015) 1675–1699. [CrossRef] [MathSciNet] [Google Scholar]
  34. P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford Univ. Press, New York (2003). [Google Scholar]
  35. F.L. Teixeira and W.C. Chew, Advances in the theory of perfectly matched layers, edited by W.C. Chew et al. In: Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, Boston (2001) 283–346. [Google Scholar]
  36. F. Trèves, Basic Linear Partial Differential Equations. Academic Press, New York (1975). [Google Scholar]
  37. C. Wei and J. Yang, Analysis of a time-dependent fluid-solid interaction problem above a local rough surface. Sci. Chin. Math. 63 (2020) 887–906. [CrossRef] [Google Scholar]
  38. C. Wei, J. Yang and B. Zhang, Convergence of the perfectly matched layer method for transient acoustic-elastic interaction above an unbounded rough surfacePreprint: arXiv:1907.09703 (2019). [Google Scholar]
  39. C. Wei, J. Yang and B. Zhang, A time-dependent interaction problem between an electromagnetic field and an elastic body. Acta Math. Appl. Sin. Engl. Ser. 36 (2020) 95–118. [CrossRef] [MathSciNet] [Google Scholar]
  40. C. Wei, J. Yang and B. Zhang, Convergence analysis of the PML method for time-domain electromagnetic scattering problems. SIAM J. Numer. Anal. 58 (2020) 1918–1940. [CrossRef] [MathSciNet] [Google Scholar]

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