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Preface
An anisotropic perfectly matched layer method for Helmholtz scattering problems with discontinuous wave number
1. | LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, China, China |
References:
[1] |
J. P. Bérenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), 185-200.
doi: 10.1006/jcph.1994.1159. |
[2] |
J. H. Bramble and J. E. Pasciak, Analysis of a cartesian PML approximation to acoustic scattering problems in $\mathbb{R}^2$ and $\mathbb{R}^3$, J. Appl. Comput. Math., to appear. |
[3] |
Z. Chen and H. Wu, An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM J. Nummer. Anal., 41 (2003), 799-826.
doi: 10.1137/S0036142902400901. |
[4] |
Z. Chen and X. Liu, An adaptive perfectly matched layer technique for time-harmonic scattering problems, SIAM J. Numer. Anal., 43 (2005), 645-671. |
[5] |
Z. Chen and X. M. Wu, An adaptive uniaxial perfectly matched layer technique for time-Harmonic scattering problems, Numer. Math. Theory Methods Appl., 1 (2008), 113-137. |
[6] |
J. Chen and Z. Chen, An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems, Math. Comp., 77 (2008), 673-698.
doi: 10.1090/S0025-5718-07-02055-8. |
[7] |
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.
doi: 10.1137/090750603. |
[8] |
Z. Chen, T. Cui and L. Zhang, An adaptive anisotropic perfectly matched layer method for 3D time harmonic electromagnetic scattering problems, Numer. Math., to appear. |
[9] |
W. C. Chew, "Waves and Fields in Inhomogeneous Media," Springer, New York, 1990.
doi: 10.1109/9780470547052. |
[10] |
W. C. Chew and W. Weedon, A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates, Microwave Opt. Tech. Lett., 7 (1994), 599-604.
doi: 10.1002/mop.4650071304. |
[11] |
F. Collino and P. B. Monk, The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput., 19 (1998), 2061-2090.
doi: 10.1137/S1064827596301406. |
[12] |
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 (electronic).
doi: 10.1137/S0036141002406485. |
[13] |
S. Kim and J. E. Pasciak, Analysis of a cartisian PML approximation to acoustic scattering problems in $\mathbb{R}^2$, J. Math. Anal. Appl., 370 (2010), 168-186.
doi: 10.1016/j.jmaa.2010.05.006. |
[14] |
M. Lassas and E. Somersalo, On the existence and convergence of the solution of PML equations, Computing, 60 (1998), 229-241.
doi: 10.1007/BF02684334. |
[15] |
M. Lassas and E. Somersalo, Analysis of the PML equations in general convex geometry, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1183-1207.
doi: 10.1017/S0308210500001335. |
[16] |
K. C. Meza-Fajardo and A. S. Papageorgiou, A nonconventional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: Stability analysis, Bulletin Seismological Soc. Am., 98 (2008), 1811-1836. |
[17] |
A. F. Oskooi, L. Zhang, Y. Avniel and S. G. Johnson, The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers, Optical Express, 16 (2008), 11376-11392.
doi: 10.1364/OE.16.011376. |
[18] |
F. L. Teixeira and W. C. Chew, Advances in the theory of perfectly matched layers, In: "Fast and Efficient Algorithms in Computational Electromagnetics" (eds W.C. Chew et al), Artech House, (2001), 283-346. |
[19] |
D. V. Trenev, "Spatial Scaling for the Numerical Approximation of Problems on Unbounded Domains," Thesis (Ph.D.), Texas A & M University, 2009, 112 pp. |
[20] |
E. Turkel and A. Yefet, Absorbing PML boundary layers for wave-like equations, Absorbing boundary conditions, Appl. Numer. Math., 27 (1998), 533-557.
doi: 10.1016/S0168-9274(98)00026-9. |
[21] |
L. Zschiedrich, R. Klose, A. Schödle and F. Schmidt, A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions, J. Comput. Appl. Math., 188 (2006), 12-32.
doi: 10.1016/j.cam.2005.03.047. |
show all references
References:
[1] |
J. P. Bérenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), 185-200.
doi: 10.1006/jcph.1994.1159. |
[2] |
J. H. Bramble and J. E. Pasciak, Analysis of a cartesian PML approximation to acoustic scattering problems in $\mathbb{R}^2$ and $\mathbb{R}^3$, J. Appl. Comput. Math., to appear. |
[3] |
Z. Chen and H. Wu, An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM J. Nummer. Anal., 41 (2003), 799-826.
doi: 10.1137/S0036142902400901. |
[4] |
Z. Chen and X. Liu, An adaptive perfectly matched layer technique for time-harmonic scattering problems, SIAM J. Numer. Anal., 43 (2005), 645-671. |
[5] |
Z. Chen and X. M. Wu, An adaptive uniaxial perfectly matched layer technique for time-Harmonic scattering problems, Numer. Math. Theory Methods Appl., 1 (2008), 113-137. |
[6] |
J. Chen and Z. Chen, An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems, Math. Comp., 77 (2008), 673-698.
doi: 10.1090/S0025-5718-07-02055-8. |
[7] |
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.
doi: 10.1137/090750603. |
[8] |
Z. Chen, T. Cui and L. Zhang, An adaptive anisotropic perfectly matched layer method for 3D time harmonic electromagnetic scattering problems, Numer. Math., to appear. |
[9] |
W. C. Chew, "Waves and Fields in Inhomogeneous Media," Springer, New York, 1990.
doi: 10.1109/9780470547052. |
[10] |
W. C. Chew and W. Weedon, A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates, Microwave Opt. Tech. Lett., 7 (1994), 599-604.
doi: 10.1002/mop.4650071304. |
[11] |
F. Collino and P. B. Monk, The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput., 19 (1998), 2061-2090.
doi: 10.1137/S1064827596301406. |
[12] |
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 (electronic).
doi: 10.1137/S0036141002406485. |
[13] |
S. Kim and J. E. Pasciak, Analysis of a cartisian PML approximation to acoustic scattering problems in $\mathbb{R}^2$, J. Math. Anal. Appl., 370 (2010), 168-186.
doi: 10.1016/j.jmaa.2010.05.006. |
[14] |
M. Lassas and E. Somersalo, On the existence and convergence of the solution of PML equations, Computing, 60 (1998), 229-241.
doi: 10.1007/BF02684334. |
[15] |
M. Lassas and E. Somersalo, Analysis of the PML equations in general convex geometry, Proc. Roy. Soc. Edinburgh Sect. A, 131 (2001), 1183-1207.
doi: 10.1017/S0308210500001335. |
[16] |
K. C. Meza-Fajardo and A. S. Papageorgiou, A nonconventional, split-field, perfectly matched layer for wave propagation in isotropic and anisotropic elastic media: Stability analysis, Bulletin Seismological Soc. Am., 98 (2008), 1811-1836. |
[17] |
A. F. Oskooi, L. Zhang, Y. Avniel and S. G. Johnson, The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers, Optical Express, 16 (2008), 11376-11392.
doi: 10.1364/OE.16.011376. |
[18] |
F. L. Teixeira and W. C. Chew, Advances in the theory of perfectly matched layers, In: "Fast and Efficient Algorithms in Computational Electromagnetics" (eds W.C. Chew et al), Artech House, (2001), 283-346. |
[19] |
D. V. Trenev, "Spatial Scaling for the Numerical Approximation of Problems on Unbounded Domains," Thesis (Ph.D.), Texas A & M University, 2009, 112 pp. |
[20] |
E. Turkel and A. Yefet, Absorbing PML boundary layers for wave-like equations, Absorbing boundary conditions, Appl. Numer. Math., 27 (1998), 533-557.
doi: 10.1016/S0168-9274(98)00026-9. |
[21] |
L. Zschiedrich, R. Klose, A. Schödle and F. Schmidt, A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions, J. Comput. Appl. Math., 188 (2006), 12-32.
doi: 10.1016/j.cam.2005.03.047. |
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