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A time domain analysis of PML models in acoustics. (English) Zbl 1119.76046

Summary: We present a time domain analysis of perfectly matched layers (PMLs) for non-advective and advective acoustics. We focus our attention on time-stability and error estimates (with respect to the parameters of the layers). The main new technical tool is Cagniard-de Hoop method. Our theoretical results are validated and illustrated by various numerical results.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76Q05 Hydro- and aero-acoustics
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References:

[1] Bérenger, J. P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114, 185-200 (1994) · Zbl 0814.65129
[2] Tam, C. K.W.; Auriault, L.; Cambuli, F., Perfectly matched layer as an absorbing boundary condition for the linearized Euler equations in open and ducted domains, J. Comput. Phys., 144, 1, 213-234 (1998) · Zbl 1392.76054
[3] Zhao, L.; Cangellaris, A. C., A general approach for the development of unsplit-field time-domain implementations of perfectly matched layers for FDTD grid truncation, IEEE Microwave Guided Lett., 6, 5 (1996)
[4] Collino, F.; Tsogka, C., Application of the pml absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, 66, 1, 294-307 (2001)
[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
[6] Bérenger, J. P., Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 127, 363-379 (1996) · Zbl 0862.65080
[7] S. Fauqueux, Eléments finis mixtes spectraux et couches absorbantes parfaitement adaptées pour la propagation d’ ondes élastiques en régime transitoire, Ph.D. thesis, Université Paris, IX, 2003.; S. Fauqueux, Eléments finis mixtes spectraux et couches absorbantes parfaitement adaptées pour la propagation d’ ondes élastiques en régime transitoire, Ph.D. thesis, Université Paris, IX, 2003.
[8] Collino, F.; Monk, P., The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput., 164, 157-171 (1998) · Zbl 1040.78524
[9] Abarbanel, S.; Gottlieb, D., A mathematical analysis of the PML method, J. Comput. Phys., 134, 2, 357-363 (1997) · Zbl 0887.65122
[10] Bécache, E.; Fauqueux, S.; Joly, P., Stability of perfectly matched layers, group velocities and anisotropic waves, J. Comput. Phys., 188, 2, 399-433 (2003) · Zbl 1127.74335
[11] Collino, F.; Monk, P., Optimizing the perfectly matched layer, Comput. Methods Appl. Mech. Engrg., 164, 157-171 (1998) · Zbl 1040.78524
[12] Lassas, M.; Somersalo, E., On the existence and convergence of the solution of pml equations, Computing—Wien, 60, 3, 229-242 (1998) · Zbl 0899.35026
[13] Hohage, T.; Schmidt, F.; Zschiedrich, L., Solving time-harmonic scattering problems based on the pole condition. II. Convergence of the PML method, SIAM J. Math. Anal., 35, 3, 547-560 (2003), (Electronic) · Zbl 1052.65110
[14] Bécache, E.; Bonnet-Ben Dhia, A.-S.; Legendre, G., Perfectly matched layers for the convected Helmholtz equation, SIAM J. Numer. Anal., 42, 1, 409-433 (2004), (Electronic) · Zbl 1089.76045
[15] Diaz, J.; Joly, P., An analysis of higher boundary conditions for the wave equation, SIAP, 65, 5, 1547-1575 (2005) · Zbl 1078.35062
[16] Cagniard, L., Reflection and Refraction of Progressive Seismic Waves (1962), McGraw-Hill · Zbl 0116.24001
[17] de Hoop, A. T., The surface line source problem, Appl. Sci. Res. B, 8, 349-356 (1959)
[18] A.T. de Hoop, P. van den Berg, F. Remis, Analytic time-domain performance analysis of absorbing boundary conditions and perfectly matched layers, in: Proceedings of IEEE Antennas and Propagation Society International Symposium, vol. 4, 2001, pp. 502-505.; A.T. de Hoop, P. van den Berg, F. Remis, Analytic time-domain performance analysis of absorbing boundary conditions and perfectly matched layers, in: Proceedings of IEEE Antennas and Propagation Society International Symposium, vol. 4, 2001, pp. 502-505.
[19] J. Diaz, P. Joly, Stabilized perfectly matched layer for advective acoustics, in: The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Waves 2003), 2003, pp. 115-119.; J. Diaz, P. Joly, Stabilized perfectly matched layer for advective acoustics, in: The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation (Waves 2003), 2003, pp. 115-119. · Zbl 1047.76116
[20] T. Hagström, I. Nazarov, Absorbing layers and radiation boundary condition for jet flow simulations, Technical Report AIAA 2002-2606, AIAA, 2002.; T. Hagström, I. Nazarov, Absorbing layers and radiation boundary condition for jet flow simulations, Technical Report AIAA 2002-2606, AIAA, 2002.
[21] Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S., Well-posed perfectly matched layers for advective acoustics, J. Comput. Phys., 154, 2, 266-283 (1999) · Zbl 0947.76076
[22] Hu, F. Q., A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables, J. Comput. Phys., 173, 2, 455-480 (2001) · Zbl 1051.76593
[23] J. Diaz, Approches analytiques et numériques de problèmes de transmission en propagation d’ondes en régime transitoire. application au couplage fluide-structure et aux méthodes de couches parfaitement adaptées, Ph.D. thesis, Université Paris 6, 2005.; J. Diaz, Approches analytiques et numériques de problèmes de transmission en propagation d’ondes en régime transitoire. application au couplage fluide-structure et aux méthodes de couches parfaitement adaptées, Ph.D. thesis, Université Paris 6, 2005.
[24] Bécache, E.; Joly, P., On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations, M2AN Math. Model. Numer. Anal., 36, 1, 87-119 (2002) · Zbl 0992.78032
[25] Hesthaven, J. S., On the analysis and construction of perfectly matched layers for the linearized Euler equations, J. Comput. Phys., 142, 1, 129-147 (1998) · Zbl 0933.76063
[26] Lions, J.-L.; Métral, J.; Vacus, O., Well-posed absorbing layer for hyperbolic problems, Numer. Math., 92, 3, 535-562 (2002) · Zbl 1010.65038
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