Bérenger, J.-P., A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114:2 (1994), 185–200.
Chew, W.C., Weedon, W.H., A 3d perfectly matched medium from modified Maxwell's equations with stretched coordinates. Microw. Opt. Technol. Lett. 7:13 (1994), 599–604.
Teixeira, F.L., Chew, W.C., Complex space approach to perfectly matched layers: a review and some new developments. Int. J. Numer. Model. 13:5 (2000), 441–455.
Collino, F., Monk, P., The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19:6 (1998), 2061–2090.
Modave, A., Delhez, E., Geuzaine, C., Optimizing perfectly matched layers in discrete contexts. Int. J. Numer. Methods Eng. 99:6 (2014), 410–437.
Bermúdez, A., Hervella-Nieto, L., Prieto, A., Rodríguez, R., An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. J. Comput. Phys. 223:2 (2007), 469–488.
Bermúdez, A., Hervella-Nieto, L., Prieto, A., Rodríguez, R., An exact bounded perfectly matched layer for time-harmonic scattering problems. SIAM J. Sci. Comput. 30:1 (2008), 312–338.
Johnson, S.G., Notes on Perfectly Matched Layers. Lecture Notes, Massachusetts Institute of Technology, (PMLs) https://math.mit.edu/~stevenj/18.369/pml.pdf, 2007.
Hu, F.Q., On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer. J. Comput. Phys. 129:1 (1996), 201–219.
Hesthaven, J.S., On the analysis and construction of perfectly matched layers for the linearized Euler equations. J. Comput. Phys. 142:1 (1998), 129–147.
Abarbanel, S., Gottlieb, D., Hesthaven, J.S., Well-posed perfectly matched layers for advective acoustics. J. Comput. Phys. 154:2 (1999), 266–283.
Appelö, D., Hagstrom, T., Kreiss, G., Perfectly matched layers for hyperbolic systems: general formulation, well-posedness, and stability. SIAM J. Appl. Math. 67:1 (2006), 1–23.
Hu, F.Q., A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys. 173:2 (2001), 455–480.
Hu, F.Q., A perfectly matched layer absorbing boundary condition for linearized Euler equations with a non-uniform mean flow. J. Comput. Phys. 208:2 (2005), 469–492.
Bécache, E., Bonnet-Bendhia, A.S., Legendre, G., Perfectly matched layers for the convected Helmholtz equation. SIAM J. Numer. Anal. 42:1 (2004), 409–433.
Hagstrom, T., A new construction of perfectly matched layers for hyperbolic systems with applications to the linearized Euler equations. Mathematical and Numerical Aspects of Wave Propagation, WAVES 2003, 2003, Springer, 125–129.
Hagstrom, T., Nazarov, I., Absorbing layers and radiation boundary conditions for jet flow simulations. 8th AIAA/CEAS Aeroacoustics Conference & Exhibit, 2002, 2606.
Nataf, F., A new approach to perfectly matched layers for the linearized Euler system. J. Comput. Phys. 214:2 (2006), 757–772.
Dubois, F., Duceau, E., Marechal, F., Terrasse, I., Lorentz transform and staggered finite differences for advective acoustics. preprint arXiv:1105.1458.
Diaz, J., Joly, P., A time domain analysis of PML models in acoustics. Comput. Methods Appl. Mech. Eng. 195:29–32 (2006), 3820–3853.
Bécache, E., Fauqueux, S., Joly, P., Stability of perfectly matched layers, group velocities and anisotropic waves. J. Comput. Phys. 188:2 (2003), 399–433.
Parrish, S.A., Hu, F.Q., PML absorbing boundary conditions for the linearized and nonlinear Euler equations in the case of oblique mean flow. Int. J. Numer. Methods Fluids 60:5 (2009), 565–589.
Astley, R.J., Numerical methods for noise propagation in moving flows, with application to turbofan engines. Acoust. Sci. Technol. 30:4 (2009), 227–239.
Gabard, G., Bériot, H., Prinn, A., Kucukcoskun, K., Adaptive, high-order finite-element method for convected acoustics. AIAA J. 56:8 (2018), 3179–3191.
Amiet, R., Sears, W., The aerodynamic noise of small-perturbation subsonic flows. J. Fluid Mech. 44:2 (1970), 227–235.
Taylor, K., A transformation of the acoustic equation with implications for wind-tunnel and low-speed flight tests. Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 363:1713 (1978), 271–281.
Chapman, C., Similarity variables for sound radiation in a uniform flow. J. Sound Vib. 233:1 (2000), 157–164.
Jackson, J.D., Classical Electrodynamics. 2007, John Wiley & Sons.
Gregory, A.L., Sinayoko, S., Agarwal, A., Lasenby, J., An acoustic space-time and the Lorentz transformation in aeroacoustics. Int. J. Aeroacoust. 14:7 (2015), 977–1003.
Gregory, A., Agarwal, A., Lasenby, J., Sinayoko, S., Geometric algebra and an acoustic space time for propagation in non-uniform flow. preprint arXiv:1701.04715.
Hu, F.Q., Pizzo, M.E., Nark, D.M., On the use of a Prandtl-Glauert-Lorentz transformation for acoustic scattering by rigid bodies with a uniform flow. J. Sound Vib. 443 (2019), 198–211.
Mancini, S., Boundary integral methods for sound propagation with subsonic potential mean flows. Ph.D. thesis, 2017, University of Southampton.
Balin, N., Casenave, F., Dubois, F., Duceau, E., Duprey, S., Terrasse, I., Boundary element and finite element coupling for aeroacoustics simulations. J. Comput. Phys. 294 (2015), 274–296.
Visser, M., Acoustic black holes: horizons, ergospheres and Hawking radiation. Class. Quantum Gravity, 15(6), 1998, 1767.
Glauert, H., The effect of compressibility on the lift of an aerofoil. Proc. R. Soc. Lond. Ser. A, Contain. Pap. Math. Phys. Character 118:779 (1928), 113–119.
Bécache, E., Joly, P., Kachanovska, M., Vinoles, V., Perfectly matched layers in negative index metamaterials and plasmas. ESAIM Proc. Surv. 50 (2015), 113–132.
Vinoles, V., Problèmes d'interface en présence de métamatériaux: modélisation, analyse et simulations. Ph.D. thesis, 2016, Université Paris-Saclay.
S.W. Rienstra, A. Hirschberg, An Introduction to Acoustics, https://www.win.tue.nl/~sjoerdr/papers/boek.pdf, extended and revised edition of IWDE 92-06 (2004).
Geuzaine, C., Remacle, J.-F., Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79:11 (2009), 1309–1331.
Solin, P., Segeth, K., Dolezel, I., Higher-Order Finite Element Methods. 2003, Chapman and Hall/CRC.
Bériot, H., Prinn, A., Gabard, G., Efficient implementation of high-order finite elements for Helmholtz problems. Int. J. Numer. Methods Eng. 106:3 (2016), 213–240.
Bériot, H., Gabard, G., Perrey-Debain, E., Analysis of high-order finite elements for convected wave propagation. Int. J. Numer. Methods Eng. 96:11 (2013), 665–688.
Düster, A., Rank, E., Szabó, B., The p-version of the finite element and finite cell methods. Encyclopedia of Computational Mechanics, Second Edition, 2017, 1–35.
Cimpeanu, R., Martinsson, A., Heil, M., A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation. J. Comput. Phys. 296 (2015), 329–347.
Kim, S., Error analysis of PML-FEM approximations for the Helmholtz equation in waveguides. Modél. Math. Anal. Numér. 53:4 (2019), 1191–1222.
El Kacimi, A., Laghrouche, O., Ouazar, D., Mohamed, M., Seaid, M., Trevelyan, J., Enhanced conformal perfectly matched layers for Bernstein–Bézier finite element modelling of short wave scattering. Comput. Methods Appl. Mech. Eng. 355 (2019), 614–638.
Michler, C., Demkowicz, L., Kurtz, J., Pardo, D., Improving the performance of perfectly matched layers by means of hp-adaptivity. Numer. Methods Partial Differ. Equ. 23:4 (2007), 832–858.
Köppl, T., Wohlmuth, B., Optimal a priori error estimates for an elliptic problem with Dirac right-hand side. SIAM J. Numer. Anal. 52:4 (2014), 1753–1769.
Dohnal, T., Perfectly matched layers for coupled nonlinear Schrödinger equations with mixed derivatives. J. Comput. Phys. 228:23 (2009), 8752–8765.
Bériot, H., Gabard, G., Anisotropic adaptivity of the p-fem for time-harmonic acoustic wave propagation. J. Comput. Phys. 378 (2019), 234–256.
Lieu, A., Gabard, G., Bériot, H., A comparison of high-order polynomial and wave-based methods for Helmholtz problems. J. Comput. Phys. 321 (2016), 105–125.
Ozgun, O., Kuzuoglu, M., Non-Maxwellian locally-conformal PML absorbers for finite element mesh truncation. IEEE Trans. Antennas Propag. 55:3 (2007), 931–937.
Bériot, H., Tournour, M., On the locally-conformal perfectly matched layer implementation for Helmholtz equation. INTER-NOISE and NOISE-CON Congress and Conference Proceedings, no. 8, 2009, Institute of Noise Control Engineering, 503–513.
