Perfectly matched layers for hyperbolic systems: General formulation, well-posedness, and stability

SIAM Journal on Applied Mathematics

Volumn 67, Issue 1, 2006, Pages 1-23

  Appelö, Daniel ^a   Hagstrom, Thomas ^b   Kreiss, Gunilla ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Perfectly matched layers; Stability

Indexed keywords

COMPUTATIONAL ELECTROMAGNETICS; HYPERBOLIC SYSTEMS; MATHEMATICAL ANALYSIS; PERFECTLY MATCHED LAYERS;

COMPUTATIONAL METHODS; EULER EQUATIONS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PARAMETER ESTIMATION; WAVE PROPAGATION;

MAGNETOELECTRIC EFFECTS;

EID: 33847744194     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/050639107     Document Type: Article

References (24)

1. S. ABARBANEL, D. GOTTLIEB, AND J. HESTHAVEN, Well-posed perfectly matched layers for advective acoustics, J. Comput. Phys., 154 (1999), pp. 266-283.
2. S. ABARBANEL AND D. GOTTLIEB, A mathematical analysis of the PML method, J. Comput. Phys., 134 (1997), p. 357-363.
3. S. ABARBANEL AND D. GOTTLIEB, On the construction and analysis of absorbing layers in CEM, Appl. Numer. Math., 27 (1998), pp. 331-340.
4. D. APPELÖ AND T. HAGSTROM, Construction of stable PMLs for general 2 × 2 symmetric hyperbolic systems, in Proceedings of the Tenth International Conference on Hyperbolic Problems: Theory, Numerics, Applications, F. Asakura, H. Aiso, S. Kawashima, A. Matsumura, S. Nishibata, and K. Nishihara, eds., Yokahama Publishers, Japan, 2004, pp. 262-270.
5. E. BÉCACHE, S. FAUQUEUX, AND P. JOLY, Stability of perfectly matched layers, group velocities and anisotropic waves, J. Comput. Phys., 188 (2003), pp. 399-433.
6. E. BÉCACHE AND P. JOLY, On the analysis of Berenger's perfectly matched layers for Maxwell's equations, Math. Model Numer. Anal., 36 (2002), pp. 87-119.
7. E. BÉCACHE, P. PETROPOULOS, AND S. GEDNEY, On the long-time behavior of unsplit Perfectly Matched Layers, IEEE Trans. Antennas Prop., 54 (2004), pp. 1335-1342.
8. J. BÉRENGER, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), p. 185.
9. W. CHEW AND W. WEEDON, A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates, Microwave Optical Technol. Lett., 7 (1994), pp. 599-604.
10. F. COLLINO AND C. TSOGKA, Application of the PML absorbing layer model to the linear elastodynamic problem in aniotropic heterogeneous media, Geophys., 66 (2001), pp. 294-307.
11. J. DIAZ AND P. JOLY, Stabilized perfectly matched layer for advective acoustics, in Mathematical and Numerical Aspects of Wave Propagation, Proceedings of Waves2003, G. Cohen, P. Joly, E. Heikkola, and P. Neittaanmäki, eds., Springer-Verlag, New York, 2003, pp. 115-119.
12. F. R. GANTMACHER, The Theory of Matrices, Vol. 1, Chelsea, New York, 1959.
13. S. GEDNEY, An anisotropic perfectly matched layer-absorbing medium for the truncation of fdtd lattices., IEEE Trans. Antennas Propagation, 44 (1996), pp. 1630-1639.
14. T. HAGSTROM AND D. APPELÖ, Automatic Symmetrization and Energy Estimates Using Local Operators for Partial Differential Equations. Communications in Partial Differential Equations, in press.
15. T. HAGSTROM, Radiation boundary conditions for the numerical simulation of waves, Acta. Numer., 8 (1999), pp. 47-106.
16. T. HAGSTROM, New Results on Absorbing Layers and Radiation Boundary Conditions, in Topics in Computational Wave Propagation, Lecture Notes in Comput. Sci. Engrg. 31, M. Ainsworth, P. Davies, D. Duncan, P. Martin, and B, Rynne, eds., Springer-Verlag, New York, 2003, pp. 1-42.
17. T. HAGSTROM, Perfectly matched layers for hyperbolic systems with applications to the linearized Euler equations, in Mathematical and Numerical Aspects of Wave Propagation, Proceedings of Waves2003, G. Cohen, P. Joly, E. Heikkola, and P. Neittaanmäki, eds., Springer-Verlag, New York, 2003, pp. 125-129.
18. F. Q. HU, On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer, J. Comput. Phys., 129 (1996), pp. 201-209.
19. F. Q. HU, A stable perfectly matched layer for linearized Euler equations in unsplit physical variables, J. Comput. Phys., 173 (2001), pp. 455-480.
20. H.-O. KREISS AND J. LORENZ, Initial-Boundary Value Problems and the Navier-Stokes Equations, Academic Press, New York, 1989.
21. M. MARDEN, The Geometry of the Zeros of a Polynomial in a Complex Variable, American Mathematical Society, Providence, RI, 1949.
22. I. NAVON, B. NETA, AND M. HUSSAINI, A perfectly matched layer approach to the linearized shallow water equations models, Monthly Weather Rev., 132 (2004), pp 1369-1378.
23. S. TSYNKOV, Numerical solution of problems on unbounded domains, A review, Appl. Numer. Math., 27 (1998), pp. 465-532.
24. L. ZHAO AND A. CANGELLARIS, GT-PML: Generalized theory of perfectly matched layers and its application to reflectionless truncation of finite-difference time-domain grids, IEEE Trans. Microwave Theory Tech., 44 (1996), pp. 2555-2563.