An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems

Journal of Computational Physics

Volumn 223, Issue 2, 2007, Pages 469-488

  Bermudez A ^a   Hervella Nieto, L ^b   Prieto, A ^a   Rodriguez R ^c  

^a UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

^b UNIVERSITY OF A CORUÑA   (Spain)

^c UNIVERSITY OF CONCEPCIÓN   (Chile)

Author keywords

Finite element method; Helmholtz equation; Perfectly matched layer; Time harmonic scattering

Indexed keywords

ACOUSTIC WAVE SCATTERING; NUMERICAL METHODS;

ACOUSTIC SCATTERING PROBLEM; DISCRETE PROBLEMS; HELMHOLTZ'S EQUATIONS; ITS EFFICIENCIES; NUMERICAL TESTS; PERFECTLY MATCHED LAYER; PERFECTLY MATCHED LAYER TECHNIQUES; SPURIOUS REFLECTIONS; TIME-HARMONIC; TIME-HARMONIC SCATTERING;

FINITE ELEMENT METHOD;

EID: 33947252305     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.09.018     Document Type: Article

References (34)

1. Abarbanel S., Gottlieb D., and Hesthaven J.S. Well-posed perfectly matched layers for advective acoustics. J. Comput. Phys. 154 (1999) 266-283
2. Astley R.J. Infinite elements for wave problems: a review of current formulations and an assessment of accuracy. Int. J. Numer. Methods Eng. 49 (2000) 951-976
3. Asvadurov S., Druskin V., Guddati M.N., and Knizhnerman L. On optimal finite-difference approximation of PML. SIAM J. Numer. Anal. 41 (2003) 287-305
4. Basu U., and Chopra A.K. Perfectly matched layers for time-harmonic elastodynamics of unbounded domains: theory and finite-element implementation. Comput. Methods Appl. Mech. Eng. 192 (2003) 1337-1375
5. Bayliss A., and Turkel E. Radiation boundary conditions for wave-like equations. Comm. Pure Appl. Math. 33 (1980) 707-725
6. Bécache E., Bonnet-Benn Dhia A.-S., and Legendre G. Perfectly matched layer for the convected Helmholtz equation. SIAM J. Numer. Anal. 42 (2004) 409-433
7. Bécache E., and Joly P. On the analysis of Bérenger's perfectly matched layers for Maxwell's equations, M2AN. Math. Model. Numer. Anal. 36 (2002) 87-119
8. Berenger J.P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185-200
9. Berenger J.P. Perfectly matched layer for the FDTD solution of wave-structure interaction problems. IEEE Trans. Antennas Propag. 44 (1996) 110-117
10. Berenger J.P. Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1996) 363-379
11. Bermúdez A., Hervella-Nieto L.M., Prieto A., and Rodri{dotless}́guez R. An exact bounded PML for the Helmholtz equation. C.R. Acad. Sci. Paris Ser. I Math. 339 (2004) 803-808
12. Chew W.C., and Weedom W.H. PML 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates. Microwave Opt. Technol. Lett. 7 (1994) 599-604
13. Collino F., and Monk P. The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19 (1998) 2061-2090
14. Collino F., and Monk P. Optimizing the perfectly matched layer. Comput. Methods Appl. Mech. Eng. 164 (1998) 157-171
15. Collino F., and Tsogka C. Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 66 (2001) 294-307
16. Demkowicz L., and Ihlenburg F. Analysis of a coupled finite-infinite element method for exterior Helmholtz problems. Numer. Math. 88 (2001) 43-73
17. Engquist B., and Majda A. Absorbing boundary conditions for the numerical simulation of waves. Math. Comp. 31 (1977) 629-651
18. K. Feng, Finite element method and natural boundary reduction, Proceedings of the International Congress of Mathematicians, Warsaw, Poland, 1983, pp. 1439-1453.
19. Givoli D. Nonreflecting boundary conditions. J. Comput. Phys. 94 (1991) 1-29
20. Givoli D., and Neta B. High-order non-reflecting boundary scheme for time-dependent waves. J. Comput. Phys. 186 (2004) 24-46
21. Harari I., Slavutin M., and Turkel E. Analytical and numerical studies of a finite element PML for the Helmholtz equation. J. Comput. Acoust. 8 (2000) 121-137
22. Hohage T., Schmidt F., and Zschiedrich L. Solving time-harmonic scattering problems based on the pole condition II: convergence of the PML method. SIAM J. Math. Anal. 35 (2003) 547-560
23. Hu F.Q. A stable, perfectly matched layer for linearized Euler equations in unsplit physical variables. J. Comput. Phys. 173 (2001) 455-480
24. Ihlenburg F. Finite Element Analysis of Acoustical Scattering (1998), Springer-Verlag, New York
25. van Joolen V.J., Neta B., and Givoli D. High-order Higdon-like boundary conditions for exterior transient problems. Int. J. Numer. Methods. Eng. 63 (2005) 1041-1068
26. Lassas M., and Somersalo E. On the existence and convergence of the solution of PML equations. Computing 60 (1998) 228-241
27. Lions J.L., Métral J., and Vacus O. Well-posed absorbing layer for hyperbolic problems. Numer. Math. 92 (2002) 535-562
28. Navon I.M., Neta B., and Hussaini M.Y. A perfectly matched layer approach to the linearized shallow water equations models. Monthly Weather Rev. 132 (2004) 1369-1378
29. Nédélec J.-C. Acoustic and electromagnetic equations. Integral Representations for Harmonic Problems (2000), Springer-Verlag, New York
30. Qi Q., and Geers T.L. Evaluation of the perfectly matched layer for computational acoustics. J. Comput. Phys. 139 (1998) 166-183
31. Shirron J.J., and Babuška I. A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems. Comput. Methods Appl. Mech. Eng. 164 (1998) 121-139
32. Sjogreen B., and Petersson N.A. Perfectly matched layers for Maxwell's equations in second order formulation. J. Comput. Phys. 209 (2005) 19-46
33. Turkel E., and Yefet A. Absorbing PML boundary layers for wave-like equations. Appl. Numer. Math. 27 (1998) 533-557
34. Zeng Y.Q., He J.Q., and Liu Q.H. The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media. Geophysics 66 (2001) 1258-1266