Higher-order boundary infinite elements

Computer Methods in Applied Mechanics and Engineering

Volumn 164, Issue 1-2, 1998, Pages 107-119

  Harari, Isaac ^a   Shalom, Rami ^a   Barbone, Paul E ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY ELEMENT METHOD; BOUNDARY VALUE PROBLEMS; FINITE ELEMENT METHOD;

HIGHER-ORDER BOUNDARY INFINITE ELEMENTS; TIME-HARMONIC ACOUSTICS;

WAVE EQUATIONS;

EID: 0032475729     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00049-8     Document Type: Article

References (31)

1. [1] N.N. Abboud and P.M. Pinsky, Finite element dispersion analysis for the three-dimensional second-order scalar wave equation, Int. J. Numer. Methods Engrg. 35(6) (1992) 1183-1218.
2. [2] R.J. Astley, FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach, Comm. Numer. Methods Engrg. 12(4) (1996) 257-267.
3. [3] R.J. Astley, G.J. Macaulay and J.-P. Coyette, Mapped wave envelope elements for acoustical radiation and scattering, J. Sound Vib. 170(1) (1994) 97-118.
4. [4] I. Babuška, F. Ihlenburg, E.T. Paik and S.A. Sauter, A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution, Comput. Methods Appl. Mech. Engrg. 128(3-4) (1995) 325-359.
5. [5] P. Bettess, Infinite elements, Int. J. Numer. Methods Engrg. 11(1) (1977) 53-64.
6. [6] D.S. Burnett, A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion, J. Acoust. Soc. Am. 96(5) (1994) 2798-2816.
7. [7] H.S. Chen and C.C. Mei, Oscillations and wave forces in a man-made harbor in the open sea, in: Tenth Symposium on Naval Hydrodynamics, pp. 573-594, Cambridge, Massachusetts, 1974. Office of Naval Research, Department of the Navy.
8. [8] K. Feng, Asymptotic radiation conditions for reduced wave equation, J. Comput. Math. 2(2) (1984) 130-138.
9. [9] R.H. Gallagher, E. Haugeneder and H.A. Mang, Limitations on methods of handling incompatible basis functions in boundary value problems, Trans. Am. Nucl. Soc. 33 (1979) 326-327.
10. [10] K. Gerdes and L. Demkowicz, Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements, Comput. Methods Appl. Mech. Engrg. 137(3-4) (1996) 239-273.
11. [11] D. Givoli, Numerical methods for problems in infinite domains, in: Vol. 33 Studies in Applied Mechanics (Elsevier Scientific Publishing Co., Amsterdam, 1992).
12. [12] D. Givoli and J.B. Keller, A finite element method for large domains, Comput. Methods Appl. Mech. Engrg. 76(1) (1989) 41-66.
13. [13] K. Grosh and P.M. Pinsky, Complex wave-number dispersion analysis of Galerkin and Galerkin least squares methods for fluid-loaded plates, Comput. Methods Appl. Mech. Engrg. 113(1-2) (1994) 67-98.
14. [14] I. Harari, P.E. Barbone and J.M. Montgomery. Finite element formulations for exterior problems: Application to hybrid methods, non-reflecting boundary conditions and infinite elements, Int. J. Numer. Methods Engrg. 40(15) (1997) 2791-2805.
15. [15] I. Harari, P.E. Barbone, M. Slavutin and R. Shalom, Boundary infinite elements for the Helmholtz equation in exterior domains, Int. J. Numer. Methods Engrg. 41(6) (1998) 1105-1131.
16. [16] I. Harari, K. Grosh, T.J.R. Hughes, M. Malhotra, P.M. Pinsky, J.R. Stewart and L.L. Thompson, Recent developments in finite element methods for structural acoustics, Arch. Comput. Methods Engrg. 3(2-3) (1996) 131-309.
17. [17] I. Harari and T.J.R. Hughes, Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains, Comput. Methods Appl. Mech. Engrg. 97(1) (1992) 103-124.
18. [18] I. Harari and T.J.R. Hughes, Galerkin/least-squares finite element methods for the reduced wave equation with nonreflecting boundary conditions in unbounded domains, Comput. Methods Appl. Mech. Engrg. 98(3) (1992) 411-454.
19. [19] I. Harari and T.J.R. Hughes, Studies of domain-based formulations for computing exterior problems of acoustics, Int. J. Numer. Methods Engrg. 37(17) (1994) 2935-2950.
20. [20] E. Haugeneder and H.A. Mang, On an improper modification of a variational principle for finite element plate analysis, Z. Angew. Math. Mech. 59(11) (1979) 637-640.
21. [21] E. Haugeneder and H.A. Mang, Admissible and inadmissible simplifications of variational methods in finite element analysis, in: S. Nemat-Nasser, ed., Variational Methods in the Mechanics of Solids, (Pergamon Press, Oxford, 1980) 187-198.
22. [22] S.W. Key, A specialization of Jones' generalization of the direct-stiffness method of structural analysis, AIAA J. 9(5) (1971) 984-985.
23. [23] H.A. Mang and R.H. Gallagher, A critical assessment of the simplified hybrid displacement method, Int. J. Numer. Methods Engrg. 11(1) (1977) 145-167.
24. [24] M. Masmoudi, Numerical solution for exterior problems, Numer. Math. 51(1) (1987) 87-101.
25. [25] A. Oberai and P.M. Pinsky, A multiscale finite element method for the Helmholtz equation, Comput. Methods Appl. Mech. Engrg., 154(3-4) (1998) 281-297.
26. [25] R.P. Shaw, Integral equation methods in acoustics, in: C.A. Brebbia, ed. Boundary Elements X, Vol. 4 (Computational Mechanics Publications, Southampton, 1988) 221-244.
27. [27] I. Stakgold, Boundary Value Problems of Mathematical Physics. Vol. II (Macmillan, New York, 1968).
28. [28] J.R. Stewart and T.J.R. Hughes, h-adaptive finite element computation of time-harmonic exterior acoustics problems in two dimensions, Comput. Methods Appl. Mech. Engrg. 146(1-2) (1997) 65-89.
29. [29] L.L. Thompson and P.M. Pinsky, A Galerkin least-squares finite element method for the two-dimensional Helmholtz equation, Int. J. Numer. Methods Engrg. 38(3) (1995) 371-397.
30. [30] C.H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains (Springer-Verlag, Berlin, 1975).
31. [31] O.C. Zienkiewicz, K. Bando, P. Bettess, C. Emson and T.C. Chiam, Mapped infinite elements for exterior wave problems, Int. J. Numer. Methods Engrg. 21(7) (1985) 1229-1251.