Boundary infinite elements for the Helmholtz equation in exterior domains

International Journal for Numerical Methods in Engineering

Volumn 41, Issue 6, 1998, Pages 1105-1131

  Harari, Isaac ^a   Barbone, Paul E ^b   Slavutin, Michael ^c   Shalom, Rami ^a  

^a TEL AVIV UNIVERSITY   (Israel)

^b BOSTON UNIVERSITY   (United States)

^c NONE

Author keywords

Acoustics; Finite element methods; Infinite elements; Unbounded domains

Indexed keywords

ACOUSTICS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; INTEGRATION;

BOUNDARY INFINITE ELEMENTS; HELMHOLTZ EQUATIONS;

BOUNDARY ELEMENT METHOD;

EID: 0032024388     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980330)41:6<1105::AID-NME327>3.0.CO;2-0     Document Type: Article

References (46)

1. R. P. Shaw, 'Integral equation methods in acoustics', in C. A. Brebbia (ed.), Boundary Elements X, Vol. 4, Springer, Berlin, 1988, pp. 221-244.
2. N. N. Abboud and P. M. Pinsky, 'Finite element dispersion analysis for the three-dimensional second-order scalar wave equation', Int. J. Numer. Meth. Engng., 35, 1183-1218 (1992).
3. I. Babuška, F. Ihlenburg, E. T. Paik and St. A. Sauter, 'A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution', Comput. Meth. Appl. Mech. Engng., 128, 325-359 (1995).
4. K. Grosh and P. M. Pinsky, 'Complex wave-number dispersion analysis of Galerkin and Galerkin least squares methods for fluid-loaded plates', Comput. Meth. Appl. Mech. Engng., 113, 67-98 (1994).
5. I. Harari and T. J. R. Hughes, 'Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains', Comput. Meth. Appl. Mech. Engng., 98, 411-454 (1992).
6. A. Oberai and P. M. Pinsky, 'A new stabilized finite element method for the Helmholtz equation with minimal dispersion', Int. J. Numer. Meth. Engng., to be submitted.
7. J. R. Stewart and T. J. R. Hughes, 'Adaptive finite element methods for the Helmholtz equation in exterior domains', in Proc. Symp. on Large-Scale Structures in Acoustics and Electromagnetics, National Academy Press, 1995.
8. L. L. Thompson and P. M. Pinsky, 'A Galerkin least squares finite element method for the two-dimensional Helmholtz equation', Int. J. Numer. Meth. Engng., 38, 371-397 (1995).
9. 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. Meth. Engg., 3, 131-309 (1996).
10. D. Givoli, Numerical Methods for Problems in Infinite Domains, Elsevier, Amsterdam, 1992.
11. D. Givoli and J. B. Keller, 'A finite element method for large domains', Comput. Meth. Appl. Mech. Engng., 76, 41-66 (1989).
12. K. Feng, 'Asymptotic radiation conditions for reduced wave equation', J. Comput. Math., 2, 130-138 (1984).
13. M. Masmoudi, 'Numerical solution for exterior problems', Numer. Math., 51, 87-101 (1987).
14. R. J. Astley, 'FE mode-matching schemes for the exterior Helmholtz problem and their relationship to the FE-DtN approach', Comm. Numer. Meth. Engng., 12, 257-267 (1996).
15. H. S. Chen and C. C. Mei, 'Oscillations and wave forces in a man-made harbor in the open sea', in Proc. 10th Symp. on Naval Hydrodynamics, Cambridge, MA, 1974, pp. 573-594, Office of Naval Research, Department of the Navy.
16. R. J. Astley, G. J. Macaulay and J. -P. Coyette, 'Mapped wave envelope elements for acoustical radiation and scattering', J. Sound Vib., 170, 97-118 (1994)
17. P. Bettess, 'Infinite elements', Int. J. Numer. Meth. Engng., 11, 53-64 (1977).
18. D. S. Burnett, 'A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion', J. Acoust. Soc. Am., 96, 2798-2816 (1994).
19. K. Gerdes and L. Demkowicz, 'Solution of 3D-Laplace and Helmholtz equations in exterior domains using hp-infinite elements', Comput. Meth. Appl. Mech. Engng., 137, 239-273 (1996).
20. O. C. Zienkiewicz, K. Bando, P. Bettess, C. Emson and T. C. Chiam, 'Mapped infinite elements for exterior wave problems', Int. J. Numer. Meth. Engng., 21, 1229-1251 (1985).
21. I. Harari, P. E. Barbone and J. M. Montgomery, 'Finite element formulations for exterior domains: application to hybrid methods, non-reflecting boundary conditions and infinite elements', Int. J. Numer. Meth. Engng., 40, 2791-2805 (1997).
22. S. W. Key, 'A specialization of Jones' generalization of the direct-stiffness method of structural analysis', AIAA J., 9, 984-985 (1971).
23. 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, 326-327 (1979).
24. E. Haugeneder and H. A. Mang, 'On an improper modification of a variational principle for finite element plate analysis', Angewandt Mathematik Mechanik, 59, 637-640 (1979).
25. 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, pp. 187-198.
26. H. A. Mang and R. H. Gallagher, 'A critical assessment of the simplified hybrid displacement method', Int. J. Numer. Meth. Engng., 11, 145-167 (1977).
27. I. Stakgold, Boundary Value Problems of Mathematical Physics, Vol. II, Macmillan, New York, 1968.
28. C. H. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domains, Springer, Berlin, 1975.
29. T. J. R. Hughes, 'Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods', Comput. Meth. Appl. Mech. Engng., 127, 387-401 (1995).
30. I. Harari and T. J. R. Hughes, 'Analysis of continuous formulations underlying the computation of time-harmonic acoustics in exterior domains', Comput. Meth. Appl. Mech. Engng., 97, 103-124 (1992).
31. I. Harari and T. J. R. Hughes, 'Studies of domain-based formulations for computing exterior problems of acoustics', Int. J. Numer. Meth. Engng., 37, 2935-2950 (1994).
32. J.-L. Lions and E. Magenes, Non-homogeneous Boundary Value Problems and Applications, Vol. 1, Springer, New York, 1972.
33. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991.
34. D. Givoli and J. B. Keller, 'Non-reflecting boundary conditions for elastic waves', Wave Motion, 12, 261-279 (1990).
35. R. Courant, 'Variational methods for the solution of problems of equilibrium and vibrations', Bull. Am. Math. Soc., 49, 1-23 (1943).
36. I. Babuska, 'The finite element method with Lagrangian multipliers', Numer. Math., 20, 179-192 (1973).
37. R. E. Jones, 'A generalization of the direct-stiffness method of structural analysis', AIAA J., 2, 821-826 (1964).
38. J. R. O'Leary and I. Harari, 'Finite element analysis of stiffened plates', Comput. Struct., 21, 973-985 (1985).
39. M. A. Aminpour, J. B. Ransom and S. L. McCleary, 'Coupled analysis method for structures with independently modelled finite element subdomains', Int. J. Numer. Meth. Engng., 38, 3695-3718 (1995).
40. C. Farhat and M. Geradin, 'Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations', Comput. Meth. Appl. Mech. Engng., 97, 333-354 (1992).
41. H. J. C. Barbosa and T. J. R. Hughes, 'The finite element method with Lagrange multipliers on the boundary: Circumventing the Babuška-Brezzi condition', Comput. Meth. Appl. Mech. Engng., 85, 109-128 (1991).
42. R. Stenberg, 'On some techniques for approximating boundary conditions in the finite element method', J. Comput. Appl. Math., 63, 139-148 (1995).
43. J. Nitsche, 'Über ein Variationsprinzip zur lösung von Dirichlet-problemen bei Verwendung von teilräumen, die keinen randbedingungen unterworfen sind', Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 36; 1971, pp. 9-15.
44. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1987.
45. A. Mizukami, 'A mixed finite element method for boundary flux computation', Comput. Meth. Appl. Mech. Engng., 57, 239-243 (1986).
46. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, U.S. Department of Commerce, National Bureau of Standards, Washington DC, 1972.