A review of infinite element methods for exterior Helmholtz problems

Journal of Computational Acoustics

Volumn 8, Issue 1, 2000, Pages 43-62

  Gerdes, Klaus ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034345509     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X00000042     Document Type: Review

References (64)

1. R. J. Astley, "Wave envelope and infinite elements for acoustical radiation," Int. J. Num. Meth. Flu. 3 (1983), 507-526.
2. R. J. Astley and W. Eversman, "A note on the utility of a wave envelope approach in finite element duct transmission studies," J. Sound Vib. 76 (1981), 595-601.
3. R. J. Astley and W. Eversman, "Finite element formulations for acoustic radiation," J. Sound Vib. 88 (1983), 47-64.
4. R. J. Astley and W. Eversman, "Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets," J. Am. Inst. Aero. Ast. 2 (1984), 1719-1726.
5. R. J. Astley, G. J. Macaulay, and J. P. Coyette, "Mapped wave envelope elements for acoustical radiation and scattering," J. Sound Vib. 170 (1994), 97-118.
6. R. J. Astley, "Infinite elements for wave problems: A review of current formulations and an assessment of accuracy," Int. J. Num. Meth. Eng. submitted.
7. G. Beer and J. L. Meek, "Infinite domain elements," Int. J. Num. Meth. Eng. 17 (1981), 43-52.
8. P. Bettess, "Infinite elements," Int. J. Num. Meth. Eng. 11 (1977) 53-64.
9. P. Bettess and O. C. Zienkiewicz, "Diffraction and refraction of surface waves using finite and infinite elements," Int. J. Num. Meth. Eng. 11 (1977), 1271-1290.
10. P. Bettess, "More on infinite elements," Int. J. Num. Meth. Eng. 15 (1980), 1613-1626.
11. P. Bettes, C. Emson, and T. C. Chiam, "A new mapped infinite element for exterior wave problems," in Numerical Methods in Coupled Systems, eds. R. W. Lewis, P. Bettess, and E. Hinton (John Wiley & Sons Ltd., 1984), pp. 489-504.
12. P. Bettess, "Finite element modeling for exterior electromagnetic problems," Proc. COMPUMAG (Graz, 1987), pp. 49-54.
13. P. Bettess, Infinite Elements (Penshaw, Sunderland, UK, 1992).
14. P. Bettess and J. A. Bettess, "Infinite elements for dynamic problems: Part 1," Eng. Comp. 8 (1991), 99-124.
15. P. Bettess and J. A. Bettess, "Infinite elements for dynamic problems: Part 2," Eng. Comp. 8 (1991), 125-151.
16. D. S. Burnett, "A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion," J. Acoust. Soc. Am., 96 (1994), 2798-2816.
17. D. S. Burnett and R. L. Holford, "An ellipsoidal acoustic infinite element," Comput. Meths. Appl. Mech. Eng. 164 (1998), 49-76.
18. W. Cecot, L. Demkowicz, and W. Rachowicz, "A two-dimensional infinite element for Maxwell's equation," submitted.
19. Y. K. Chow and I. M. Smith, "Static and periodic infinite solid elements," Int. J. Num. Meth. Eng. 17 (1981), 503-526.
20. J. L. Cipolla and M. J. Butler, "Infinite elements in the time domain using a prolate spheroidal multipole expansion," Int. J. Num. Meth. Eng. 43 (1998), 889-908.
21. J. P. Coyette, "Application of a new envelope formulation to exterior acoustic and elastoacoustic problems," J. de Physique IV 2 (1992), 1069-1072.
22. L. Cremers, K. R. Fyfe, and J. P. Coyette, "A Variable order infinite acoustic wave envelope element," J. Sound Vib. 171 (1994), 483-508.
23. L. Cremers and K. R. Fyfe, "On the use of variable order infinite wave envelope elements for acoustic radiation and scattering," J. Acoust. Soc. Am. 97 (1995), 2028-2040.
24. L. Demkowicz, "Asymptotic convergence in finite and boundary element methods: Part 1: Theoretical results," Comp. Math. Appl. 27 (1994), 69-84.
25. L. Demkowicz, "Asymptotic convergence in finite and boundary element methods: Part 2: The LBB constant for rigid and elastic scattering problems," Comp. Math. Appl. 28 (1994), 93-109.
26. L. Demkowicz and J. T. Oden, "Recent progress on application of hp-adaptive BE/FE methods to elastic scattering," Int. J. Num. Meth. Eng. 37 (1994), 2893-2910.
27. L. Demkowicz and K. Gerdes, "Convergence of the infinite element methods for the Helmholtz equation in separable domains," Numerische Mathematik 79 (1998), 11-42.
28. L. Demkowicz, K. Gerdes, C. Schwab, A. Bajer, and T. Walsh, "A new flexible implementation of general hp-FEM in 2D," Comp. Vis. Sci. 1 (1998), 145-163.
29. L. Demkowicz and F. Ihlenburg, "Analysis of a coupled finite-infinite element method for exterior Helmholtz problems," submitted.
30. L. Demkowicz and M. Pal, "An infinite element for Maxwell's equations," Comput. Meths. Appl. Mech. Eng. 164 (1998), 77-94.
31. T. L. Geers, Computational Methods for Unbounded Domains (Kluwer Academic Publishers, 1998).
32. K. Gerdes, "Solution of the 3D Laplace and Helmholtz equation in exterior domains of arbitrary shape using HP-finite-infinite elements," Ph.D. Thesis, The University of Texas at Austin, 1996.
33. K. Gerdes and L. Demkowicz, "Solution of 3D Laplace and Helmholtz equations in exterior domains using hp infinite element methods," Comput. Meths. Appl. Mech. Eng. 137 (1996), 239-273.
34. K. Gerdes and F. Ihlenburg, "On the pollution effect in FE simulations of the 3D-Helmholtz equation," Comput. Meths. Appl. Mech. Eng. 170 (1999), 155-172.
35. K. Gerdes, "The conjugated versus the unconjugated infinite element method for the Helmholtz equation in exterior domains," Comput. Meths. Appl. Mech. Eng. 152 (1998) 125-145.
36. K. Gerdes, "Solution of the 3D Helmholtz equation in exterior domains of arbitrary shape using hp-Finite-Infinite Elements," Fin. Ele. Anal. Des. 29 (1998) 1-20.
37. K. Gerdes, "A summary of Infinite Element Formulations for Exterior Helmholtz Problems," Comput. Meths. Appl. Mech. Eng. 164 (1998) 95-105.
38. K. Gerdes, "Infinite element methods for low frequency scattering problems," in preparation.
39. D. Givoli, Numerical Methods for Problems in Infinite Domains (Elsevier, Amsterdam, 1992).
40. M. D. Greenberg, Foundation of Applied Mathematics (Prentice Hall, 1978).
41. I. Harari, P. E. Barbone, M. Slavutin, and R. Shalom, "Boundary infinite elements for the Helmholtz Equation in exterior domains," preprint.
42. R. L. Holford, "A multipoly expansion for the acoustic field exterior to a prolate or oblate spheroid," submitted.
43. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Applied Mathematical Sciences Vol. 132, Springer, 1998).
44. Y. Kagawa, T. Yamabuchi, and K. Kawakami, "Numerical analysis of unbounded Poisson and Helmholtz problems using an infinite element approach," Electron. Commun. Japan 65 (1982), 45-54.
45. L. F. Kallivokas and J. Bielak, "A simple impedance-infinite element for the finite element solution of the three-dimensional wave equation in unbounded domains" in print.
46. L-H. Kim, H.-K. Jumg, G.-S. Lee, and S.-Y. Hahn, "Magnetic field computations by infinite elements," J. Appl. Phys. 53 (1982), 8372-8374.
47. R. Leis, Initial Boundary Value Problems in Mathematical Physics (Teubner, 1986).
48. n type decays," Int. J. Num. Meth. Eng. 17 (1981), 347-355.
49. F. Medina, "An axisymmetric infinite element," Int. J. Num. Meth. Eng. 17 (1981), 1177-1185.
50. P. M. Morse and J. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953).
51. A. A. Oberai, M. Malhotra, and P. M. Pinsky, "On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation," Appl. Num. Math. 27 (1998), 443-464.
52. Patent Nos. US005604891/US005604893, "3-D acoustic infinite element based on an oblate/ prolate spheroidal multipole expansion," (1997).
53. S. Pissanetzky, "Solution of three-dimensional, anisotropic, nonlinear problems of magnetostatics using two scalar potentials and infinite multipolar elements and automatic mesh generation," IEEE Trans. Magnetics 18 (1981), 346-370.
54. S. Pissanetzky, "An infinite element and a formula for numerical quadrature over an infinite interval," Int. J. Num. Meth. Eng. 19 (1983), 913-928.
55. S. Pissanetzky, "A simple infinite element," COMPEL 3 (1984), 107-114.
56. L. Resende, "Review of Infinite Elements," Nonlinear Structural Mechanics Research Unit, Cape Town Univ. (1982).
57. J. J. Shirron, "Solution of exterior Helmholtz problems using finite and infinite elements," Ph.D. Thesis, University of Maryland, 1995.
58. J. J. Shirron and I. Babuska, "A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems," Comput. Meths. Appl. Mech. Eng. 164 (1998), 121-139.
59. A. Toselli, "A new family of exponential infinite elements for the analysis of lossless electromagnetic waveguides," Comput. Meths Appl. Mech. Eng. 140 (1997), 221-235.
60. C. H. Wilcox, "A generalisation of theorems of Rellich and Atkinson," Proc. Am. Math. Soc. 7 (1956), 271-276.
61. J. P. Wolf and C. Song, Finite-Element Modelling of Unbounded Media (Wiley, 1996).
62. O. C. Zienkiewicz and P. Bettess, "Infinite elements in the study of fluid structure interaction problems," Proc. 2nd Int. Symp. Comp. Methods Appl. Sci., Versailles, 1975.
63. O. C. Zienkiewicz, C. Emson, and P. Bettess, "A novel boundary infinite element," Int. J. Num. Meth. Eng. 19 (1983), 393-404.
64. O. C. Zienkiewicz, K. Bando, P. Bettess, C. Emson, and T. C. Chiam, "Mapped infinite elements for exterior wave problems," Int. J. Num. Meth. Eng. 21 (1985), 1229-1251.