Local absorbing boundaries of elliptical shape for scalar waves

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 45-47, 2004, Pages 4979-5015

  Kallivokas, Loukas F ^a   Lee, Sanghoon ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Absorbing; Artificial boundaries; Elliptical shape; Scalar waves; Time and frequency domains

Indexed keywords

ABSORPTION; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; HARMONIC ANALYSIS;

COMPUTATIONAL SAVINGS; FREQUENCY DOMAIN; SCALAR WAVES; TRUNCATION;

WAVE EQUATIONS;

MATHEMATICAL METHOD;

EID: 4243130914     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.04.007     Document Type: Article

References (59)

1. Harari I. Hughes T.J.R. A cost comparison of boundary element and finite element methods for problems in time-harmonic acoustics Comput. Methods Appl. Mech. Engrg. 97 1992 77-102
2. Mindlin R.D. Bleich H.H. Response of an elastic cylindrical shell to a transverse, step shock wave ASME J. Appl. Mech. 20 1953 189-195
3. Kausel E. Tassoulas J.L. Transmitting boundaries : a closed-form comparison Bull. Seismol. Soc. Am. 71 1981 143-159
4. Wolf J.P. A comparison of time-domain transmitting boundaries Earthq. Engrg. Str. Dyn. 14 1986 655-673
5. Kausel E. Local transmitting boundaries ASCE J. Engrg. Mech. 114 6 1988 1011-1027
6. Givoli D. Non-reflecting boundary conditions: A review J. Comput. Phys. 94 1 1991 1-29
7. Tsynkov S.V. Numerical solution of problems on unbounded domains. A review Appl. Numer. Math. 27 1998 465-532
8. Engquist B. Majda A. Absorbing boundary conditions for the numerical simulation of waves Math. Comput. 31 1977 629-651
9. Engquist B. Majda A. Radiation boundary conditions for acoustic and elastic wave calculations Commun. Pure Appl. Math. 32 1979 313-357
10. Bayliss A. Turkel E. Radiation boundary conditions for wave-like equations Commun. Pure Appl. Math. 33 1980 707-725
11. Bayliss A. Turkel E. Far field boundary conditions for compressible flows J. Comput. Phys. 48 1982 182-199
12. Bayliss A. Gunzburger M. Turkel E. Boundary conditions for the numerical solution of elliptic equations in exterior regions SIAM J. Appl. Math. 42 2 1982 430-451
13. Assaad J. Decarpigny J.-N. Bruneel C. Bossut R. Hamonic B. Application of the finite element method to two-dimensional radiation problems J. Acoust. Soc. Am. 94 1 1993 562-573
14. Bossut R. Decarpigny J.-N. Finite element modeling of radiating structures using dipolar damping elements J. Acoust. Soc. Am. 86 4 1989 1234-1244
15. Abboud N.N. Pinsky P.M. Finite element solution and dispersion analysis for the transient structural acoustics problem Appl. Mech. Rev. 43 5 1990 S381- S388 Pt. 2
16. Pinsky P.M. Abboud N.N. Transient finite element analysis of the exterior structural acoustics problem ASME J. Vibrat. Acoust. 112 1990 245-256
17. Pinsky P.M. Abboud N.N. Finite element solution of the transient exterior structural acoustics problem based on the use of radially asymptotic boundary operators Comput. Methods Appl. Mech. Engrg. 85 1991 311-348
18. MacCamy R.C. Marin S.P. A finite element method for exterior interface problems Int. J. Math. Math. Sci. 3 1980 311-350
19. Givoli D. Keller J.B. A finite element method for large domains Comput. Methods Appl. Mech. Engrg. 76 1989 41-66
20. Keller J.B. Givoli D. Exact non-reflecting boundary conditions J. Comput. Phys. 82 1989 172-192
21. Harari I. Hughes T.J.R. Design and analysis of finite element methods for the Helmholtz equation in exterior domains Appl. Mech. Rev. 43 5 1990 S366-S373 Pt. 2
22. Harari I. Hughes T.J.R. Finite element methods for the Helmholtz equation in an exterior domain: Model problems Comput. Methods Appl. Mech. Engrg. 87 1991 59-96
23. Harari I. Hughes T.J.R. Galerkin/least-squares finite element methods for the reduced wave equation with non-reflecting boundary conditions in unbounded domains Comput. Methods Appl. Mech. Engrg. 98 1992 411-454
24. Lubich C. Schädle A. Fast convolution for nonreflecting boundary conditions SIAM J. Sci. Comput. 24 1 2002 161-182
25. Alpert B. Greengard L. Hagstrom T. Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation SIAM J. Numer. Anal. 37 4 2000 1138-1164
26. Bettess P. Zienkiewicz O.C. Diffraction and refraction of surface waves using finite and infinite elements Int.J. Numer. Methods Engrg. 11 1977 1271-1290
27. Bettess P. Infinite elements Int. J. Numer. Methods Engrg. 11 1977 53-64
28. Burnett D.S. A three-dimensional acoustic infinite element based on a prolate spheroidal multipole expansion J. Acoust. Soc. Am 96 5 1994 2798-2816
29. Burnett D.S. Holford R.L. Prolate and oblate spheroidal acoustic infinite elements Comput. Methods Appl. Mech. Engrg. 158 1998 117-142
30. Burnett D.S. Holford R.L. An ellipsoidal acoustic infinite element Comput. Methods Appl. Mech. Engrg. 164 1998 49-76
31. Astley J. Transient wave envelope elements for wave problems J. Sound Vibrat. 192 1996 245-261
32. Astley J. Transient spheroidal elements for unbounded wave problems Comput. Methods Appl. Mech. Engrg. 164 1998 3-15
33. Bérenger J.P. A perfectly matched layer for the absorption of electromagnetic waves J. Comput. Phys. 41 1994 115-135
34. Qi Q. Geers T.L. Evaluation of the perfectly matched layer for computational acoustics J. Comput. Phys. 139 1 1998 166-183
35. Abarbanel S. Gottlieb D. A mathematical analysis of the PML method J. Comput. Phys. 134 1997 357-363
36. Kriegsmann G.A. Taflove A. Umashankar K.R. A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach IEEE Trans. Antennas Propagat. AP-35 2 1987 153-160
37. Jones D.S. An approximate boundary condition in acoustics J. Sound. Vibrat. 121 1 1988 37-45
38. Khebir A. Ramahi O. Mittra R. An efficient partial differential equation technique for solving the problem of scattering by objects of arbitrary shape Microwave Opt. Tech. Lett. 2 1989 229-233
39. Lee C.F. Shin R.T. Kong J.A. McCartin B.J. Absorbing boundary conditions on circular and elliptical boundaries J. Electromagn. Waves Applicat. 4 10 1990 945-962
40. Li Y. Cendes Z.J. Modal expansion absorbing boundary conditions for two-dimensional electromagnetic scattering IEEE Trans. Magn. 29 1993 1835-1838
41. Stupfel B. Absorbing boundary conditions on arbitrary boundaries for the scalar and wave equations IEEE Trans. Antennas Propagat. 42 6 1994 773-780
42. Grote M.J. Keller J.B. On nonreflecting boundary conditions J. Comput. Phys. 122 1995 231-243
43. Antoine X. Barucq H. Bendali A. Bayliss-Turkel-like radiation conditions on surfaces of arbitrary shape J. Math. Anal. Applicat. 229 1999 184-211
44. Barry A. Bielak J. MacCamy R.C. On absorbing boundary conditions for wave propagation J. Comput. Phys. 79 1988 449-468
45. Kallivokas L.F. Bielak J. MacCamy R.C. Symmetric local absorbing boundaries in time and space ASCE J. Engrg. Mech. 117 9 1991 2027-2048
46. L.F. Kallivokas, Absorbing boundary conditions and finite elements for transient and harmonic steady-state acoustic fluid-structure interaction, Thesis presented to Carnegie Mellon University in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Pittsburgh, 1995
47. L.F. Kallivokas, J. Bielak, R.C. MacCamy, Absorbing boundary conditions of arbitrary shape for the three-dimensional wave equation, in: Proceedings of the IUTAM Symposium on Computational Methods for Unbounded Domains, Kluwer Academic Publishers, Boulder, CO, July 1997, 221-228
48. Kallivokas L.F. Bielak J. MacCamy R.C. A simple impedance-infinite element for the finite element solution of the three-dimensional wave equation in unbounded domains Comput. Methods Appl. Mech. Engrg. 147 1997 235-262
49. Djellouli R. Farhat C. Macedo A. Tezaur R. Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries J. Comput. Acoust. 8 1 2000 81-99
50. Bhattacharyya S.K. Sathyapal S. Vendhan C.P. Absorbing boundary condition on elliptic boundary for the finite element analysis of water wave diffraction by large elongated bodies Int. J. Numer. Methods Fluids 37 2001 249-277
51. Meade D.B. Slade G.W. Peterson A.F. Webb K.J. Comparison of local radiation boundary conditions for the scalar Helmholtz equation with general boundary shape IEEE Trans. Antennas Propagat. 43 1995 1-5
52. Lichtenberg B. Webb K.J. Meade D.B. Peterson A.F. Comparison of two-dimensional conformal local radiation boundary conditions Electromagnetics 16 1996 359-384
53. Kallivokas L.F. Bielak J. Time-domain analysis of transient structural acoustics problems based on the finite element method and a novel absorbing boundary element J. Acoust. Soc. Am. 94 6 1993 3480-3492
54. Kallivokas L.F. Bielak J. An element for the analysis of transient exterior fluid-structure interaction problems using the FEM Finite Elem. Anal. Design 15 1993 69-81
55. Courant R. Hilbert D. Methods of Mathematical Physics, Vol. II Partial Differential Equations Wiley Classics Edition 1989 Interscience Publishers New York, NY
56. T. Hagstrom, and S.I. Hariharan, Progressive wave expansions and open boundary problems, In: B. Engquist, G.A. Kriegsmann (Eds.), Computational Wave Propagation, IMA Volumes in Mathematics and its Applications, vol. 86, 1997, 23-43
57. Hagstrom T. Hariharan S.I. A formulation of asymptotic and exact boundary conditions using local operators Appl. Numer. Math. 27 1998 403-416
58. Givoli D. High-order non-reflecting boundary conditions without high-order derivatives J. Computat. Phys. 170 2001 849-870
59. Givoli D. Neta B. High-order non-reflecting boundary scheme for time-dependent waves J. Computat. Phys. 186 2003 24-46