Computation of far-field solutions based on exact nonreflecting boundary conditions for the time-dependent wave equation

Computer Methods in Applied Mechanics and Engineering

Volumn 190, Issue 11-12, 2000, Pages 1551-1577

  Thompson, Lonny L ^a   Huan, Runnong ^a  

^a Clemson University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; PROBLEM SOLVING; TIME DOMAIN ANALYSIS;

EXACT NONREFLECTING BOUNDARY CONDITIONS; TIME-DEPENDENT WAVE EQUATIONS;

WAVE EQUATIONS;

EID: 0034514844     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(00)00178-X     Document Type: Article

References (41)

1. K.M. Mitzner, Numerical solution forvtransient scattering from a hard surface of arbitrary shape - retarded potential technique, J. Acoust. Soc. Am. 42 (1967) 391-397.
2. C.L.S. Farn, H. Huan, Transient acoustic fields generated by a body of arbitrary shape, J. Acoust. Soc. Am. 43 (1968) 252-257.
3. H. Huan, G.C. Everstine and Y.F. Wang, Retarded potential techniques for the analysis of submerged structures impinged by weak shock waves, in: T. Belytschko, T. Geers (Eds.), Computational Methods for Fluid-Structure Interaction Problems, ASME AMD 26, 1977.
4. P.H.L. Groenenboom, Solution of the retarded potential equation and numerical stability, in: C.A. Brebbia (Ed.), Boundary Elements VI. in: Proceedings of the Sixth International Conference, July 1984.
5. C.T. Dyka, R.P. Ingel, G.C. Kirby, Stabilizing the retarded potential method for transient fluid-structure interaction problems, Int. J. Numer. Methods Engrg. 40 (1997) 3767-3783.
6. D. Givoli, Numerical methods for problems in infinite domains, Studies in Applied Mechanics, 33, Elsevier, Amsterdam, 1992.
7. S. Tsynkov, Numerical solution of problems on unbounded domains: A review, Appl. Numer. Math. 27 (1998) 465-532.
8. A. Bayliss, E. Turkel, Radiation boundary conditions for wave-like equations, Commun. Pure Appl. Math. 33 (1980) 707-725.
9. P.M. Pinsky, N.N. Abboud, 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.
10. P.M. Pinsky, L.L. Thompson, N.N. Abboud, Local high-order radiation boundary conditions for the two-dimensional time-dependent structural acoustics problem, J. Acoust. Soc. Am. 91 (3) (1992) 1320-1335.
11. L.L. Thompson, P.M. Pinsky, A space-time finite element method for the exterior acoustics problem, J. Acoust. Soc. Am. 99 (6) (1996) 3297-3311.
12. M.J. Grote, J.B. Keller, Exact nonreflecting boundary conditions for the time dependent wave equation, SIAM J. Appl. Math. 55 (1995) 280-297.
13. M.J. Grote, J.B. Keller, Nonreflecting boundary conditions for time dependent scattering, J. Comput. Phys. 127 (1996) 52-65.
14. L.L. Thompson, R. Huan, Implementation of exact nonreflecting boundary conditions in the finite element method for the time-dependent wave equation, Comput. Methods Appl. Mech. Engrg. 187 (2000) 137-159.
15. L.L. Thompson, R. Huan, Finite element formulation of exact nonreflecting boundary conditions for the time-dependent wave equation, Int. J. Numer. Methods Engrg. 45 (1999) 1607-1630.
16. R. Huan, L.L.Thompson, Accurate radiation boundary conditions for the time-dependent wave equation on unbounded domains, Int. J. Numer. Methods Engrg. 47 (2000) 1569-1603.
17. T. Hagstrom, S. Hariharan, A formulation of asymptotic and exact boundary conditions using local operators, Appl. Numer. Math. 27 (1998) 403-416.
18. B. Alpert, L. Greengard and T. Hagstrom, Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation, SIAM J. Numer. Anal., in press.
19. J.P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 185-200.
20. X. Yuan, D. Borup, J.W. Wiskin, M. Berggren, R. Eidens, S.A. Johnson, Formulation and validation of berengers PML absorbing boundary for the FDTD simulation of acoustic scattering, IEEE Trans. Ultrason. Ferro Freq. Control. 44 (4) (1997) 517-522.
21. L. Ting, M. Miksis, Exact boundary conditions for scattering problems, J. Acoust. Soc. Am. 80 (1986) 1825-1827.
22. D. Givoli, D. Kohen, Nonreflecting boundary conditions based on Kirchoff-type formulae, J. Comput. Phys. 117 (1995) 102-113.
23. J.B. Keller, D. Givoli, Exact nonreflecting boundary conditions, J. Comput. Phys. 82 (1989) 172-192.
24. L.W. Pearson, R.A. Whitaker, L.J. Bahrmasel, An exact radiation boundary condition for the finite-element solution of electromagnetic scattering on an open domain, IEEE Trans. Magn. 25 (4) (1989) 3046-3048.
25. I. Sofronov, Conditions for complete transparency on the sphere for the three-dimensional wave equation, Russian Acad. Sci. Dokl. Math. 46 (1993) 397-401.
26. I. Sofronov, Artificial boundary conditions for absolute transparency for two- and three-dimensional external time-dependent scattering problems, Euro. J. Appl. Math., 1999.
27. L. L. Thompson, P. M. Pinsky, New space-time finite element methods for fluid-structure interaction in exterior domains, Comput. Methods Fluid/Structure Interac. AMD-vol. 178, ASME (1993) 101-120.
28. L.L. Thompson, P.M. Pinsky, A space-time finite element method for structural acoustics in infinite domains, part 2: Exact time-dependent non-reflecting boundary conditions, Comput. Methods Appl. Mech. Engrg. 132 (1996) 229-258.
29. H. Lamb, Hydrodynamics, fourth Ed., Cambridge University Press, Cambridge, 1916, p. 517, Eq. (4).
30. L.L.Thompson and R.Huan, Accurate radiation boundary conditions for the two-dimensional wave equation on unbounded domains, submitted 1999.
31. N.N. Abboud, G.L. Wojcik, D.K. Vaughan, J. Mould, D.J. Powell, L. Nikodym, Finite Element Modeling for Ultrasonic Transducers, Proc. SPIE Int. Symp. Medical Imaging 1998, Ultrasonic Transducer Engineering Conference, San Diego, CA., 21-27 Feb., 1998.
32. A.S. Lyrintzis, Review: the use of Kirchoffs method in computational aeroacoustics, J. Fluids Engrg. 116 (12) (1994) 665-676.
33. J.P. Wright, Direct time integration methods for structural acoustics and far-field scattering computations, ASME J. Vib. Acoust. 117 (1995) 488-492.
34. A. Sommerfeld, Partial Differential Equations in Physics, Academic Press, New York, 1964.
35. M.J. Mohlenkamp, A fast transform for spherical harmonics, Preprint, 1997.
36. J. Driscoll, D. Healy, D. Rockmore, Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs, SIAM J. Comput. 26 (1997) 1066-1099.
37. M. Abramowitz, I. Stegun, (Eds.), Handbook of Mathematical Functions, Washington, DC: National Bureau of Standards, 1964. Reprinted by Dover Publications, New York, 1968, pp. 751-770.
38. W. Strauss, L. Vazquez, Numerical solution of a nonlinear Klein-Gordon equation, J. Comput. Phys. 28 (1978) 271-278.
39. P.M. Morse and H. Feshbach, Methods of Theoretical Physics, vol. II, McGraw-Hill, New York, 1953.
40. N.H. Ricker, Transient Waves in Visco-Elastic Media, Elsevier, Amsterdam, Netherlands, 1977.
41. P.R. Stepanishen, Transient radiation from pistons in an infinite planar baffle, J. Acoust. Soc. Am. 49 (1971) 1629-1638.