Near- and far-field boundary conditions for a finite element method for the Helmholtz equation in axisymmetric problems of underwater acoustics

Acta Acustica united with Acustica

Volumn 93, Issue 6, 2007, Pages 888-898

  Mitsoudis, Dimitrios A ^a,b  

^a UNIVERSITY OF CRETE   (Greece)

^b INSTITUTE OF COMPUTER SCIENCE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

BACKSCATTERING; BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; HELMHOLTZ EQUATION; WAVEGUIDES;

AXISYMMETRIC PROBLEMS; DTN MAPS; FAR FIELD BOUNDARY;

UNDERWATER ACOUSTICS;

EID: 37249027815     PISSN: 16101928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (32)

1. G. J. Fix, S. P. Marin: Variational methods for underwater acoustic problems. J. Comp. Physics 28 (1978) 253-270.
2. C. I. Goldstein: A finite element method for solving Helmholtz type equations in waveguides and other unbounded domains. Math. Comp. 39 (1982) 309-324.
3. J. B. Keller, D. Givoli: Exact non-reflecting boundary conditions. J. Comp. Physics 82 (1989) 172-192.
4. D. Givoli: Numerical methods for problems in infinite domains. Elsevier, 1992.
5. L. L. Thompson: A review of finite-element methods for time-harmonic acoustics. J. Acoust. Soc. Am. 119 (2005) 1315-1330.
6. M. J. Buckingham: Ocean-acoustic propagation models. J. Acoustique 3 (1992) 223-287.
7. C. A. Boyles: Acoustic waveguides: Applications to oceanic science. Wiley, 1984.
8. F. B. Jensen, W. A. Kuperman, M. B. Porter, H. Schmidt: Computational ocean acoustics. American Institute of Physics, 1993.
9. R. B. Evans: A coupled mode solution for the acoustic propagation in a waveguide with stepwise depth variations of a penetrable bottom. J. Acoust. Soc. Am. 74 (1983) 188-195.
10. R. B. Evans: COUPLE: a user's manual. NORDA TN-332, 1986.
11. S. R. Rutherford, K. E. Hawker: Consistent coupled mode theory of sound propagation for a class of nonseparable problems. J. Acoust. Soc. Am. 70 (1981) 554-564.
12. M. I. Taroudakis, G. A. Athanassoulis, J. P. Ioannidis: A variational principle for underwater acoustic propagation in a three-dimensional ocean environment. J. Acoust. Soc. Am. 88 (1990) 1515-1521.
13. J. A. Fawcett: A derivation of the differential equations of coupled mode propagation. J. Acoust. Soc. Am. 97 (1992) 290-295.
14. th International Conference on Mathematical and Numerical Aspects of Wave Propagation (Waves 2003). G. C. Cohen, E. Heikkola, P. Joly, P. Neittaanmäki (eds.). Springer, 2003, 451-456.
15. N. A. Kampanis, V. A. Dougalis: A finite element code for the numerical solution of the Helmholtz equation in axially symmetric waveguides with interfaces. J. Comp. Acoustics 7 (1999) 83-110.
16. th European Conference in Underwater Acoustics. A. Alippi, G. B. Cannelli (eds.). CNR-IDAC, Rome, 1998, Vol. II, pp. 649-654.
17. G. A. Athanassoulis, K. A. Belibassakis, D. A. Mitsoudis, N. A. Kampanis, V. A. Dougalis: Coupled mode and finite element solutions of underwater sound propagation problems in stratified environments. J. Comp. Acoustics to appear.
18. D. A. Mitsoudis: Finite element methods for axisymmetric, indefinite boundary-value problems and applications in underwater acoustics (in Greek). Ph.D. Thesis, University of Athens, Greece, 2003.
19. M. Bernadou, P. L. George, A. Hassim, P. Joly, P. Laug, A. Perronnet, E. Saltel, D. Steer, G. Vanderborck, M. Vidrascu: MODULEF: A modular library of finite elements. INRIA, 1988.
20. P. L. George: Automatic mesh generation: Application to finite element methods. Wiley, 1991.
21. B. T Smith, J. M. Boyle, B. S. Garbow, Y. Ikebe, V. C. Klema, C. B. Moler: Matrix eigensystem routines - EISPACK guide. Springer, 1976.
22. I. Babuška, J. Osborn: Eigenvalue problems. - In: Handbook of numerical analysis, Vol. II. P. G. Ciarlet, J. L. Lions (eds.). Elsevier, 1991, 641-787.
23. R. W. Freund, N. M. Nachtigal: QMRPACK: A package of QMR algorithms. ACM Trans. Math. Software 22 (1996) 46-77.
24. R. W. Freund, N. M. Nachtigal: QMR: a quasi-minimal residual method for non-Hermitian linear systems. Numer. Math. 60 (1991) 315-339.
25. R. W. Freund, N. M. Nachtigal: An implementation of the QMR method based on coupled two-term recurrences. SIAM J. Sci. Comput. 15 (1994) 313-337.
26. M. Benzi, D. B. Szyld, A. Van Duin: Orderings for incomplete factorization preconditioning for nonsymmetric problems. SIAM J. Sci. Comput. 20 (1999) 1652-1670.
27. Partial differential equation toolbox user's guide (for use with MATLAB). The Mathworks Inc., 1996
28. A. Bayliss, C. I. Goldstein, E. Turkel: On accuracy conditions for the numerical computation of waves. J. Comp. Physics 59 (1985) 396-404.
29. A. Bayliss, C. I. Goldstein, E. Turkel: The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics. Comp. Maths, with Appls. 11 (1985) 655-665.
30. A. A. Oberai, P. M. Pinsky: A numerical comparison of finite element methods for the Helmholtz equation. J. Comp. Acoustics 8 (2000) 211-221.
31. F. Ihlenburg, I. Babuška: Finite element solution of the Helmholtz equation with high wave number, Part I: The h-version of the FEM. Computers Math. Applic. 30 (1995) 9-37.
32. F. Ihlenburg: Finite element analysis of acoustic scattering. Springer, 1998.