Short wave modelling using special finite elements

Journal of Computational Acoustics

Volumn 8, Issue 1, 2000, Pages 189-210

  Laghrouche, Omar ^a   Bettess, Peter ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034345542     PISSN: 0218396X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218396X00000121     Document Type: Article

References (29)

1. O. C. Zienkiewicz and P. Bettess, "Infinite elements in the study of fluid-structure interaction problems," Computing Methods in Applied Sciences, Lecture Notes in Physics 58 (Springer-Verlag, Berlin, 1975), pp. 133-169.
2. 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.
3. 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.
4. R. J. Astley, "Wave envelope and infinite elements for acoustical radiation," Int. J. Num. Meth. Flu. 3 (1983), 507-526.
5. R. J. Astley and W. Eversman, "Finite element formulation for acoustical radiation," J. Sound Vib. 88 (1983), 47-64.
6. 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.
7. P. Bettess, "A simple wave envelope element example," Comm. Appl. Numer. Methods 3 (1987), 77-80.
8. P. Bettess and E. A. Chadwick, "Wave envelope examples for progressive waves," Int. J. Num. Meth. Eng. 38 (1995), 2487-2508.
9. E. A. Chadwick and P. Bettess, "Modelling of progressive short waves using wave envelopes," Int. J. Num. Meth. Eng. 40 (1997), 3229-3245.
10. E. A. Chadwick, P. Bettess, and O. Laghrouche, "Diffraction of short waves modelled using new mapped wave envelope finite and infinite elements," Int. J. Num. Meth. Eng. 45 (1999), 335-354.
11. I. Herrera and F. J. Sabena, "Connectivity as an alternative to boundary integral equations," Proc. Natl. Acad. Sci. USA 75 (1978), 2059-2063.
12. F. J. Sánchez-Sesma, I. Herrera, and J. Avilés, "A boundary method for elastic wave diffraction: application to scattering of S H waves by surface irregularities," Bull. Seism. Soc. Am. 72 (1982), 491-506.
13. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method (McGrawHill, London, 1989).
14. E. Trefftz, "Ein Gegenstück zum Ritz'schen Verfahren," Proc. 2nd Int. Congr. Appl Mech., Zurich (1926), 131-137.
15. Y. K. Cheung, W. G. Jin and O. C. Zienkiewicz, "Solution of Helmholtz equation by Trefftz method," Int. J. Num. Meth. Eng. 32 (1991), 63-78.
16. M. Stojek, "Least-squares Trefftz-type elements for the Helmholtz equation," Int. J. Num. Meth. Eng. 41 (1998), 831-849.
17. J. M. Melenk, "On generalized Finite Element Methods," Ph.D. Thesis, (University of Maryland, 1995).
18. J. M. Melenk and I. Babuška, "The Partition of Unity Finite Element Method. Basic theory and applications," Comput. Meths. Appl. Mech. Eng. 139 (1996), 289-314.
19. J. M. Melenk and I. Babuška, "The Partition of Unity Method," Int. J. Num. Meth. Eng. 40 (1997), 727-758.
20. F. Ihlenburg, Finite Element Analysis of Acoustic Scattering (Springer-Verlag, New York, 1998).
21. F. Ihlenburg and I. Babuška, "Solution of Helmholtz problems by knowledge-based FEM," Comp. Ass. Mech. Eng. Sci. 4 (1997), 397-415.
22. A. de la Bourdonnaye, "High frequency approximation of integral equations modeling scattering phenomena," Mathematical Modelling and Numerical Analysis 28 (1994), 223-241.
23. A. de la Bourdonnaye, "Une méthode de discrétisation microlocale et son application à un problème de diffraction," C. R. Acad. Sci., Paris, t. 318, Série I (1994), 385-388.
24. H. Lamb, Hydrodynamics (Cambridge University Press, 1932).
25. P. A. Martin and R. A. Dalrymple, "On amphidromic points," Proc. Roy. Soc. Lon., Series A 444 (1994), 91-104.
26. A. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1965).
27. T. H. Havelock, "The pressure of water waves upon a fixed obstacle," Proc. Roy. Soc. Lon., Series A 963 (1940), 409-421.
28. R. C. MacCamy and R. A. Fuchs, "Wave forces on piles. A diffraction theory," Beach Erosion Board Tech. Mem. No. 69 (1954).
29. K. Bando, P. Bettess, and C. Emson, "The effectiveness of dampers for the analysis of exterior scalar wave diffraction by cylinders and ellipsoids," Int. J. Num. Meth. Eng. 4 (1984), 599-617.