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Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. (English) Zbl 0996.76058
Summary: We report on a generalization of Bayliss-Gunzburger-Turkel non-reflecting boundary conditions to arbitrarily shaped convex artificial boundaries. For elongated scatterers such as submarines, we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three-dimensional acoustic scattering problems.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76Q05 Hydro- and aero-acoustics
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[1] Burton, Proceedings of the Society Series A 323 pp 201– (1971)
[2] Integral equation methods in sound radiation and scattering from arbitrary surfaces. Naval Ship Research and Development Center: Washington, DC., Ship Acoustic Dept, Research and Development Report 3538, 1971.
[3] Ha-Duong, Mathematical Methods in the Applied Sciences 2 pp 191– (1980)
[4] Hamdi, C.R.A.S., Série II 292 pp 17– (1981)
[5] Integral equation methods in acoustics. In Boundary Elements X, Vol. 4, (ed.). Springer: Berlin, 1988; 221-244.
[6] Liu, Computer Methods in Applied Mechanics and Engineering 96 pp 271– (1992)
[7] Harari, Computer Methods in Applied Mechanics and Engineering 97 pp 77– (1992)
[8] Engquist, Mathematics of Computation 31 pp 629– (1977)
[9] Bayliss, SIAM Journal of Applied Mathematics 42 pp 430– (1982)
[10] Kallivokas, Computer Methods in Applied Mechanics and Engineering 147 pp 235– (1997)
[11] Bettes, International Journal for Numerical Methods in Engineering 11 pp 53– (1977)
[12] Astley, Journal of Sound and Vibration 170 pp 97– (1994)
[13] Burnett, Journal of Acoustical Society of America 96 pp 2798– (1994)
[14] Harari, Computer Methods in Applied Mechanics and Engineering 164 pp 107– (1998)
[15] Berenger, Journal of Computational Physics 114 pp 185– (1994) · Zbl 0814.65129
[16] Harari, Journal of Computational Acoustics 8 pp 121– (2000) · Zbl 1360.76139
[17] Givoli, Computer Methods in Applied Mechanics and Engineering 76 pp 41– (1989)
[18] Keller, Journal of Computational Physics 82 pp 172– (1989)
[19] Harari, International Journal for Numerical Methods in Engineering 37 pp 2935– (1994)
[20] Numerical Methods for Problems in Infinite Domains. Elsevier: Amsterdam, 1992.
[21] Malhotra, International Journal for Numerical Methods in Engineering 39 pp 3705– (1996)
[22] Shirron, Computer Methods in Applied Mechanics and Engineering 164 pp 121– (1998)
[23] Jones, IMA Journal of Applied Mathematics 41 pp 21– (1980)
[24] Kriegsmann, IEEE Transactions on Antennas and Propagation 35 pp 153– (1987)
[25] Djellouli, Journal of Computational Acoustics 8 pp 81– (2000) · Zbl 1360.76131
[26] Antoine, Journal of Mathematical Analysis and Applications 229 pp 184– (1999)
[27] Differential Geometry of Curves and Surfaces. Prentice-Hall: Englewood Cliffs, NJ, 1976.
[28] Curvature approximation for triangulated surfaces. Computing Supplement 1993; 139-153. · Zbl 0865.41003
[29] Sobolev Spaces. Academic Press: New York, 1975. · Zbl 0314.46030
[30] Inverse Acoustic in Electromagnetic Scattering Theory. Applied Mathematical Sciences, vol. 93, Springer, Berlin, 1992.
[31] Babuska, SIAM Journal of Numerical Analysis 34 pp 2392– (1997)
[32] Farhat, Numerische Mathematik 85 pp 283– (2000)
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