Finite element formulation of exact Dirichlet-to-Neumann radiation conditions on elliptic and spheroidal boundaries

American Society of Mechanical Engineers, Noise Control and Acoustics Division (Publication) NCA

Volumn 26, Issue , 1999, Pages 497-509

  Thompson, Lonny L ^a   Huan, Runnong ^a   Ianculescu, Cristian ^a  

^a AMRL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; FINITE ELEMENT METHOD; MATRIX ALGEBRA; PARTIAL DIFFERENTIAL EQUATIONS; THREE DIMENSIONAL; TWO DIMENSIONAL;

EXACT DIRICHLET TO NEUMANN RADIATION BOUNDARY CONDITION; HELMHOLTZ EQUATION;

ACOUSTIC WAVE SCATTERING;

EID: 0033296385     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Article

References (20)

1. S. Tsynkov, 'Numerical solution of problems on unbounded domains. A review', Appl. Num. Math. 27, 465-532, 1998.
2. L. W. Pearson and R. A. Whitaker, L. J. Bahrmasel, 'An exact radiation boundary condition for the finite-element solution of electromagnetic scattering on an open domain', IEEE Transactions on Magnetics, Vol. 25, No. 4, (1989), pp. 3046-3048.
3. J. B. Keller and D. Givoli, 'Exact non-reflecting boundary conditions', J. Comp. Phys., 82 (1989), pp. 172-192.
4. I. Harari and T.J.R. Hughes, 'Analysis of continuous formulations underlying the computation of time harmonic acoustics in exterior domains', Comput. Methods Appl. Mech. Engrg., 97, 103-124, 1992.
5. D. Burnett, 'A 3-D acoustic infinite element based on a generalized multipole expansion', J. Acoust. Soc. Am., 96, (1994), pp. 2798-2816.
6. R.J. Astley, G.J. Macaulay, J.-P. Coyette, and L. Cremers, 'Three-dimensional wave-envelope elements of variable order for acoustic radiation and scattering. Part I. Formulation in the frequency domain', J. Acoust. Soc. Am., 103, (1998), pp. 49-63.
7. L.L. Thompson 'Finite element methods for time-harmonic structural acoustics in exterior domains: Derivation of exact DtN maps for elliptic and spheroidal radiation boundaries', ONR Contract Review Meeting, Stanford University, Stanford, CA., April 19, 1994. Technical Report: CMCU-94-01, Advanced Computational Mechanics Laboratory, Clemson University, August, 1994.
8. M. J. Grote and J. B. Keller, 'On nonreflecting boundary conditions', J. of Comput. Phys., 122, 231-243, 1995.
9. G. Ben-Porat and D. Givoli, "Solution of unbounded domain problems using elliptic artificial boundaries", Commun. Numer. Meth. Engr., 11, 735-741, 1995.
10. A. A. Oberai, M. Malhotra, P.M. Pinsky, 'On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation', Applied Numerical Mathematics, 27, 443-464, 1998.
11. M. Malhotra and P.M. Pinsky, 'A matrix-free interpretation of the nonlocal Dirichlet-to-Neumann radiation boundary condition', Internat. J. Numer. Methods Engrg., 39, 3705-3713, 1996.
12. M. Abramowitz and I. Stegun, Eds., Handbook of Mathematical Functions, Washington, DC: National Bureau of Standards, 1964. Reprinted by Dover Publications, New York, 1968, pp. 751-770.
13. C. Flammer, Spheroidal Wave Functions, Stanford, CA: Stanford University Press, 1957.
14. A. Bayliss, M. Gunzberger, and E. Turkel, 'Boundary conditions for the numerical solution of elliptic equations in exterior domains', SIAM J. Appl. Math., 42, 430-451, 1982.
15. R. L. Holford, 'A multipole expansion for the acoustic field exterior to a Prolate or Oblate Spheroid', in preparation.
16. N. W. McLachlan, Theory and Application of Mathieu Functions, Oxford: Clarendon Press, 1947.
17. M. Malhotra, and P.M. Pinsky, 'Parallel preconditioning based on h-hierarchical finite elements with application to acoustics', Comput. Methods Appl. Mech. Engrg., 155, 97-117, 1998.
18. R.W. Freund, 'Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices', SIAM J. Sci. Statist. Comput., 13 (1992) 425-448.
19. R.W. Freund and N.M. Nachtigal, 'QMR: a quasi-minimal residual method for non-Hermitian linear systems', Numer. Math. 60, (1991) 315-339.
20. S.C. Eisenstat, 'Efficient implementation of a class of preconditioned conjugate gradient methods', SIAM J. Sci. Statist. Comput. 2 (2) (1984) 130-138.