On the implementation of the Dirichlet-to-Neumann radiation condition for iterative solution of the Helmholtz equation

Applied Numerical Mathematics

Volumn 27, Issue 4, 1998, Pages 443-464

  Oberai, Assad A ^a   Malhotra, Manish ^a   Pinsky, Peter M ^a  

^a Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATRIX ALGEBRA;

HELMHOLTZ EQUATION; UNBOUNDED DOMAINS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 0032137480     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00024-5     Document Type: Article

References (17)

1. A. Bayliss, M. Gunzberger and E. Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior domains, SIAM J. Appl. Math. 42 (1982) 430-451.
2. G. Beylkin, On the fast Fourier transform of functions with singularities, Appl. Comput. Harmon. Anal. 2 (1995) 363-381.
3. J.W. Cooley and J.W. Tukey, An algorithm for the machine computation of complex Fourier series, Math. Comp. 19 (1965) 297-301.
4. A. Dutt and V. Rokhlin, Fast Fourier transform for nonequispaced data, SIAM J. Sci. Statist. Comput. (1993).
5. S.C. Eisenstat, Efficient implementation of a class of preconditioned conjugate gradient methods, SIAM J. Sci. Statist. Comput. 2(2) (1984) 130-138.
6. K. Feng, Asymptotic radiation conditions for reduced wave equation, J. Comput. Math. 2 (1984) 1-4.
7. R.W. Freund, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Statist. Comput. 13 (1992) 425-448.
8. R.W. Freund and F. Jarre, A QMR-based interior point algorithm for solving linear programs, Numerical Analysis Manuscript 94-19, AT&T Bell Laboratories, Murray Hill (1994).
9. R.W. Freund and N.M. Nachtigal, QMR: a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315-339.
10. D. Givoli, Numerical Methods for Problems in Infinite Domains (Elsevier, Amsterdam, 1992).
11. M.J. Grote and J.B. Keller, On non-reflecting boundary conditions, J. Comput. Phys. (1993).
12. 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 (1992) 103-124.
13. D.M. Healy Jr, D. Rockmore and S.S.B. Moore, FFTs for the 2-sphere-improvements and variations, Technical Report PCS-TR96-292, Dartmouth College, Department of Computer Science (1996).
14. J.B. Keller and D. Givoli, Numerical methods for problems in infinite domains, J. Comput. Phys. 82(1) (1989) 172-192.
15. M. Malhotra, R.W. Freund and P.M. Pinsky, Solution of multiple radiation and scattering problems in structural acoustics using a block quasi-minimal residual iterative method, Comput. Methods Appl. Mech. Engrg. 146 (1997) 173-196.
16. M. Malhotra and P.M. Pinsky, Parallel preconditioning based on h-hierarchical finite elements with application to acoustics, Comput. Methods Appl. Mech. Engrg. 155 (1998) 97-117.
17. 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 (1996) 3705-3713.