An iterative scheme for dense, complex-symmetric, linear systems in acoustics boundary-element computations

SIAM Journal on Scientific Computing

Volumn 19, Issue 5, 1998, Pages 1450-1470

  Natarajan, Ramesh ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

Acoustics; Boundary elements; Helmholtz equation; Iterative methods

Indexed keywords

EID: 0042223767     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595296288     Document Type: Article

References (20)

1. E. ANDERSON, Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, S. OSTROUCHOV, AND D. SORENSEN, LAPACK Users' Guide, 2nd Ed., SIAM, Philadelphia, 1995.
2. R. BARRETT, M. BERRY, T. CHAN, J. DEMMEL, J. DONATO, J. DONGARRA, V. EIJKHOUT, R. POZO, C. ROMINE, AND H. VAN DER VORST, TEMPLATES for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1995.
3. W. E. BOYSE AND A. A. SEIDL, A block QMR method for computing multiple simultaneous solutions to complex symmetric systems, SIAM J. Sci. Statist. Comput., 17 (1996), pp. 263-274.
4. A. J. BURTON AND G. F. MILLER, The application of integral equations to the numerical solution of some exterior boundary value problems, Proc. Roy. Soc. London Ser. A., 323 (1971), pp. 201-210.
5. J. P. COYETTE, A refined boundary element technique for modeling acoustic radiation from complex structural models, in Proc. 17th International Seminar on Modal Analysis, KU Leuven, Belgium, 1992, pp. 995-1010.
6. J. CULLUM AND R. A. WILLOUGHBY, Lanczos Algorithms for Large Symmetric Eigenvalue Problems, Vol. I. Theory, Birkhauser, Boston, 1985.
7. S. C. EISENSTAT, Efficient implementation of a class of preconditioned conjugate gradient methods, SIAM J. Sci. Statist. Comput., 2 (1981), pp. 1-4.
8. P. F. FISCHER, Projection Techniques for Iterative Solution of Ax = b with Successive Right-Hand Sides, ICASE Report 93-90, NASA CR-191571, 1993.
9. R. FLETCHER, Practical Methods of Optimization, 2nd Ed., Wiley-Interscience, New York, 1987.
10. R. W. FREUND, Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 425-448.
11. R. W. FREUND AND N. M. NACHTIGAL, QMRPACK, a package of QMR algorithms, ACM TOMS, 22 (1996), pp. 46-77.
12. P. E. GILL AND W. MURRAY, Newton type methods for linearly constrained optimization, in Numerical Methods for Constrained Optimization, P. E. Gill and W. Murray, eds., Academic Press, New York, 1974, pp. 29-65.
13. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd Ed., Johns Hopkins University Press, Baltimore, 1989.
14. P. GUISSET AND R. CISKOWSKI, personal communication, 1995.
15. K. GURU PRASAD, D. E. KEYES, AND J. H. KANE, GMRES for Sequentially Multiple Nearby Systems, 1994, manuscript.
16. J. RAHOLA, Solution of dense systems of linear equations in the discrete-dipole approximation, SIAM J. Sci. Statist. Comput., 17 (1996), pp. 78-89.
17. H. A. SCHENCK AND G. W. BENTHIEN, The application of a coupled finite-element boundaryelement technique to large-scale structural acoustic problems, in Advances in Boundary Elements, Vol. 2, C. A. Brebbia and J. J. Connor, eds., Computation Mechanics Publications, Southampton, 1989.
18. SYSNOISE THEORETICAL MANUAL REVISION 5.1, Numerical Integration Technologies, Ambachtenlaan, 11a, B-3001, Leuven, Belgium, 1993.
19. U. VIERSBACH, R. MAURELL, P. GUISSET, J. P. ROISSON AND H. WYNENDAELE, Comparing acoustic measurements with combined MSC/NASTRAN-SYSNOISE sound radiation predictions of an engine block, in Proc. 1994 MSC World User's Conference, Lake Buena Vista, FL, 1994.
20. X.-F. Wu, Faster calculations of sound radiation from vibrating cylinders using variational formulation, ASME Journal of Vibration, Acoustics, Stress and Reliability in Design, 111 (1989), pp. 101-107.