Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
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Investigation of Efficiency of Starting Iteration Vectors for Calculating Natural Modes

고유모드 계산을 위한 초기 반복벡터의 효율성 연구

  • 김병완 (한국해양연구원 해양시스템안전연구소) ;
  • 경조현 (한국해양연구원 해양시스템안전연구소) ;
  • 홍사영 (한국해양연구원 해양시스템안전연구소) ;
  • 조석규 (한국해양연구원 해양시스템안전연구소) ;
  • 이인원 (한국과학기술원)
  • Published : 2005.01.01
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Abstract

Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in order to accelerate the convergence of the subspace iteration method. Proposed methods are divided into two forms according to the number of starting vectors. The first method composes 2p starting vectors when the number of required modes is p and the second method uses 1.5p starting vectors. To investigate the efficiency of proposed methods, two numerical examples are presented.

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References

  1. 허덕재, 정재엽, 조연, 박태원, 1999, '모드해석을 이용한 L, T자형 구조물의 결합 강성 평가 방법에 대한 연구,' 한국소음진동공학회논문집, 제 9권, 제 5호, pp. 975-983
  2. Lanczos, C., 1950, 'An Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators,' J. Res. Natl. Bur. Stand., Vol. 45, No. 4, pp. 255-282
  3. Bathe, K. J. and Wilson, E. L., 1972, 'Large Eigenvalue Problems in Dynamic Analysis,' ASCE J. Engrg. Mech., Vol. 98, pp. 1471-1485
  4. Akl, F. A., Dilger, W. H. and Irons, B. M., 1979, 'Over-Relaxation and Subspace Iteration,' Int. J. Numer. Meth. Engrg., Vol. 14, pp. 629-630 https://doi.org/10.1002/nme.1620140414
  5. Bathe, K. J. and Ramaswamy, S., 1980, 'An Accelerated Subspace Iteration Method,' Comput. Meth. Appl. Mech. Engrg., Vol. 23, pp. 313-331 https://doi.org/10.1016/0045-7825(80)90012-2
  6. Wilson, E. L. and Itoh, T., 1983, 'An Eigensolution Strategy for Large Systems,' Comput. Struct., Vol. 16, pp. 259-265 https://doi.org/10.1016/0045-7949(83)90166-9
  7. Grosso, G., Martinelli. L. and Parravicini, G. P., 1993, 'A New Method for Determining Excited States of Quantum Systems,' Nuovo Cimento D, Vol. 15, No. 2-3, pp. 269-277 https://doi.org/10.1007/BF02456910
  8. Cordelli, A., 1994, 'Application of Accelerated-Convergence Technique to Modified Lanczos Calculations.' II Nuovo Cimento D, Vol. 16, pp. 45-53 https://doi.org/10.1007/BF02452001
  9. Bevilacqua, G., Martinelli, L. and Parravicini, G. P., 1996, 'Jahn-Teller Effect in ZnS:$Fe^{2+}$ Revisited with a Modified Lanczos-Type Algorithm.' Phys. Rev. B. Vol. 54, pp. 7626-7629 https://doi.org/10.1103/PhysRevB.54.7626
  10. Lam, Y. C. and Bertolini, A. F., 1994, 'Acceleration of the Subspace Iteration Method by Selective Repeated Inverse Iteration,' FE Anal. Design, Vol. 18, pp. 309-317 https://doi.org/10.1016/0168-874X(94)90110-4
  11. Qian, Y. Y. and Dhatt, G., 1995, 'An Accelerated Subspace Method for Generalized Eigenproblems,' Comp. and Struct., Vol. 54, No. 6, pp, 1127-1134 https://doi.org/10.1016/0045-7949(94)00387-I
  12. Wang. X. and Zhou. J., 1999. 'An Accelerated Subspace Iteration Method for Generalized Eigenproblems,' Comput. Struct., Vol. 71. pp. 293-301 https://doi.org/10.1016/S0045-7949(98)00153-9
  13. Paige. C. C., 1972. 'Computational Variants of the Lanczos Method for the Eigenproblem,' J. Inst. Math. Appl., Vol. 10. pp. 373-381 https://doi.org/10.1093/imamat/10.3.373
  14. Parlett. B. N. and Scott. D. S., 1979. 'The Lanczos Algorithm with Selective Oorthogonalization.' Math. Comput., Vol. 33, pp. 217-238 https://doi.org/10.2307/2006037
  15. Ruhe, A., 1979. 'Implementation Aspects of Band Lanczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices.' Math. Comput., Vol. 33. pp. 680-687 https://doi.org/10.2307/2006302
  16. Ericsson. T. and Ruhe. A., 1980. 'The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems,' Math. Comput., Vol. 35, pp, 1251-1268 https://doi.org/10.2307/2006390
  17. Nour-Omid, B., Parlett, B. N. and Taylor. R.L., 1983, 'Lanczos versus Subspace Iteration for Solution of Eigenproblems.' Int. J. Numer. Meth. Engrg., Vol. 19. pp. 859-871 https://doi.org/10.1002/nme.1620190608
  18. Simon, H. D., 1984. 'The Lanczos Algorithm with Partial Reorthogonalization,' Math. Comput., Vol. 42. pp. 115-142 https://doi.org/10.2307/2007563
  19. Matthies. H. G., 1985. 'A Subspace Lanczos Method for the Generalized Symmetric Eigenproblem,' Comput. Struct., Vol. 21. pp. 319-325 https://doi.org/10.1016/0045-7949(85)90252-4
  20. Chen. H. C. and Taylor. R. L., 1988. 'Solution of Eigenproblems for Damped Structural Systems by the Lanczos Algorithm.' Comput. Struct., Vol. 30. pp. 151-161 https://doi.org/10.1016/0045-7949(88)90223-4
  21. Rajakumar. C., 1993. 'Lanczos Algorithm for the Quadratic Eigenvalue Problem in Engineering Applications.' Comput, Meth. Appl. Mech. Engrg., Vol. 105, 1-22 https://doi.org/10.1016/0045-7825(93)90113-C
  22. Smith. H. A., Sorensen. D. C. and Singh. R. K., 1993. 'A Lanczos-Based Technique for Exact Vibration Analysis of Skeletal Structures.' Int. J. Numer. Meth. Engrg., Vol. 36, pp. 1987-2000 https://doi.org/10.1002/nme.1620361203
  23. Bathe. K. J., 1996. Finite Element Procedures. Prentice-Hall

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