대한기계학회논문집A (Transactions of the Korean Society of Mechanical Engineers A)

  • 제27권4호
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  • Pages.551-558
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  • 2003
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  • 1226-4873(pISSN)
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  • 2288-5226(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
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대형 유한요소 고유치 해석에서의 부공간 축차법 효율 개선

Improvement of Computational Efficiency of the Subspace Iteration Method for Large Finite Element Models

  • 주병현 (한국과학기술원 기계공학과) ;
  • 이병채 (한국과학기술원 기계공학과)
  • 발행 : 2003.04.01
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⟨ 이전 논문 다음 논문 ⟩

초록

An efficient and reliable subspace iteration algorithm using the block algorithm is proposed. The block algorithm is the method dividing eigenpairs into several blocks when a lot of eigenpairs are required. One of the key for the faster convergence is carefully selected initial vectors. As the initial vectors, the proposed method uses the modified Ritz vectors for guaranteering all the required eigenpairs and the quasi-static Ritz vectors for accelerating convergency of high frequency eigenvectors. Applying the quasi-static Ritz vectors, a shift is always required, and the proper shift based on the geometric average is proposed. To maximize efficiency, this paper estimates the proper number of blocks based on the theoretical amount of calculation in the subspace iteration. And it also considers the problems generated in the process of combining various algorithms and the solutions to the problems. Several numerical experiments show that the proposed subspace iteration algorithm is very efficient, reliable ,and accurate.

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참고문헌

  1. Bathe, K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, New Jersey
  2. Bertolini, A. F. and Lam, Y. C., 1998, 'Accelerated Subspace Iteration Using Adaptive Multiple Inverse Iteration,' Computers & Structures, Vol. 66, pp. 45-57 https://doi.org/10.1016/S0045-7949(97)00062-X
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  7. Bathe, K. J. and Ramaswamy, S., 1980, 'An Acceleration Subspace Iteration Method,' Computer Methods in Applied Mechanics and Engineering, Vol. 23, pp. 313-331 https://doi.org/10.1016/0045-7825(80)90012-2
  8. Gu, J., Ma, Z-D. and G. M. Hulbert, 2000, 'A New Load-Dependent Ritz Vector Method for Structural Dynamics Analyses: Quasi-Static Ritz Vectors,' Finite Elements in Analysis and Design, Vol. 36, pp. 261-278 https://doi.org/10.1016/S0168-874X(00)00036-6
  9. Jiaxian, X., 1989, 'An Improved Method for Partial Eigensolution of Large Structures,' Computers & Structures, Vol. 32, pp, 1055-1060 https://doi.org/10.1016/0045-7949(89)90407-0
  10. Trefethen, L. N. and Bau, D., 1997, Numerical Linear Algebra, SIAM, Philadelphia

피인용 문헌

  1. Efficient Modal Analysis of Prestressed Structures via Model Order Reduction vol.35, pp.10, 2011, https://doi.org/10.3795/KSME-A.2011.35.10.1211