한국전산구조공학회논문집 (Journal of the Computational Structural Engineering Institute of Korea)

  • 제20권6호
  • /
  • Pages.743-749
  • /
  • 2007
  • /
  • 1229-3059(pISSN)
  • /
  • 2287-2302(eISSN)
한국전산구조공학회 (Computational Structural Engineering Institute of Korea)
권호 표지

대수학 부구조법을 이용한 내부 고유치 계산

Interior Eigenvalue Computation Using Algebraic Substructuring

  • 고진환 (건국대학교 항공우주정보시스템공학과) ;
  • 변도영 (건국대학교 항공우주정보시스템공학과)
  • 발행 : 2007.12.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

대수학 부구조법은 대형 문제들의 고유치 계산에 최고 성능을 지닌 방법이지만 근본적으로 최소 고유치만을 계산하기 위해 설계되었다. 본 논문에서는 이동값을 이용하여 특정범위 안의 내부 고유치를 계산하기 위해 대수학 부구조법의 갱신된 버전을 제안하고, 이를 이동 대수학 부구조법이라 명명한다. 그리고 구조문제의 유한요소모델에 대한 수치실험을 통해 제안된 방법이 다수의 내부고유치를 계산하는데 란쵸스방법보다 월등한 효율성을 가지고 있음을 보였다.

Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large size problems, but, originally, it was designed to calculate only the smallest eigenvalues. In this paper, an updated version of AS is proposed to calculate the interior eigenvalues over a specified range by using a shift value, which is referred to as the shifted AS. Numerical experiments demonstrate that the proposed method has better efficiency to compute numerous interior eigenvalues for the finite element models of structural problems than a Lanczos-type method.

키워드

참고문헌

  1. Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Harnmarling, S., McKenney, A., Sorensen, D. (1999) LAPACK Users' Guide 3-rd. SIAM
  2. Arbenz, P., Geus, R. (1999) A comparison solvers for large eigenvalue problems occuring in the design of resonant cavities, Numer. Linear Algebra Appl., 6. pp.3-16 https://doi.org/10.1002/(SICI)1099-1506(199901/02)6:1<3::AID-NLA142>3.0.CO;2-I
  3. Bai, Z., Demmel, J., Dongarra, J., Ruhe, A., van der Vorst, H. (2000) Templates for the solution of Algebraic Eigenvalue Problems: A Practical Guide, SIAM, Philadelphia
  4. Bennighof, J. K., Kim, C. K. (1992) An adaptive multi-level substructuring method for efficient modeling of complex structures. Proceedings of the AIAA 33rd SDM Conference, Dallas. Texas. pp. 1631-1639
  5. Bennighof', J. K. Lehoucq, R. B. (2004) An Automated Multilevel Substructuring Method for Eigenspace Computation in Linear Elasto Dynamics, SIAM J. Sci. Comput., 25(6), pp.208- 2106 https://doi.org/10.1137/S1064827503429132
  6. Craig, Jr. R. R. (1981) Structural Dynamics: An Introduction to Computer Methods. John Wiley and Sons. Inc. Publishers
  7. Craig, Jr. R .R., Bampton, M.C.C. (1968) Coupling of substructures for dynamic analysis. AIAA Journal, 6(7), pp.1313-1319 https://doi.org/10.2514/3.4741
  8. Demmel, J.W., Eisenstat, S. C., Gilbert, J. R. , Li, X. S., Liu, J. W. H. (1999) A supernodal approach to sparse partial pivoting. SIAM J. Matrix Anal. Appl., 20(3). pp. 720-755 https://doi.org/10.1137/S0895479895291765
  9. Gao, W., Li, X.S., Yang, C., Bai, Z. (2006) An implementation and evaluation of the AMLS method for sparse eigenvalue problems. Technical Report LBNL-57438, Lawrence Berkeley National Laboratory
  10. Grimes, R G., Lewis, J. G., Simon H. D. (1994) A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems, SIAM J. Matrix Anal. Appl., 15(1). pp.228-272 https://doi.org/10.1137/S0895479888151111
  11. Kaplan, M. F. (2001) Implementation of automated multilevel substructuring for frequency response analysis of structures, PhD thesis. University of Texas at Austin
  12. Karypls, G. (2006) METIS. Department of Computer Science and Engineering at the University of Minnesota. http://www-users.cs.umn.edu/~karypis/metis/ metis/index.html
  13. Katili, I. (1993) A new discrete Krichhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain field: Part II, International Journal for Numerical Methods in Engineering, 36. pp.1884-1908
  14. Kropp, A., Heiserer, D. (2002) Efficient Broadband Vibro-Acoustic Analysis of Passenger Car Bodies Using an FE-based Component Mode Synthesis Approach. Fifth World Congress on Computational Mechanics, Vienna, Austria
  15. Lehoucq, R, Sorensen, D. C., Yang, C. (1998) ARPACK User's Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM. Philadelphia
  16. Parlett, B. N. (1980) the symmetric eigenvalues problems. Prentice-Hall
  17. Yang, C., Gao, W., Bai, Z., Li, X., Lee, L., Husbands, P., Ng, E. (2005) An algebraic sub structuring method for large-scale eigenvalue calculations. SIAM J. Sci. Comput., 27(3). pp. 873-892 https://doi.org/10.1137/040613767