BazEkon - Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie

BazEkon home page

Meny główne

Fialko Sergiy (Tadeusz Kościuszko Cracow University of Technology, Poland), Żegleń Filip (Tadeusz Kościuszko Cracow University of Technology, Poland)
Block Preconditioned Conjugate Gradient Method for Extraction of Natural Vibration Frequencies in Structural Analysis
Annals of Computer Science and Information Systems, 2015, vol. 5, s. 655-662, tab., bibliogr. 18 poz.
Słowa kluczowe
Macierze, Algorytmy, Informatyka
Matrix, Algorithms, Information science
The block preconditioned conjugate gradient method for extraction of eigenfrequencies and eigenmodes is presented for finite element software in structural analysis. The proposed approach is focused on multi-core desktops and laptops and allows us to effectively analyze large design models, when classical methods based on the factoring of stiffness matrix, significantly reduce performance by intensive use of disk memory. The main attention is paid to proper construction of preconditioning, application of shift technique and creation of the block algorithm allowing the improvement of computing stability and multithreaded parallelization. (original abstract)
Pełny tekst
  1. V. E. Bulgakov, M. E. Belyi and K. M. Mathisen, "Multilevel aggregation method for solving large-scale generalized eigenvalue problems in structural dynamics," Int. J. Numer. Methods Eng., vol. 40. pp. 453- 471, 1997, http://DOI: 10.1002/(SICI)1097-0207(19970215)40:33.0. CO;2-2
  2. Y. T. Feng and D. R. J. Owen, "Conjugate gradient methods for solving the smallest eigenpair of large symmetric eigenvalue problems," Int. J. Numer. Methods Eng., vol. 39. pp. 2209 - 2229, 1996, http://DOI: 10.1002/(SICI)1097-0207(19960715)39:13<2209::AIDNME951>3.0.CO;2-R.
  3. S. Yu. Fialko, "Natural vibrations of complex bodies," Int. Applied Mechanics, vol. 40, no. 1, pp. 83 - 90, 2004, http://DOI:10.1023/B: INAM.0000023814.13805.34.
  4. S. Fialko, "Aggregation Multilevel Iterative Solver for Analysis of Large-Scale Finite Element Problems of Structural Mechanics: Linear Statics and Natural Vibrations", in PPAM 2001, R. Wyrzykowski et al. (Eds.), LNCS 2328, Springer-Verlag Berlin Heidelberg, 2002, pp. 663-670, http://DOI: 10.1007/1-4020-5370-3_41.
  5. S. Yu. Fialko, E. Z. Kriksunov and V. S. Karpilovskyy, "A block Lanczos method with spectral transformations for natural vibrations and seismic analysis of large structures in SCAD software," in Proc. CMM-2003 - Computer Methods in Mechanics, Gliwice, Poland, 2003, pp. 129 -130.
  6. S. Yu. Fialko, "Iterative methods for solving large-scale problems of structural mechanics using multi-core computers," Archieves of Civil and Mechanical Engineering, vol. 14, pp. 190 - 203, 2014, http:// doi:10.1016/j.acme.2013.05.009.
  7. S. Yu. Fialko, "PARFES: A method for solving finite element linear equations on multi-core computers," Advances in Engineering software, vol. 40, no. 12, pp. 1256-1265, 2010, http:// doi:10.1016/j.advengsoft.2010.09.002.
  8. G. Gambolati, G. Pini and F. Sartoretto, "An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices," J. Comp. Phys., no 74, pp. 41 - 60, 1988, http://doi: 10.1016/0021-9991(88)90067-8.
  9. C. K. Gan, P. D. Haynes and M. C. Payne, "Preconditioned conjugate gradient method for sparse generalized eigenvalue problem in electronic structure calculations," Computer Physics Communications, vol 134, nr. 1, pp. 33 - 40, 2001, http://DOI: 10.1016/S0010- 4655(00)00188-0.
  10. V. Hernbadez, J. E. Roman, A. Tomas and V. Vidal, "A survey a software for sparse eigenvalue problems," Universitat Politecnica De Valencia, SLEPs technical report STR-6, 2009.
  11. G. Karypis and V. Kumar, "METIS: Unstructured Graph Partitioning and Sparse Matrix Ordering System,". Technical report, Department of Computer Science, University of Minnesota, Minneapolis, 1995.
  12. A. V. Knyazev and K. Neymayr, "Efficient solution of symmetric eigenvalue problem using multigrid preconditioners in the locally optimal block conjugate gradient method," Electronic Transactions on Numerical Analysis, vol. 15, pp. 38 - 55, 2003.
  13. R. B. Morgan, "Preconditioning eigenvalues and some comparison of solvers," Journal of computational and applied mathematics, vol. 123, pp. 101 - 115, 2000, http://doi: 10.1016/S0377-0427(00)00395-2.
  14. M. Papadrakakis, "Solution of partial eigenproblem by iterative methods," Int. J. Num. Meth Eng., vol. 20. pp. 2283-2301, 1984, http://DOI: 10.1002/nme.1620201209.
  15. A. V. Perelmuter, S. Yu. Fialko, "Problems of computational mechanics relate to finite-element analysis of structural constructions," International Journal for Computational Civil and Structural Engineering, vol. 1, no 2, 2005, pp. 72 - 86.
  16. Y. Saad, Numerical methods for large eigenvalue problems, Revised edition, Classics in applied mathematics. SIAM, 2011, http://dx.-
  17. S. Tomov, J. Langou, A. Canning, Lin-Wang Wang, J. Dongarra, "Conjugate-gradient eigenvalue solver in computing electronic properties of nanostructure architecture," Int. J. Computational Science and Engineering, vol. 2, nr. 3-4, pp. 205 - 212, 2006.
  18. Intel Math Kernel Library Reference Manual. URL: ttps:// doclib/iss/2013/mkl/mklman/index.htm (Last access: 16.04.2015).
Cytowane przez
Udostępnij na Facebooku Udostępnij na Twitterze Udostępnij na Google+ Udostępnij na Pinterest Udostępnij na LinkedIn Wyślij znajomemu