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2015 | 5 | 655--662
Tytuł artykułu

Block Preconditioned Conjugate Gradient Method for Extraction of Natural Vibration Frequencies in Structural Analysis

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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)
Słowa kluczowe
Rocznik
Tom
5
Strony
655--662
Opis fizyczny
Twórcy
  • Tadeusz Kościuszko Cracow University of Technology, Poland
  • Tadeusz Kościuszko Cracow University of Technology, Poland
Bibliografia
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  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
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  • 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.
  • 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.
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  • 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.
  • 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.
  • 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.
  • 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.
  • Y. Saad, Numerical methods for large eigenvalue problems, Revised edition, Classics in applied mathematics. SIAM, 2011, http://dx.- doi.org/10.1137/1.9781611970739.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ekon-element-000171422668

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