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Some progress on parallel modal and vibration analysis using the JAUMIN framework. (English) Zbl 1394.74189
Summary: In the development of large and complex equipment, a large-scale finite element analysis (FEA) with high efficiency is often strongly required. This paper provides some progress on parallel solution of large-scale modal and vibration FE problems. Some predominant algorithms for modal and vibration analysis are firstly reviewed and studied. Based on the newly developed JAUMIN framework, the corresponding procedures are developed and integrated to form a parallel modal and vibration solution system; the details of parallel implementation are given. Numerical experiments are carried out to evaluate the parallel scalability of our procedures, and the results show that the maximum solution scale attains ninety million degrees of freedom (DOFs) and the maximum parallel CPU processors attain 8192 with favorable computing efficiency.
74S05 Finite element methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
Full Text: DOI
[1] Humar, J., Dynamics of Structures (3rd edition), (2012), Leiden, The Netherlands: CRC Press/Balkema, Leiden, The Netherlands · Zbl 1246.74001
[2] Newland, D. E., Mechanical Vibration Analysis and Computation, (2006), New York, NY, USA: Dover, New York, NY, USA
[3] Itoh, T., Damped vibration mode superposition method for dynamic response analysis, Earthquake Engineering & Structural Dynamics, 2, 1, 47-57, (1973)
[4] Edwards, C.; Stewart, J. R.; Bathe, K. J., SIERRA: a software environment for developing complex multi-physics applications, Proceedings of the 1st MIT Conference on Computational Fluid and Solid Mechanics, Elsevier Science
[5] Zhang, L. B.
[6] Mo, Z. Y.; Zhang, A. Q.; Cao, X. L., JASMIN: a software infrastructure for large scale parallel adaptive structured mesh applications, Frontiers of Computer Science, 4, 4, 480-488, (2010)
[7] Bai, Z.; Demmel, J.; Dongarra, J., Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, Software, Environments, and Tools, 11, (2000), Philadelphia, Pa, USA: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA · Zbl 0965.65058
[8] Xue, F., Numerical solution of Eigenvalue problems with spectral transformations [Ph.D. thesis], (2009), Maryland, Md, USA: University of Maryland, Maryland, Md, USA
[9] Saad, Y., Numerical Methods for Large Eigenvalue Problems, (1992), Manchester, UK: Manchester University Press, Manchester, UK · Zbl 0991.65039
[10] Lanczos, C., An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, Journal of Research of the National Bureau of Standards, 45, 255-282, (1950)
[11] Arnoldi, W. E., The principle of minimized iteration in the solution of the matrix eigenvalue problem, Quarterly of Applied Mathematics, 9, 17-29, (1951) · Zbl 0042.12801
[12] Sorensen, D. C., Implicit application of polynomial filters in a \(k\)-step Arnoldi method, SIAM Journal on Matrix Analysis and Applications, 13, 1, 357-385, (1992) · Zbl 0763.65025
[13] Stewart, G. W., A Krylov-Schur algorithm for large eigenproblems, SIAM Journal on Matrix Analysis and Applications, 23, 3, 601-614, (2001/02) · Zbl 1003.65045
[14] Davidson, E. R., The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices, Journal of Computational Physics, 17, 1, 87-94, (1975) · Zbl 0293.65022
[15] Morgan, R. B.; Scott, D. S., Generalizations of Davidson’s method for computing eigenvalues of sparse symmetric matrices, Society for Industrial and Applied Mathematics. Journal on Scientific and Statistical Computing, 7, 3, 817-825, (1986) · Zbl 0602.65020
[16] Sleijpen, G. L.; Van der Vorst, H. A., A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM Journal on Matrix Analysis and Applications, 17, 2, 401-425, (1996) · Zbl 0860.65023
[17] Fan, X.; Chen, P.; Wu, R.; Xiao, S., Parallel computing study for the large-scale generalized eigenvalue problems in modal analysis, Science China Physics, Mechanics and Astronomy, 57, 3, 477-489, (2014)
[18] Hernandez, V.; Roman, J. E.; Vidal, V., SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems, Association for Computing Machinery. Transactions on Mathematical Software, 31, 3, 351-362, (2005) · Zbl 1136.65315
[19] Zhao, W. B.; Liu, Q. K.; Qin, G. M., Parallel computation for finite element method based on hierarchical data structure, Computer Engineering & Science, 34, 8, 107-111, (2012)
[20] Balay, S.; Buschelman, K.; Eijkhout, V., PETSc users manual, (2008), Argonne National Laboratory
[21] Alkhaleefi, A. M.; Ali, A., An efficient multi-point support-motion random vibration analysis technique, Computers and Structures, 80, 22, 1689-1697, (2002)
[22] Chopra, A. K., Dynamics of Structures-Theory and Applications to Earthquake Engineering, (2012), New Jersey, NJ, USA: Prentice Hall, New Jersey, NJ, USA
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