Structural Engineering and Mechanics

  • 제38권4호
  • /
  • Pages.405-416
  • /
  • 2011
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A two-level parallel algorithm for material nonlinearity problems

  • Lee, Jeeho (Department of Civil and Environmental Engineering, Dongguk University-Seoul) ;
  • Kim, Min Seok (Department of Civil and Environmental Engineering, Dongguk University-Seoul)
  • 투고 : 2010.04.28
  • 심사 : 2010.11.24
  • 발행 : 2011.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

An efficient two-level domain decomposition parallel algorithm is suggested to solve large-DOF structural problems with nonlinear material models generating unsymmetric tangent matrices, such as a group of plastic-damage material models. The parallel version of the stabilized bi-conjugate gradient method is developed to solve unsymmetric coarse problems iteratively. In the present approach the coarse DOF system is solved parallelly on each processor rather than the whole system equation to minimize the data communication between processors, which is appropriate to maintain the computing performance on a non-supercomputer level cluster system. The performance test results show that the suggested algorithm provides scalability on computing performance and an efficient approach to solve large-DOF nonlinear structural problems on a cluster system.

키워드

참고문헌

  1. ABAQUS (2005), ABAQUS Theory Manual, ABAQUS Inc., RI, USA.
  2. Balay, S., Buschelman, K., Gropp, W., Kaushik, D., Knepley, M., McInnes, L.C., Smith, B. and Zhang, H. (2002), PETSc Users' Manual, Report 95/11-Rev. 2.2.3, Argonne National Laboratory, IL.
  3. Blackford, L.S., Choi, J., Cleary, A., D'Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D. and Whaley, R.C. (1997), ScaLAPACK Users' Guide, SIAM Publications, Philadelphia, PA.
  4. Brill, S.H. and Pinder, G.F. (2002), "Parallel implementation of the Bi-CGSTAB method with block red-black Gauss-Seidel preconditioner applied to the Hermite collocation discretization of partial differential equations", Parallel Comput., 28(3), 399-414. https://doi.org/10.1016/S0167-8191(01)00131-4
  5. Davis, T.A. (2004), "A column pre-ordering strategy for the unsymmetric-pattern multifrontal method", ACM T. Math. Software, 30(2), 165-195. https://doi.org/10.1145/992200.992205
  6. Gropp, W., Lusk, E. and Skjellum, A. (1994), Using MPI: Portable Parallel Programming with the Message Passing Interface, The MIT Press.
  7. Lee, J. and Fenves, G.L. (1998), "Plastic-damage model for cyclic loading of concrete structures", J. Eng. Mech.-ASCE, 124(8), 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892)
  8. Lee, J. and Fenves, G.L. (2001), "A return-mapping algorithm for plastic-damage models: 3-D and plane stress formulation", Int. J. Numer. Meth. Eng., 50(2), 487-506. https://doi.org/10.1002/1097-0207(20010120)50:2<487::AID-NME44>3.0.CO;2-N
  9. Lubliner, J., Oliver, J., Oller, S. and Onate, E. (1989), "A plastic-damage model for concrete", Int. J. Solids Struct., 25(3), 299-326. https://doi.org/10.1016/0020-7683(89)90050-4
  10. Mandel, J. (1993), "Balancing domain decomposition", Commun. Numer. Meth. Eng., 9(3), 233-241. https://doi.org/10.1002/cnm.1640090307
  11. Mazars, J. and Pijaudier-Cabot, G. (1989), "Continuum damage theory-application to concrete", J. Eng. Mech.-ASCE, 115(2), 345-365. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:2(345)
  12. Simo, J.C. and Ju, J.W. (1987), "Stress and strain based continuum damage models - I. Formulation", Int. J. Solids Struct., 23(7), 821-840. https://doi.org/10.1016/0020-7683(87)90083-7
  13. Simo, J.C. and Taylor, R.L. (1986), "A return mapping algorithm for plane stress elastoplasticity", Int. J. Numer. Meth. Eng., 22(3), 649-670. https://doi.org/10.1002/nme.1620220310
  14. Smith, B.F., Bjorstad, P. and Gropp, W.D. (1996), Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press.
  15. Toselli, A. and Widlund, O.B. (2004), Domain Decomposition Methods - Algorithms and Theory, Springer.
  16. Van der Vorst, H.A. (1992), "Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems", SIAM J. Sci. Comput., 13(2), 631-644. https://doi.org/10.1137/0913035

피인용 문헌

  1. Integrated Fluid–Structure Simulation for Full Burning of a Solid-Propellant Rocket Interior vol.30, pp.4, 2014, https://doi.org/10.2514/1.B35107