Structural Engineering and Mechanics

  • 제4권6호
  • /
  • Pages.589-600
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  • 1996
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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On a new fourth order self-adaptive time integration algorithm

  • Zhong, Wanxie (Research Institute of Engineering Mechanics, Dalian University of Technology) ;
  • Zhu, Jianping (Department of Mathematics and Statistics, Mississippi State University)
  • 발행 : 1996.11.25
⟨ 이전 논문 다음 논문 ⟩

초록

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

키워드

참고문헌

  1. Choi, C.K. and Chung, H.J. (1994), "An adaptive procedure in finite element analysis of elastodynamic problems", Proceedings of International Conference Computational Methods in Structural and Geotechnical Engineering, Hong Kong, December.
  2. Press, W.H., Teukolsky, S.A., Vetterling, W.T. and Flannery, B.P. (1992), Numerical Recipes, 2nd ed. Cambridge University Press, New York.
  3. Wang, H.Z. (1994), "A posteriori error estimator of energy and adaptive coordination of spatial-temporal discretization for FEM and direct integration in transient dynamic analysis", Proceedings of International Conference on Computational Methods in Structural and Geotechnical Engineering, Hong Kong, December.
  4. Zeng, L.F., Wiberg, N.E. and Li, X.D. (1992), "A posteriori local error estimation and adaptive time-stepping for Newark integration in dynamic analysis", Earthquake Engineering and Structural Dynamics, 21, 555-571. https://doi.org/10.1002/eqe.4290210701
  5. Zhong, W. (1995), "Subdomain precise time integration and numerical solution of partial differential equations", Computational Structural Mechanics and Its Applications, to appear (in Chinese).
  6. Zhong, W.X. (1993), Computational Mechanics and Optimal Control, Dalian University Press, Dalian, China.
  7. Zhong, W.X. and Zhu, J.P. (1994), "Rethinking to finite difference time-step integrations", Proceedings of International Conference on Computational Methods in Structural and Geotechnical Engineering, Hong Kong, December.
  8. Zienkiewicz, O.C. and Taylor, R.L. (1991), The Finite Element Method, 4th ed., McGraw-Hill, New York.
  9. Zienkiewicz, O.C. and Xie, Y.M. (1991), "A simple error estimator and adaptive time stepping procedure for dynamic analysis", Earthquake Engineering and Structural Dynamics, 20, 871-887. https://doi.org/10.1002/eqe.4290200907
  10. Zhong, W.X. and Yang, Z.S. (1991), "An algorithm for computing the main eigenpairs in time continuous LQ control", Applied Mathematics and Mechanics, 12, 45-50.

피인용 문헌

  1. Extended implicit integration process by utilizing nonlinear dynamics in finite element vol.64, pp.4, 1996, https://doi.org/10.12989/sem.2017.64.4.495