Open Access
Volume 57, Number 1, January-February 2023
Page(s) 243 - 269
Published online 03 February 2023
  1. T. Belytschko and R. Mullen, Stability of explicit-implicit mesh partitions in time integration. Int. J. Numer. Methods Eng. 12 (1978) 1575–1586. [CrossRef] [Google Scholar]
  2. P. Smolinski, T. Belytschko and M. Neal, Multi-time-step integration using nodal partitioning. Int. J. Numer. Methods Eng. 26 (1988) 349–359. [CrossRef] [Google Scholar]
  3. T.J.R. Hughes and W.K. Liu, Implicit-explicit finite elements in transient analysis: stability theory. J. Appl. Mech. 45 (1978) 371–374. [CrossRef] [Google Scholar]
  4. T.J. Hughes, K.S. Pister and R.L. Taylor, Implicit-explicit finite elements in nonlinear transient analysis. Comput. Methods Appl. Mech. Eng. 17–18 (1979) 159–182. [CrossRef] [Google Scholar]
  5. T. Belytschko, H.-J. Yen and R. Mullen, Mixed methods for time integration. Comput. Methods Appl. Mech. Eng. 17–18 (1979) 259–275. [CrossRef] [Google Scholar]
  6. Y. Wu and P. Smolinski, A multi-time step integration algorithm for structural dynamics based on the modified trapezoidal rule. Comput. Methods Appl. Mech. Eng. 187 (2000) 641–660. [CrossRef] [Google Scholar]
  7. A. Combescure and A. Gravouil, A numerical scheme to couple subdomains with different time-steps for predominantly linear transient analysis. Comput. Methods Appl. Mech. Eng. 191 (2002) 1129–1157. [CrossRef] [Google Scholar]
  8. A. Bonelli, O.S. Bursi, L. He, G. Magonette and P. Pegon, Convergence analysis of a parallel interfield method for heterogeneous simulations with dynamic substructuring. Int. J. Numer. Methods Eng. 75 (2008) 800–825. [CrossRef] [Google Scholar]
  9. O. Bursi, L. He, A. Bonelli and P. Pegon, Novel generalized-α methods for interfield parallel integration of heterogeneous structural dynamic systems. J. Comput. Appl. Math. 234 (2010) 2250–2258. [CrossRef] [MathSciNet] [Google Scholar]
  10. N. Mahjoubi, A. Gravouil, A. Combescure and N. Greffet, A monolithic energy conserving method to couple heterogeneous time integrators with incompatible time steps in structural dynamics. Comput. Methods Appl. Mech. Eng. 200 (2011) 1069–1086. [CrossRef] [Google Scholar]
  11. E. Zafati, M. Brun, I. Djeran-Maigre and F. Prunier, Design of an efficient multi-directional explicit/implicit rayleigh absorbing layer for seismic wave propagation in unbounded domain using a strong form formulation. Int. J. Numer. Methods Eng. 106 (2015) 83–112. [Google Scholar]
  12. M. Brun, A. Gravouil, A. Combescure and A. Limam, Two FETI-based heterogeneous time step coupling methods for newmark and α-schemes derived from the energy method. Comput. Methods Appl. Mech. Eng. 283 (2015) 130–176. [CrossRef] [Google Scholar]
  13. S. Karimi and K. Nakshatrala, A monolithic multi-time-step computational framework for first-order transient systems with disparate scales. Comput. Methods Appl. Mech. Eng. 283 (2015) 419–453. [CrossRef] [Google Scholar]
  14. F.-E. Fekak, M. Brun, A. Gravouil and B. Depale, A new heterogeneous asynchronous explicit-implicit time integrator for nonsmooth dynamics. Comput. Mech. 60 (2017) 1–21. [CrossRef] [MathSciNet] [Google Scholar]
  15. E. Zafati and J.A. Hout, Reflection error analysis for wave propagation problems solved by a heterogeneous asynchronous time integrator. Int. J. Numer. Methods Eng. 115 (2018) 651–694. [CrossRef] [Google Scholar]
  16. M. Beneš, T. Krejč and J. Kruis, A FETI-based mixed explicit–implicit multi-time-step method for parabolic problems. J. Comput. Appl. Math. 333 (2018) 247–265. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Brun, E. Zafati, I. Djeran-Maigre and F. Prunier, Hybrid asynchronous perfectly matched layer for seismic wave propagation in unbounded domains. Finite Elem. Anal. Des. 122 (2016) 1–15. [CrossRef] [MathSciNet] [Google Scholar]
  18. S. Li, M. Brun, I. Djeran-Maigre and S. Kuznetsov, Benchmark for three-dimensional explicit asynchronous absorbing layers for ground wave propagation and wave barriers. Comput. Geotech. 131 (2021) 103808. [CrossRef] [Google Scholar]
  19. J. Nunez-Ramirez, J.-C. Marongiu, M. Brun and A. Combescure, A partitioned approach for the coupling of SPH and FE methods for transient nonlinear FSI problems with incompatible time-steps. Int. J. Numer. Methods Eng. 109 (2016) 1391–1417. [Google Scholar]
  20. N. Newmark, A method of computation for structural dynamics. J. Eng. Mech. Div. (ASCE) 85 (1959) 67–94. [CrossRef] [Google Scholar]
  21. H. Hilber, T. Hughes and R. Taylor, Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng. Struct. Dyn. 5 (1977) 283–292. [CrossRef] [Google Scholar]
  22. W.L. Wood, M. Bossak and O.C. Zienkiewicz, An alpha modification of newmark’s method. Int. J. Numer. Methods Eng. 15 (1980) 1562–1566. [CrossRef] [Google Scholar]
  23. J. Chung and G. Hulbert, A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. J. Appl. Mech. 60 (1993) 371–375. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Springer Berlin Heidelberg (1996). [Google Scholar]
  25. A. Prakash and K.D. Hjelmstad, A FETI-based multi-time-step coupling method for newmark schemes in structural dynamics. Int. J. Numer. Methods Eng. 61 (2004) 2183–2204. [CrossRef] [Google Scholar]
  26. E. Zafati, Discussions on a macro multi-time scales coupling method: existence and uniqueness of the numerical solution and strict non-negativity of the schur complement. Numer. Algorithms 90 (2021) 1389–1417. [Google Scholar]
  27. R.A. Nicolaides, Existence, uniqueness and approximation for generalized saddle point problems. SIAM J. Numer. Anal. 19 (1982) 349–357. [Google Scholar]
  28. C. Bernardi, C. Canuto and Y. Maday, Generalized inf-sup conditions for chebyshev spectral approximation of the stokes problem. SIAM J. Numer. Anal. 25 (1988) 1237–1271. [Google Scholar]
  29. F. Brezzi, On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers. ESAIM: Math. Modell. Numer. Anal. – Modélisation Mathématique et Analyse Numérique 8 (1974) 129–151. [Google Scholar]
  30. R.A. Adams, Sobolev Spaces. Pure and Applied Mathematics. Vol. 140. Academic Press (2003). [Google Scholar]
  31. G.S. Jones, Fundamental inequalities for discrete and discontinuous functional equations. J. Soc. Ind. Appl. Math. 12 (1964) 43–57. [Google Scholar]
  32. Y. Qin, Integral and Discrete Inequalities and Their Applications. Springer International Publishing (2016). [Google Scholar]
  33. E. Zeidler, Nonlinear Functional Analysis and its Applications. Springer New York (1990). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you