Multi-time-step integration
In numerical analysis, multi-time-step integration, also referred to as multiple-step or asynchronous time integration, is a numerical time-integration method that uses different time-steps or time-integrators for different parts of the problem. There are different approaches to multi-time-step integration. They are based on domain decompostition[1][2] and can be classified into strong (monolithic) or weak (staggered) schemes.[3] Using different time-steps or time-integrators in the context of a weak algorithm is rather straightforward, because the numerical solvers operate independently. However, this is not the case in a strong algorithm. In the past few years a number of research articles have addressed the development of strong multi-time-step algorithms.[4][5][6][7] In either case, strong or weak, the numerical accuracy and stability needs to be carefully studied. Other approaches to multi-time-step integration in the context of operator splitting methods have also been developed; i.e., multi-rate GARK method and multi-step methods for molecular dynamics simulations.[8]
References
- ^ Domain Decomposition Methods for Partial Differential Equations.
- ^ Toselli, Andrea; Widlund, Olof B. Domain Decomposition Methods — Algorithms and Theory – Springer. doi:10.1007/b137868.
- ^ Felippa, Carlos A.; Park, K. C.; Farhat, Charbel (2001-03-02). "Partitioned analysis of coupled mechanical systems". Computer Methods in Applied Mechanics and Engineering. Advances in Computational Methods for Fluid-Structure Interaction. 190 (24–25): 3247–3270. doi:10.1016/S0045-7825(00)00391-1.
- ^ Gravouil, Anthony; Combescure, Alain (2001-01-10). "Multi-time-step explicit–implicit method for non-linear structural dynamics". International Journal for Numerical Methods in Engineering. 50 (1): 199–225. doi:10.1002/1097-0207(20010110)50:13.0.CO;2-A. ISSN 1097-0207.
- ^ Prakash, A.; Hjelmstad, K. D. (2004-12-07). "A FETI-based multi-time-step coupling method for Newmark schemes in structural dynamics". International Journal for Numerical Methods in Engineering. 61 (13): 2183–2204. doi:10.1002/nme.1136. ISSN 1097-0207.
- ^ Karimi, S.; Nakshatrala, K. B. (2014-09-15). "On multi-time-step monolithic coupling algorithms for elastodynamics". Journal of Computational Physics. 273: 671–705. arXiv:1305.6355. doi:10.1016/j.jcp.2014.05.034.
- ^ Karimi, S.; Nakshatrala, K. B. (2015-01-01). "A monolithic multi-time-step computational framework for first-order transient systems with disparate scales". Computer Methods in Applied Mechanics and Engineering. 283: 419–453. doi:10.1016/j.cma.2014.10.003.
- ^ Jia, Zhidong; Leimkuhler, Ben (2006-01-01). "Geometric integrators for multiple time-scale simulation". Journal of Physics A: Mathematical and General. 39 (19): 5379. doi:10.1088/0305-4470/39/19/S04. ISSN 0305-4470.