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 decomposition and can be classified into strong (monolithic) or weak (staggered) schemes.[1][2][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.[8] 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.[9]
^Toselli, Andrea; Widlund, Olof B. (2005). Domain Decomposition Methods — Algorithms and Theory – Springer. Springer Series in Computational Mathematics. Vol. 34. doi:10.1007/b137868. ISBN978-3-540-20696-5.
^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. Bibcode:2001CMAME.190.3247F. doi:10.1016/S0045-7825(00)00391-1.
^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. Bibcode:2004IJNME..61.2183P. doi:10.1002/nme.1136. ISSN1097-0207.
