INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2011; 87:1148–1182 Published online 23 February 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.3153 Novel partitioned time integration methods for DAE systems based on L-stable linearly implicit algorithms C. Jia, O. S. Bursi ∗, † , A. Bonelli and Z. Wang Dipartimento di Ingegneria Meccanica e Strutturale, Università di Trento, Italy SUMMARY Real-time applications based on the principle of Dynamic Substructuring require integration methods that can deal with constraints without exceeding an a priori fixed number of steps. For these applications, first we introduce novel partitioned algorithms able to solve DAEs arising from transient structural dynamics. In particular, the spatial domain is partitioned into a set of disconnected subdomains and continuity conditions of acceleration at the interface are modeled using a dual Schur formulation. Interface equations along with subdomain equations lead to a system of DAEs for which both staggered and parallel procedures are developed. Moreover under the framework of projection methods, also a parallel partitioned method is conceived. The proposed partitioned algorithms enable a Rosenbrock-based linearly implicit LSRT2 method, to be strongly coupled with different time steps in each subdomain. Thus, user-defined algorithmic damping and subcycling strategies are allowed. Secondly, the paper presents the convergence analysis of the novel schemes for linear single-Degree-of-Freedom (DoF) systems. The algorithms are generally A-stable and preserve the accuracy order as the original monolithic method. Successively, these results are validated via simulations on single- and three-DoFs systems. Finally, the insight gained from previous analyses is confirmed by means of numerical experiments on a coupled spring–pendulum system. Copyright  2011 John Wiley & Sons, Ltd. Received 13 August 2010; Revised 7 January 2011; Accepted 11 January 2011 KEY WORDS: real-time; differential-algebraic equations; interfield partitioned methods; parallel proce- dure; Rosenbrock integration methods 1. INTRODUCTION 1.1. Background and motivation Systems of ODEs arising from transient structural dynamics very often exhibit high-frequency/low- frequency and stiff/non-stiff behaviours of subsets of state variables. Hence, both linear Multistep (LMS) and Runge–Kutta (RK) algorithms integrating all state variables may exhibit limitations. Thus, several researchers resorted to the use of different time integrators for subsystems, in order to tailor each method to the solution behaviour of the corresponding subsystem, the so-called co-simulation or partitioning. For instance in the framework of multibody system dynamics, Arnold et al. [1] restricted the communication between subsystems to discrete synchronization points and required interpolation/extrapolation owing to the use of different time steps. They stated that co-simulation techniques could suffer from numerical instability that might be further exacer- bated by discretization errors introduced by interpolation/extrapolation. Thus, several modifications ∗ Correspondence to: O. S. Bursi, Dipartimento di Ingegneria Meccanica e Strutturale, Università di Trento, Via Mesiano 77, 38123 Trento, Italy. † E-mail: Oreste.Bursi@ing.unitn.it Copyright  2011 John Wiley & Sons, Ltd.