The Functional Mockup Interface (FMI) is a tool independent standard for the exchange of dynamic models and for Co-Simulation. The first version, FMI 1.0, was published in 2010. Already more than 30 tools support FMI 1.0. In this paper an overview about the upcoming version 2.0 of FMI is given that combines the formerly separated interfaces for Model Exchange and Co-Simulation in one standard. Based on the experience on using FMI 1.0, many small details have been improved and new features introduced to ease the use and increase the performance especially for larger models. Additionally, a free FMI compliance checker is available and FMI models from different tools are made available on the web to simplify testing.

A variant of the generalized-α scheme is proposed for constrained mechanical systems represented by index-3 DAEs. Based on the analogy with linear multistep methods, an elegant convergence analysis is developed for this algorithm. Second-order convergence is demonstrated both for the generalized coordinates and the Lagrange multipliers, and those theoretical results are illustrated by numerical tests.

In this paper, we present a viscoelastic rod model that is suitable for fast and accurate dynamic simulations. It is based on Cosserats geometrically exact theory of rods and is able to represent extension, shearing (stiff dof), bending and torsion (soft dof). For inner dissipation, a consistent damping potential proposed by Antman is chosen. We parametrise the rotational dof by unit quaternions and directly use the quaternionic evolution differential equation for the discretisation of the Cosserat rod curvature. The discrete version of our rod model is obtained via a finite difference discretisation on a staggered grid. After an index reduction from three to zero, the right-hand side function f and the Jacobian f/(q,v,t) of the dynamical system q=v,v=f(q,v,t) is free of higher algebraic (e.g. root) or transcendental (e.g. trigonometric or exponential) functions and, therefore, cheap to evaluate. A comparison with Abaqus finite element results demonstrates the correct m echanical behaviour of our discrete rod model. For the time integration of the system, we use well established stiff solvers like Radau5 or Daspk. As our model yields computational times within milliseconds, it is suitable for interactive applications in virtual reality as well as for multi-body dynamics simulation

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a b s t r a c tExplicit time integration methods can be employed to simulate a broad spectrum of physical phenomena. The wide range of scales encountered lead to the problem that the fastest cell of the simulation dictates the global time step. Multirate time integration methods can be employed to alter the time step locally so that slower components take longer and fewer time steps, resulting in a moderate to substantial reduction of the computational cost, depending on the scenario to simulate [S. Osher, R. Sanders, Numerical approximations to nonlinear conservation laws with locally varying time and space grids, Math. Comput. 41 (1983) 321-336; H. Tang, G. Warnecke, A class of high resolution schemes for hyperbolic conservation laws and convection-diffusion equations with varying time and pace grids, SIAM J. Sci. Comput. 26 (4) (2005) 1415-1431; E. Constantinescu, A. Sandu, Multirate timestepping methods for hyperbolic conservation laws, SIAM J. Sci. Comput. 33 (3) (2007) 239-278].In air pollution modeling the advection part is usually integrated explicitly in time, where the time step is constrained by a locally varying Courant-Friedrichs-Lewy (CFL) number. Multirate schemes are a useful tool to decouple different physical regions so that this constraint becomes a local instead of a global restriction. Therefore it is of major interest to apply multirate schemes to the advection equation. We introduce a generic recursive multirate Runge-Kutta scheme that can be easily adapted to an arbitrary number of refinement levels. It preserves the linear invariants of the system and is of third order accuracy when applied to certain explicit Runge-Kutta methods as base method.

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Complex multi-disciplinary models in system dynamics are typically composed of subsystems. This modular structure of the model reflects the modular structure of complex engineering systems. In industrial applications, the individual subsystems are often modeled separately in different mono-disciplinary simulation tools. The Functional Mock-Up Interface (FMI) provides an interface standard for coupling physical models from different domains and addresses problems like export and import of model components in industrial simulation tools (FMI for Model Exchange) and the standardization of co-simulation interfaces in nonlinear system dynamics (FMI for Co-Simulation), see [8]. In November 2011, the third β -version of FMI for Model Exchange and Co-Simulation v2.0 was released [13] that supports advanced numerical techniques in co-simulation like higher order extrapolation and interpolation of subsystem inputs, step size control including step rejection and Jacobian based linearly implicit stabilization techniques. Well known industrial simulation tools for applied dynamics support Version 1.0 of this standard and plan to support the forthcoming Version 2.0 in the near future, see the "Tools" tab of website [8] for up-to-date information. The renewed interest in algorithmic and numerical aspects of co-simulation inspired some new investigations on error estimation and stabilization techniques in FMI for Model Exchange and Co-Simulation v2.0 compatible co-simulation environments. The present paper extends recent results from [3] on reliable error estimation and communication step size control in the framework of FMI for Model Exchange and Co-Simulation v2.0. Based on a strict mathematical analysis, we study the asymptotic behaviour of the local error and two error estimates that may be used to adapt the communication step size automatically to the changing solution behaviour during time integration. These theoretical results are illustrated by numerical tests for a (linear) quarter car model and provide a basis for future investigations with more complex coupled engineering systems.