Dual-Rate Integration Using Partitioned Runge-Kutta Methods for Mechanical Systems with Interacting Subsystems#

Shome, Siddhartha S.; Haug, Edward J.; Jay, Laurent O.

doi:10.1081/lmdb-200027930

Cited by 4 publications

(4 citation statements)

References 5 publications

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“…In numerical analysis, it is custom to deal with these requirements by means of subcycling strategies. For instance, see Weiner et al [35] and Shome et al [36], among others, in the context of partitioned Runge-Kutta methods. Similarly, interfield parallel algorithms without and with numerical dissipation were developed for linear multistep methods [18,37].…”

Section: Subcycling Strategiesmentioning

confidence: 98%

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

Bursi

Cui

Vulcan

et al. 2010

Earthq Engng Struct Dyn

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SUMMARYIn this paper, Rosenbrock-based algorithms originally developed for real-time testing of linear systems with dynamic substructuring are extended for use on nonlinear systems. With this objective in mind and for minimal overhead, both two-and three-stages linearly implicit real-time compatible algorithms were endowed with the Jacobian matrices requiring only one evaluation at the beginning of each time step. Moreover, these algorithms were improved with subcycling strategies. In detail, the paper briefly introduces Rosenbrock-based L-Stable Real-Time (LSRT) algorithms together with linearly implicit and explicit structural integrators, which are now commonly used to perform real-time tests. Then, the LSRT algorithms are analysed in terms of linearized stability with reference to an emulated spring pendulum, which was chosen as a nonlinear test problem, because it is able to exhibit a large and relatively slow nonlinear circular motion coupled to an axial motion that can be set to be stiff. The accuracy analysis on this system was performed for all the algorithms described. Following this, a coupled spring-pendulum example typical of real-time testing is analysed with respect to both stability and accuracy issues. Finally, the results of representative numerical simulations and real-time substructure tests, considering nonlinearities both in the numerical and the physical substructure, are explored. These tests were used to demonstrate how the LSRT algorithms can be used for substructuring tests with strongly nonlinear components.

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Section: Subcycling Strategiesmentioning

confidence: 98%

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

Bursi

Cui

Vulcan

et al. 2010

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

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“…Some research work has been done to address the former issue. For example, Shome et al developed a partitioned Runge-Kutta method by combining multi-rate integration (dividing state variables as high-frequency and low-frequency subsets) and partitioned integration (dividing state variables as stiff and non-stiff subsets) [29]. Arnold [4] studied the multi-rate integration problem in applied dynamics and developed solutions for the key issues such as the selection and control of step size, the processing of simulation data, and the treatment of ill-structured models.…”

Section: Runtime Integration Between Computational Modelsmentioning

confidence: 99%

A variable-step interaction algorithm for multidisciplinary collaborative simulation

Wang

Mao

Zhang

2014

ICA

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Multidisciplinary collaborative simulation is an important technique for the development of complex engineering systems such as aircrafts and automobiles. It emphasizes the synergic collaboration of multidisciplinary computational models, involving the exchange of simulation data generated in parallel at runtime from the numerical integration processes of these models. Current research on the interaction of models in multidisciplinary collaborative simulation is mainly focused on performing data exchange at fixed intervals, i.e. macro time steps, and using interpolation/extrapolation to find out values at the points in time when data are not available. However, the selection of an appropriate size for macro time tends to be complex and iterative. Firstly, it is mostly based on experience rather than the estimation of simulation errors by analyzing the numerical integration processes involved. Moreover, it is hardly possible to select a fixed step size suitable for all the stages of the simulation process. This paper presents a novel variable-step algorithm which is able to adjust the step size automatically at simulation runtime based on the evaluation of truncation errors. This algorithm not only avoids the instability and inaccuracy caused by a fixed large step but also speeds up the simulation by using a smaller step when a large one is not necessary. It is demonstrated in the numerical experiments that the variable-step algorithm can achieve improved simulation performance in terms of both speed and accuracy.

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“…Some research work has been done to address these issues. For example, Shome et al proposed a partitioned Runge-Kutta method by combining a multi-rate integration method (dividing state variables as high-frequency and low-frequency subsets) with partitioned integration (dividing state variables as stiff and non-stiff subsets) [19]. Arnold studied the numerical methods for simulation and multi-rate integration in applied dynamics [17], [18].…”

Section: Run-time Integration Between Computational Modelsmentioning

confidence: 99%

A study on the run-time interaction between distributed computational models in multidisciplinary collaborative simulation

Wang

Zhang

2010

2010 IEEE International Conference on Systems, Man and Cybernetics

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Simulation technology is widely applied in product development to make forecasts on the performance of design solutions for which it is difficult or not economical to develop physical prototypes. There are some circumstances, e.g. the development of mechatronic products, under which a number of simulations need to be used together. Therefore, it is necessary to develop a collaborative simulation platform which enables design engineers in a multidisciplinary team to develop, share, reuse, and integrate computational models. Difficulties in developing such a platform include using multiple simulation tools, the run time integration of distributed models, the sharing of proprietary information, etc. Among these difficulties, run-time integration of distributed models is the one significantly affecting the accuracy, efficiency and stability of a simulation. This paper describes how multidisciplinary collaborative simulation problem can be solved, discusses different methods for run-time interaction, and presents a novel method that is proposed and implemented in a prototype system for collaborative simulation. Further evaluation on these methods shows that the novel method has better performance in terms of both accuracy and efficiency.

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Dual-Rate Integration Using Partitioned Runge-Kutta Methods for Mechanical Systems with Interacting Subsystems#

Cited by 4 publications

References 5 publications

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

Rosenbrock‐based algorithms and subcycling strategies for real‐time nonlinear substructure testing

A variable-step interaction algorithm for multidisciplinary collaborative simulation

A study on the run-time interaction between distributed computational models in multidisciplinary collaborative simulation

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