Truncation error calculation based on Richardson extrapolation for variable-step collaborative simulation

Collaborative simulation is an effective approach to performing simulation analysis for complex systems by integrating models developed for different engineering disciplines. Collaborative simulation issues include the modeling of coupled multidisciplinary systems, and the simulation running time integration of these models that are solved parallelly. Estimation of the local truncation error of coupling models is the key to solve multidisciplinary collaborative simulation problem, which is actually used to restrict the simulation step. This paper presents a variable-step method based on Richardson extrapolation for calculating the local truncation error to solve collaborative simulation problem of multidisciplinary coupling models. Formulas for estimating the local truncation error are derived through theoretical analysis by using integration methods and interpolation technologies, respectively. The simulation experiments are illustrated to validate the accuracy and efficiency of proposed collaborative simulation algorithm in comparison with the usual combinative algorithm.

[1]  Cheng Wu,et al.  Generalized gradient projection neural networks for nonsmooth optimization problems , 2010, Science China Information Sciences.

[2]  O. Wasynczuk,et al.  An efficient multirate Simulation technique for power-electronic-based systems , 2004, IEEE Transactions on Power Systems.

[3]  Robert M. O'Bara,et al.  Toward simulation-based design , 2004 .

[4]  Martin Arnold,et al.  Numerical methods for simulation in applied dynamics , 2008 .

[5]  Charbel Farhat,et al.  Partitioned analysis of coupled mechanical systems , 2001 .

[6]  Werner Schiehlen,et al.  Two Methods of Simulator Coupling , 2000 .

[7]  Heming Zhang,et al.  A novel combinative algorithm for multidisciplinary collaborative simulation , 2008, 2008 12th International Conference on Computer Supported Cooperative Work in Design.

[8]  Heming Zhang,et al.  A distributed and interactive system to integrated design and simulation for collaborative product development , 2010 .

[9]  HeMing Zhang.  A solution of multidisciplinary collaborative simulation for complex engineering systems in a distributed heterogeneous environment , 2009, Science in China Series F: Information Sciences.

[10]  Werner Schiehlen,et al.  Simulation Techniques for Applied Dynamics , 2009 .

[11]  Heming Zhang,et al.  A model-driven approach to multidisciplinary collaborative simulation for virtual product development , 2010, Adv. Eng. Informatics.

[12]  Edward J. Haug,et al.  Dual-Rate Integration Using Partitioned Runge-Kutta Methods for Mechanical Systems with Interacting Subsystems , 2004 .

[13]  Martin Arnold,et al.  Multi-Rate Time Integration for Large Scale Multibody System Models , 2007 .

[14]  Nicola Senin,et al.  Distributed Object-Based Modeling in Design Simulation Marketplace , 2003 .

[15]  Peter Eberhard.  IUTAM Symposium on Multiscale Problems in Multibody System Contacts , 2007 .

[16]  Eric Walters,et al.  An efficient multirate Simulation technique for power-electronic-based systems , 2004 .

[17]  C. W. Gear,et al.  Multirate linear multistep methods , 1984 .

[18]  Heming Zhang,et al.  Towards a collaborative modeling and simulation platform on the Internet , 2010, Adv. Eng. Informatics.

[19]  Heming Zhang,et al.  An integrated and collaborative approach for complex product development in distributed heterogeneous environment , 2008 .