Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics |
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| Affiliation: | 1. Aerospace Laboratories (LTAS-MCT), University of Liège, Chemin des Chevreuils 1, 4000 Liège, Belgium;2. SNECMA-Moteurs, Engineering Division, Centre de Villaroche, 77550 Moissy-Cramayel, France;1. Department of Chemistry, Dibrugarh University, Dibrugarh, Assam, 786004, India;2. Department of Chemistry, University of Calcutta, Kolkata, West Bengal, 700009, India;1. School of Mechanical Engineering, Jiangsu University of Technology, 1801 Zhongwu Rd., Changzhou, 213001, China;2. School of Electrical and Information Engineering, Changzhou Institute of Technology, 666 Liaohe Rd., Changzhou, 213000, China;3. College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao St., Nanjing, 210016, China;1. Department of Dynamics and Vibrations, Institute of Thermomechanics, Dolejškova 1402/5, 182 00 Prague 8, Czech Republic;2. Department of Applied Mechanics, VŠB-Technical University of Ostrava, 17. Listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic;3. IT4Innovations National Supercomputing Center, VŠB-Technical University of Ostrava, 17. Listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic;1. Niederrhein University of Applied Sciences, Institute for Pattern Recognition, Reinarzstr. 49, 47805 Krefeld, Germany;2. Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA;3. National Superconducting Cyclotron Laboratory, 640 S. Shaw Lane, East Lansing, MI 48824, USA |
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| Abstract: | When an implicit integration scheme is used, variable step strategies are especially well suited to deal with problems characterized by high non-linearities. Constant step size strategies generally lead to divergence or extremely costly computations. An automatic time stepping algorithm is proposed that is based on estimators of the integration error of the differential dynamic balance equations. Additionally, the proposed algorithm automatically takes decisions regarding the necessity of updating the tangent matrix or stopping the iterations, further reducing the computational cost. As an illustration of the capabilities of this algorithm, several numerical simulations of both academic and industrial problems are presented. |
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