Efficient exponential time integration for simulating nonlinear coupled oscillators
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer Science Program
Visual Computing Center (VCC)
Embargo End Date2022-01-27
Permanent link to this recordhttp://hdl.handle.net/10754/667422
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AbstractIn this paper, we propose an advanced time integration technique associated with explicit exponential Rosenbrock-based methods for the simulation of large stiff systems of nonlinear coupled oscillators. In particular, a novel reformulation of these systems is introduced and a general family of efficient exponential Rosenbrock schemes for simulating the reformulated system is derived. Moreover, we show the required regularity conditions and prove the convergence of these schemes for the system of coupled oscillators. We present an efficient implementation of this new approach and discuss several applications in scientific and visual computing. The accuracy and efficiency of our approach are demonstrated through a broad spectrum of numerical examples, including a nonlinear Fermi–Pasta–Ulam–Tsingou model, elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects such as stability and energy conservation, large numerical stiffness, high fidelity, and visual accuracy.
CitationLuan, V. T., & Michels, D. L. (2021). Efficient exponential time integration for simulating nonlinear coupled oscillators. Journal of Computational and Applied Mathematics, 113429. doi:10.1016/j.cam.2021.113429
SponsorsThe authors would like to thank the anonymous referees for their valuable comments and useful suggestions. The first author gratefully acknowledges the financial support of the National Science Foundation, USA under grant NSF DMS–2012022. The second author acknowledges the financial support of KAUST, Saudi Arabia baseline funding. We also thank Mississippi State University’s Center for Computational Science (CCS) for providing computing resources at the High Performance Computing Collaboratory (HPCC). Moreover, the use of the resources of KAUST’s Supercomputing Laboratory is gratefully acknowledged.