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    Efficient exponential time integration for simulating nonlinear coupled oscillators

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    Description:
    Post-print
    Embargo End Date:
    2022-01-27
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    Type
    Article
    Authors
    Luan, Vu Thai
    Michels, Dominik L.
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Computer Science Program
    Visual Computing Center (VCC)
    Date
    2021-01-27
    Embargo End Date
    2022-01-27
    Submitted Date
    2020-09-12
    Permanent link to this record
    http://hdl.handle.net/10754/667422
    
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    Abstract
    In 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.
    Citation
    Luan, 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
    Sponsors
    The 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.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational and Applied Mathematics
    DOI
    10.1016/j.cam.2021.113429
    Additional Links
    https://linkinghub.elsevier.com/retrieve/pii/S0377042721000480
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cam.2021.113429
    Scopus Count
    Collections
    Articles; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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