Efficient exponential time integration for simulating nonlinear coupled oscillators
Name:
Articlefile1.pdf
Size:
3.287Mb
Format:
PDF
Description:
Post-print
Embargo End Date:
2022-01-27
Type
ArticleAuthors
Luan, Vu ThaiMichels, Dominik L.
KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionComputer Science Program
Visual Computing Center (VCC)
Date
2021-01-27Embargo End Date
2022-01-27Submitted Date
2020-09-12Permanent link to this record
http://hdl.handle.net/10754/667422
Metadata
Show full item recordAbstract
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.2021.113429Sponsors
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 BVAdditional Links
https://linkinghub.elsevier.com/retrieve/pii/S0377042721000480ae974a485f413a2113503eed53cd6c53
10.1016/j.cam.2021.113429