Efficient exponential time integration for simulating nonlinear coupled oscillators

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:391

Article

Luan, Vu Thai¹  Michels, Dominik L.² 

[1] Mississippi State Univ, Dept Math & Stat, 410 Allen Hall,175 Presidents Circle, Mississippi State, MS 39762 USA

[2] KAUST, Visual Comp Ctr, Computat Sci Grp, Bldg 1, Thuwal 23955, Saudi Arabia

关键词: Systems of coupled oscillators;    Exponential Rosenbrock integrators;    Accurate and efficient simulation;    Visual computing;   

DOI  :  10.1016/j.cam.2021.113429

来源: Elsevier

【 摘 要 】

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. (c) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free