Efficient exponential time integration for simulating nonlinear coupled oscillators
Efficient exponential time integration for simulating nonlinear coupled oscillators
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DOI：
10.1016/j.cam.2021.113429
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Vu Thai Luan;D. Michels
中科院分区：
文献类型：
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作者：
Vu Thai Luan;D. Michels
在本文中，我们提出了一个先进的时间积分技术与显式指数Rosenbrock为基础的方法模拟大型刚性系统的非线性耦合振子。特别是，这些系统的一种新的重新制定的介绍和一般家庭的有效指数Rosenbrock计划，用于模拟重新制定的系统。此外，我们显示所需的正则性条件，并证明这些计划的耦合振子系统的收敛性。我们提出了一个有效的实现这种新的方法，并讨论了在科学和视觉计算的几个应用程序。我们的方法的准确性和效率，通过广泛的数值例子，包括非线性费米-帕斯塔-乌拉姆-Tsingou模型，弹性和非弹性变形以及碰撞的情况下，专注于相关方面，如稳定性和能量守恒，大数值刚度，高保真度和视觉精度证明。
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.