A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
复制标题
非线性Klein-Gordon方程的线性隐式保能指数积分器
DOI：
10.1016/j.jcp.2020.109690
复制
发表时间：
2020
影响因子：
4.1
通讯作者：
Cai Wenjun
中科院分区：
文献类型：
--
作者：
Jiang Chaolong;Wang Yushun;Cai Wenjun
在本文中，我们推广了最近论文中提出的指数保能积分器[j]。计算。38 (2016)A1876-A1895]的保守系统，现在通过进一步利用标量辅助变量方法的思想变得线性隐式。与原来的指数保能积分法通常得到非线性代数系统相比，新方法只涉及常系数矩阵的线性系统。以非线性Klein-Gordon方程和非线性Schrödinger方程为例，推导出了具体的节能方案，并通过数值实验证明了它们的高效性。
In this paper, we generalize the exponential energy-preserving integrator proposed in the recent paper [SIAM J. Sci. Comput. 38 (2016) A1876–A1895] for conservative systems, which now becomes linearly implicit by further utilizing the idea of the scalar auxiliary variable approach. Comparing with the original exponential energy-preserving integrator which usually leads to a nonlinear algebraic system, our new method only involves a linear system with a constant coefficient matrix. Taking the nonlinear Klein-Gordon equation and the nonlinear Schrödinger equation for examples, we derive the concrete energy-preserving schemes and demonstrate their high efficiency through numerical experiments.