TY - JOUR T1 - A Linearly-Implicit Structure-Preserving Exponential Time Differencing Scheme for Hamiltonian PDEs AU - Fu , Yayun AU - Hu , Dongdong AU - Cai , Wenjun AU - Wang , Yushun JO - Journal of Computational Mathematics VL - 4 SP - 1063 EP - 1079 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2302-m2020-0279 UR - https://global-sci.org/intro/article_detail/jcm/23046.html KW - Structure-preserving algorithm, Hamiltonian PDE, Energy quadratization method, Exponential time differencing. AB -

In the paper, we propose a novel linearly implicit structure-preserving algorithm, which is derived by combing the invariant energy quadratization approach with the exponential time differencing method, to construct efficient and accurate time discretization scheme for a large class of Hamiltonian partial differential equations (PDEs). The proposed scheme is a linear system, and can be solved more efficient than the original energy-preserving exponential integrator scheme which usually needs nonlinear iterations. Various experiments are performed to verify the conservation, efficiency and good performance at relatively large time step in long time computations.