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Volume 42, Issue 4
A Linearly-Implicit Structure-Preserving Exponential Time Differencing Scheme for Hamiltonian PDEs

Yayun Fu, Dongdong Hu, Wenjun Cai & Yushun Wang

DOI: 10.4208/jcm.2302-m2020-0279

J. Comp. Math., 42 (2024), pp. 1063-1079.

Published online: 2024-04

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  • Abstract

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.

  • Keywords

Structure-preserving algorithm, Hamiltonian PDE, Energy quadratization method, Exponential time differencing.

  • AMS Subject Headings

65M06, 65M70

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-1063, author = {Fu , YayunHu , DongdongCai , Wenjun and Wang , Yushun}, title = {A Linearly-Implicit Structure-Preserving Exponential Time Differencing Scheme for Hamiltonian PDEs}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {4}, pages = {1063--1079}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2302-m2020-0279}, url = {http://global-sci.org/intro/article_detail/jcm/23046.html} }
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.

Yayun Fu, Dongdong Hu, Wenjun Cai & Yushun Wang. (2024). A Linearly-Implicit Structure-Preserving Exponential Time Differencing Scheme for Hamiltonian PDEs. Journal of Computational Mathematics. 42 (4). 1063-1079. doi:10.4208/jcm.2302-m2020-0279
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