Third-order symplectic integration method with inverse time dispersion transform for long-term simulation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:314

Article

Gao, Yingjie^1,2  Zhang, Jinhai¹  Yao, Zhenxing¹ 

[1] Chinese Acad Sci, Inst Geol & Geophys, Key Lab Earth & Planetary Phys, Beijing, Peoples R China

[2] Univ Chinese Acad Sci, Beijing, Peoples R China

关键词: Inverse time dispersion transform;    Time-dispersion error;    Pseudospectral method;    Symplectic integration method;    Long-term simulation;   

DOI  :  10.1016/j.jcp.2016.03.031

来源: Elsevier

【 摘 要 】

The symplectic integration method is popular in high-accuracy numerical simulations when discretizing temporal derivatives; however, it still suffers from time-dispersion error when the temporal interval is coarse, especially for long-term simulations and large-scale models. We employ the inverse time dispersion transform (ITDT) to the third-order symplectic integration method to reduce the time-dispersion error. First, we adopt the pseudospectral algorithm for the spatial discretization and the third-order symplectic integration method for the temporal discretization. Then, we apply the ITDT to eliminate time-dispersion error from the synthetic data. As a post-processingmethod, the ITDT can be easily cascaded in traditional numerical simulations. We implement the ITDT in one typical exiting third-order symplectic scheme and compare its performances with the performances of the conventional second-order scheme and the rapid expansion method. Theoretical analyses and numerical experiments show that the ITDT can significantly reduce the time-dispersion error, especially for long travel times. The implementation of the ITDT requires some additional computations on correcting the time-dispersion error, but it allows us to use the maximum temporal interval under stability conditions; thus, its final computational efficiency would be higher than that of the traditional symplectic integration method for long-term simulations. With the aid of the ITDT, we can obtain much more accurate simulation results but with a lower computational cost. (C) 2016 The Authors. Published by Elsevier Inc.

【 授权许可】

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