Geometric exponential integrators
Geometric exponential integrators
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DOI：
10.1016/j.jcp.2019.01.005
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发表时间：
2017-03
期刊：
影响因子：
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通讯作者：
Xu-Hui Shen;M. Leok
中科院分区：
文献类型：
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作者：
Xu-Hui Shen;M. Leok
本文考虑半线性Poisson系统的指数积分器。构造了两类指数积分器，一类保持泊松结构，另一类保持能量。给出了半线性Possion方程组的数值实验。这些几何指数积分器表现出更好的长期稳定性相比，非几何积分器，计算效率比传统的辛积分器和能量保持方法的基础上的离散梯度法。
In this paper, we consider exponential integrators for semilinear Poisson systems. Two types of exponential integrators are constructed, one preserves the Poisson structure, and the other preserves energy. Numerical experiments for semilinear Possion systems obtained by semi-discretizing Hamiltonian PDEs are presented. These geometric exponential integrators exhibit better long time stability properties as compared to non-geometric integrators, and are computationally more efficient than traditional symplectic integrators and energy-preserving methods based on the discrete gradient method.