Geometric exponential integrators

Xuefeng Shen

doi:10.1016/j.jcp.2019.01.005

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Geometric exponential integrators

2019-04-01

Xuefeng Shen

Melvin Leok

DOI：10.1016/j.jcp.2019.01.005

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Abstract

En 中文

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. (C) 2019 Elsevier Inc. All rights reserved.

Keywords:

Geometric integrators

Exponential integrators

Symplectic integrators

Hamiltonian systems

Highly oscillatory problems

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