High order Gauss-Seidel schemes for charged particle dynamics
Yuezheng Gong Jiaquan Gao Yushun Wang
Discrete & Continuous Dynamical Systems - B 2018, 23(2): 573-585 doi: 10.3934/dcdsb.2018034

Gauss-Seidel projection methods are designed for achieving desirable long-term computational efficiency and reliability in micromagnetics simulations. While conventional Gauss-Seidel schemes are explicit, easy to use and furnish a better stability as compared to Euler's method, their order of accuracy is only one. This paper proposes an improved Gauss-Seidel methodology for particle simulations of magnetized plasmas. A novel new class of high order schemes are implemented via composition strategies. The new algorithms acquired are not only explicit and symmetric, but also volume-preserving together with their adjoint schemes. They are highly favorable for long-term computations. The new high order schemes are then utilized for simulating charged particle motions under the Lorentz force. Our experiments indicate a remarkable satisfaction of the energy preservation and angular momentum conservation of the numerical methods in multi-scale plasma dynamics computations.

keywords: Gauss-Seidel scheme high order accuracy long-time computation volume-preserving conservations

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