一种动态自适应张量方法用于Vlasov-Poisson系统
A dynamical adaptive tensor method for the Vlasov-Poisson system
AI总结：
本文提出了一种求解高维时变Vlasov-Poisson系统的数值方法，通过动态自适应张量分解和辛时间离散化方案，保持系统Hamilton性质并提高效率。
摘要：
本文提出了一种数值方法，用于求解全欧拉时间依赖的Vlasov-Poisson系统。该算法依赖于构造解的张量分解，其秩在每个时间步都进行自适应调整。该分解通过使用高效的改进型渐进广义分解（PGD）方法获得，其收敛性已证明。此外，我们还建议一种辛时间离散化分裂方案，该方案通过考虑近似解的张量结构自然获得。本文通过时间依赖的2D-2D数值例子展示了该方法的效率。
英文摘要：
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step. This decomposition is obtained through the use of an efficient modified Progressive Generalized Decomposition (PGD) method, whose convergence is proved. We suggest in addition a symplectic time-discretization splitting scheme that preserves the Hamiltonian properties of the system. This scheme is naturally obtained by considering the tensor structure of the approximation. The efficiency of our approach is illustrated through time-dependent 2D-2D numerical examples.
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