We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov-Poisson equations based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time integration in the DLRA model uses a splitting of the tangent space projector for the low-rank manifold according to the separated variables. It can also be modified to allow for rank-adaptivity. A less studied aspect is the incorporation of boundary conditions in the DLRA model. We propose a variational formulation of the projector splitting which allows to handle inflow boundary conditions on spatial domains with piecewise linear boundary. Numerical experiments demonstrate the principle feasibility of this approach.

翻译：我们考虑基于空间与速度变量分离的Vlasov-Poisson方程数值模拟中的动态低秩逼近（DLRA）方法，该方法已在近期多项工作中得到提出。DLRA模型时间积分的标准方法采用根据分离变量对低秩流形切空间投影算子的分裂技术，该技术亦可扩展以实现秩自适应性。边界条件在DLRA模型中的纳入问题则是相对较少被研究的方面。我们提出投影算子分裂的变分公式，该公式能够处理具有分段线性边界的空间域上的流入边界条件。数值实验验证了该方法的原理可行性。