Numerical simulations of kinetic problems can become prohibitively expensive due to their large memory footprint and computational costs. A method that has proven to successfully reduce these costs is the dynamical low-rank approximation (DLRA). One key question when using DLRA methods is the construction of robust time integrators that preserve the invariances and associated conservation laws of the original problem. In this work, we demonstrate that the augmented basis update & Galerkin integrator (BUG) preserves solution invariances and the associated conservation laws when using a conservative truncation step and an appropriate time and space discretization. We present numerical comparisons to existing conservative integrators and discuss advantages and disadvantages

翻译：动理学问题的数值模拟因其巨大的内存占用和计算成本而变得极其昂贵。一种已被证明能够有效降低这些成本的方法是动态低秩近似（DLRA）。使用DLRA方法时，一个关键问题在于构建鲁棒的时间积分器，以保持原始问题的不变性和相关守恒律。在本研究中，我们证明当采用保守截断步以及合适的时间和空间离散时，增广基更新与伽辽金积分器（BUG）能够保持解的不变性和相关守恒律。我们与现有保守积分器进行了数值比较，并讨论了各自的优缺点。