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：动力学问题的数值模拟由于巨大的内存占用和计算成本可能变得极其昂贵。动态低秩近似（DLRA）已被证明能有效降低这些成本。使用DLRA方法的一个关键问题是构建稳健的时间积分器，以保持原始问题的不变性和相关守恒定律。本文证明，通过采用保守截断步骤以及适当的时间和空间离散化，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定律。我们与现有守恒积分器进行了数值比较，并讨论了各自的优缺点。