论文标题
强大而保守的动力低级算法
A robust and conservative dynamical low-rank algorithm
论文作者
论文摘要
正如最近所证明的那样，动态的低级别近似在求解动力学方程时可能非常有效。但是，一个主要的缺陷是它们不能保留潜在的物理问题的结构。例如，经典的动态低级方法违反了质量，动量和节能。在[L。 Einkemmer，I。Joseph，J。Comput。物理。 443：110495，2021]提出了一种保守的动态低级方法。但是，直接整合所得的运动方程，类似于经典的动态低级方法，导致了不足的方案。在这项工作中，我们提出了一种坚固的，即适合的集成剂，用于保守的动力学低级别方法，可以保留质量和动量（直至机器精度），并显着改善能量节约。我们还报告了一些问题的定性结果，并显示了如何将方法与等级自适应方案结合在一起。
Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of the underlying physical problem. For example, the classic dynamical low-rank methods violate mass, momentum, and energy conservation. In [L. Einkemmer, I. Joseph, J. Comput. Phys. 443:110495, 2021] a conservative dynamical low-rank approach has been proposed. However, directly integrating the resulting equations of motion, similar to the classic dynamical low-rank approach, results in an ill-posed scheme. In this work we propose a robust, i.e. well-posed, integrator for the conservative dynamical low-rank approach that conserves mass and momentum (up to machine precision) and significantly improves energy conservation. We also report improved qualitative results for some problems and show how the approach can be combined with a rank adaptive scheme.
