论文标题
低排名的伴奏：低排时平行的积分器
Low-rank Parareal: a low-rank parallel-in-time integrator
论文作者
论文摘要
在这项工作中，瘫痪算法应用于允许良好的低级近似值的进化问题，并且可以将动态的低级别近似值（DLRA）用作时间步进。最近，基于将投影矢量字段拆分或应用预测的runge-kutta方法，已提出了许多DLRA的离散集成器。这些方法的成本和准确性主要受近似选择的等级的控制。这些属性以一种称为低级瘫痪的新方法使用，以获取用于进化问题的时间平行DLRA求解器。分析算法对仿射线性问题进行了分析，并以数值为单位说明结果。
In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have recently been proposed, based on splitting the projected vector field or by applying projected Runge--Kutta methods. The cost and accuracy of these methods are mostly governed by the rank chosen for the approximation. These properties are used in a new method, called low-rank Parareal, in order to obtain a time-parallel DLRA solver for evolution problems. The algorithm is analyzed on affine linear problems and the results are illustrated numerically.
