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.
翻译:在这项工作中,对进化问题应用了半官方算法,承认低级近似值良好,而低级动态近近似值可用作时间缩进器(DLRA),最近提出了许多DLRA离散集成器,其依据是分割预测的矢量场或采用预测的龙格-库塔方法。这些方法的成本和准确性主要受近近近等级决定。这些特性被用在一种叫做低级的Parareal的新方法中,以便获得一个时间-平行的DLRA演进问题解析器。该算法根据直线问题进行了分析,结果用数字说明。