论文标题
非平稳多尺度问题的时间分裂算法
Temporal Splitting algorithms for non-stationary multiscale problems
论文作者
论文摘要
在本文中，我们研究了用于多尺度问题的时间分裂算法。确切的细网上空间问题通常需要降低自由度。多尺度算法旨在表示粗网格上的细节细节，从而减少问题的大小。在解决时间依赖性问题时，可以利用解决方案的多尺度分解，并通过解决较小的维问题来进行时间分裂，这在论文中进行了研究。在提出的方法中，我们考虑基于各种低维空间近似值的时间分裂。由于多尺度空间分裂会对解决方案空间进行“良好”分解，因此可以实现有效的隐式分散时间离散化。我们在早期工作中提出了最近开发的理论结果，并在本文中采用了多尺度问题。提出了数值结果，以证明所提出的分裂算法的效率。
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale details on a coarse grid and, thus, reduce the problems' size. When solving time-dependent problems, one can take advantage of the multiscale decomposition of the solution and perform temporal splitting by solving smaller-dimensional problems, which is studied in the paper. In the proposed approach, we consider the temporal splitting based on various low dimensional spatial approximations. Because a multiscale spatial splitting gives a "good" decomposition of the solution space, one can achieve an efficient implicit-explicit temporal discretization. We present a recently developed theoretical result in our earlier work and adopt it in this paper for multiscale problems. Numerical results are presented to demonstrate the efficiency of the proposed splitting algorithm.
