To tackle heterogeneous time-dependent problems, an algorithm that constructs problem-adapted basis functions in an embarrassingly parallel and local manner in time has recently been proposed in [Schleuss, Smetana, ter Maat, SIAM J. Sci. Comput., 2022+]. Several simulations of the problem are performed for only few time steps in parallel by starting at different, randomly drawn start time points. For this purpose, data-dependent probability distributions that are based on the (time-dependent) data functions of the problem, such as leverage scores, are employed. In this paper, we suggest as a key new contribution to perform a deterministic time point selection based on the (discrete) empirical interpolation method (DEIM) within the proposed algorithm. In numerical experiments we investigate the performance of a DEIM based time point selection and compare it to the leverage score sampling approach.
翻译:为了解决不同时间依赖的问题,最近在[Schleuss, Smetana, ter Maat, SIAM J. Sci. Comput., 2022 +]中提议了一种算法,这种算法以令人尴尬的平行和当地的方式及时构建了问题适应的基础功能。通过从不同的随机抽取的起始时间点开始,对问题进行了几次模拟,只同时进行了几步。为此,采用了基于问题(时间依赖)数据功能的数据依赖概率分布,例如杠杆分数。在本文件中,我们建议作为关键的新贡献,在拟议的算法中,根据(差异)实证间推法(DEIM)进行确定性时间点选择。在数字实验中,我们调查基于DEIM时间点选择的性能,并将其与杠杆分数抽样方法进行比较。