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arXiv · 2302.00348

DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions

Julia Schleuß·Kathrin Smetana
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Abstract

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.

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Julia Schleuß, Kathrin Smetana. 2023-02-01. DEIM vs. leverage scores for time-parallel construction of problem-adapted basis functions. https://arxiv.org/abs/2302.00348

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