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

Julia Schleuß; Kathrin Smetana

doi:10.48550/arXiv.2302.00348

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

Julia Schleuß
, Kathrin Smetana

Research output: Working paper › Preprint › Academic

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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.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2302.00348
Publication status	Published - 1 Feb 2023

Keywords

math.NA
cs.NA
65C20, 65M55, 65M60, 65M75

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

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