• Medientyp: Sonstige Veröffentlichung; E-Artikel
  • Titel: Rank-adaptive dynamical low-rank integrators for first-order and second-order matrix differential equations
  • Beteiligte: Hochbruck, Marlis [Verfasser:in]; Neher, Markus [Verfasser:in]; Schrammer, Stefan [Verfasser:in]
  • Erschienen: Springer, 2023-02-07
  • Erschienen in: BIT Numerical Mathematics, 63 (1), Art.-Nr.: 9 ; ISSN: 0006-3835, 1572-9125
  • Sprache: Englisch
  • DOI: https://doi.org/10.5445/IR/1000155758; https://doi.org/10.1007/s10543-023-00942-6
  • ISSN: 0006-3835; 1572-9125
  • Schlagwörter: Matrix differential equations ; Mathematics ; Rank-adaptivity ; Dynamical low-rank approximation
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  • Beschreibung: Dynamical low-rank integrators for matrix differential equations recently attracted a lot of attention and have proven to be very efficient in various applications. In this paper, we propose a novel strategy for choosing the rank of the projector-splitting integrator of Lubich and Oseledets adaptively. It is based on a combination of error estimators for the local time-discretization error and for the low-rank error with the aim to balance both. This ensures that the convergence of the underlying time integrator is preserved. The adaptive algorithm works for projector-splitting integrator methods for first-order matrix differential equations and also for dynamical low-rank integrators for second-order equations, which use the projector-splitting integrator method in its substeps. Numerical experiments illustrate the performance of the new integrators.
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