Abstract
AbstractDynamical 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.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Computer Networks and Communications,Software
Cited by
1 articles.
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