Carmen Scalone | Searcharxiv

arXiv2026

Convergence of a Low-Rank Strang Splitting for Stiff Matrix Differential Equations

We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into a stiff linear part, treated exactly via matrix exponentials, and a nonlinear part, integrated by a second-order dynamical low-rank (DLR) scheme. Our main contribution is a rigorous convergence proof showing that, under suitable assumptions, the overall scheme achieves second-order accuracy. Numerical experiments confirm the theoretical results and demonstrate the robustness and efficiency of the proposed method.

math.NA↗

arXiv2023

A robust and conservative dynamical low-rank algorithm

Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that they do not preserve the structure of the underlying physical problem. For example, the classic dynamical low-rank methods violate mass, momentum, and energy conservation. In [L. Einkemmer, I. Joseph, J. Comput. Phys. 443:110495, 2021] a conservative dynamical low-rank approach has been proposed. However, directly integrating the resulting equations of motion, similar to the classic dynamical low-rank approach, results in an ill-posed scheme. In this work we propose a robust, i.e. well-posed, integrator for the conservative dynamical low-rank approach that conserves mass and momentum (up to machine precision) and significantly improves energy conservation. We also report improved qualitative results for some problems and show how the approach can be combined with a rank adaptive scheme.

math.NA↗