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 it does not preserve the structure of the underlying physical problem. For example, the classic dynamical low-rank methods violate mass, m...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Journal of computational physics Ročník 484; s. 112060
Hlavní autori: Einkemmer, Lukas, Ostermann, Alexander, Scalone, Carmela
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 01.07.2023
Predmet:
Complexity reduction
Conservative methods
Dynamical low-rank approximation
High-dimensional problems
Kinetic equations
Structure preserving numerical methods
Dynamical low-rank approximation
Kinetic equations
Conservative methods
Complexity reduction
Structure preserving numerical methods
High-dimensional problems
ISSN:0021-9991, 1090-2716
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:Dynamical low-rank approximation, as has been demonstrated recently, can be extremely efficient in solving kinetic equations. However, a major deficiency is that it does not preserve the structure of the underlying physical problem. For example, the classic dynamical low-rank methods violate mass, momentum, and energy conservation. In Einkemmer and Joseph (2021) [9] 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, low-rank integrator 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. •First robust dynamical low-rank integrator that exactly preserves mass and momentum.•The associated conservation laws are preserved.•Significant improvement in energy conservation.•Rank adaptive variant of the conservative integrator.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2023.112060