Implicit Low-Rank Riemannian Schemes for the Time Integration of Stiff Partial Differential Equations
© The Author(s) 2024.
| Veröffentlicht in: | Journal of scientific computing. - 1999. - 101(2024), 1 vom: 30., Seite 3 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
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2024
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| Zugriff auf das übergeordnete Werk: | Journal of scientific computing |
| Schlagworte: | Journal Article Allen–Cahn equation Fisher–KPP equation Implicit methods Manifold of fixed-rank matrices Numerical time integration Preconditioning Riemannian optimization Stiff PDEs Trust-region method |
| Zusammenfassung: | © The Author(s) 2024. We propose two implicit numerical schemes for the low-rank time integration of stiff nonlinear partial differential equations. Our approach uses the preconditioned Riemannian trust-region method of Absil, Baker, and Gallivan, 2007. We demonstrate the efficiency of our method for solving the Allen-Cahn and the Fisher-KPP equations on the manifold of fixed-rank matrices. Our approach allows us to avoid the restriction on the time step typical of methods that use the fixed-point iteration to solve the inner nonlinear equations. Finally, we demonstrate the efficiency of the preconditioner on the same variational problems presented in Sutti and Vandereycken, 2021 |
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| Beschreibung: | Date Revised 22.09.2024 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 0885-7474 |
| DOI: | 10.1007/s10915-024-02629-8 |