Towards dynamical low-rank approximation for neutrino kinetic equations. Part I: Analysis of an idealized relaxation model
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- by Peimeng Yin, Eirik Endeve, Cory D. Hauck and Stefan R. Schnake;
- Math. Comp. 94 (2025), 1199-1233
- DOI: https://doi.org/10.1090/mcom/3997
- Published electronically: August 8, 2024
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Abstract:
Dynamical low-rank approximation (DLRA) is an emerging tool for reducing computational costs and provides memory savings when solving high-dimensional problems. In this work, we propose and analyze a semi-implicit dynamical low-rank discontinuous Galerkin (DLR-DG) method for the space homogeneous kinetic equation with a relaxation operator, modeling the emission and absorption of particles by a background medium. Both DLRA and the discontinuous Galerkin (DG) scheme can be formulated as Galerkin equations. To ensure their consistency, a weighted DLRA is introduced so that the resulting DLR-DG solution is a solution to the fully discrete DG scheme in a subspace of the standard DG solution space. Similar to the standard DG method, we show that the proposed DLR-DG method is well-posed. We also identify conditions such that the DLR-DG solution converges to the equilibrium. Numerical results are presented to demonstrate the theoretical findings.References
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Bibliographic Information
- Peimeng Yin
- Affiliation: Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, Texas 79968
- MR Author ID: 1067782
- ORCID: 0000-0002-9188-8011
- Email: pyin@utep.edu
- Eirik Endeve
- Affiliation: Mathematics in Computation Section, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831; and Department of Physics and Astronomy, University of Tennessee, Knoxville, 1408 Circle Drive, Knoxville, Tennessee 37996
- MR Author ID: 1100277
- ORCID: 0000-0003-1251-9507
- Email: endevee@ornl.gov
- Cory D. Hauck
- Affiliation: Mathematics in Computation Section, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831; and Department of Mathematics, University of Tennessee, Knoxville, 1403 Circle Drive, Knoxville, Tennessee 37996
- MR Author ID: 748066
- Email: hauckc@ornl.gov
- Stefan R. Schnake
- Affiliation: Mathematics in Computation Section, Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
- MR Author ID: 1262017
- ORCID: 0000-0002-1518-3538
- Email: schnakesr@ornl.gov
- Received by editor(s): October 28, 2023
- Received by editor(s) in revised form: May 22, 2024
- Published electronically: August 8, 2024
- Additional Notes: Research at Oak Ridge National Laboratory was supported under contract DE-AC05-00OR22725 from the U.S. Department of Energy to UT-Battelle, LLC. This work was supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research via the Applied Mathematics Program and the Scientific Discovery through Advanced Computing (SciDAC) program. This research was supported by Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.
Notice: This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). - © Copyright 2024 American Mathematical Society
- Journal: Math. Comp. 94 (2025), 1199-1233
- MSC (2020): Primary 65N12, 65N30, 65F55
- DOI: https://doi.org/10.1090/mcom/3997