On the Consistency of Arnoldi-Based Krylov Methods for Conservation Laws
(2023) In PAMM - Proceedings in Applied Mathematics and Mechanics 23(1).- Abstract
- Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Re- cently, these concepts have been extended to the realm of iterative methods by defining locally conservative and flux consistent iterations. In this note, the current status of such iterative methods is summarized. In particular, it has been shown that Krylov subspace methods are locally conservative, but that they are not flux consistent. Here, we approach the problem of quantifying the flux inconsistency of Krylov subspace methods. Krylov methods introduce a time retardation factor into discretizations of linear conservation laws. It has thusfar been unknown how to compute the precise value of this factor. This issue... (More)
- Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Re- cently, these concepts have been extended to the realm of iterative methods by defining locally conservative and flux consistent iterations. In this note, the current status of such iterative methods is summarized. In particular, it has been shown that Krylov subspace methods are locally conservative, but that they are not flux consistent. Here, we approach the problem of quantifying the flux inconsistency of Krylov subspace methods. Krylov methods introduce a time retardation factor into discretizations of linear conservation laws. It has thusfar been unknown how to compute the precise value of this factor. This issue is resolved herein for Arnoldi-based Krylov subspace methods. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/9e6c8939-ea28-4207-8687-d5d0bd0e6d84
- author
- Linders, Viktor LU and Birken, Philipp LU
- organization
- publishing date
- 2023-05-31
- type
- Contribution to journal
- publication status
- published
- subject
- in
- PAMM - Proceedings in Applied Mathematics and Mechanics
- volume
- 23
- issue
- 1
- article number
- e202200157
- publisher
- John Wiley & Sons Inc.
- ISSN
- 1617-7061
- DOI
- 10.1002/pamm.202200157
- language
- English
- LU publication?
- yes
- additional info
- Volume 23 of PAMM: Special Issue: 92nd Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM)
- id
- 9e6c8939-ea28-4207-8687-d5d0bd0e6d84
- date added to LUP
- 2023-08-31 13:00:38
- date last changed
- 2023-09-14 12:19:23
@article{9e6c8939-ea28-4207-8687-d5d0bd0e6d84, abstract = {{Conservation and consistency are fundamental properties of discretizations of systems of hyperbolic conservation laws. Re- cently, these concepts have been extended to the realm of iterative methods by defining locally conservative and flux consistent iterations. In this note, the current status of such iterative methods is summarized. In particular, it has been shown that Krylov subspace methods are locally conservative, but that they are not flux consistent. Here, we approach the problem of quantifying the flux inconsistency of Krylov subspace methods. Krylov methods introduce a time retardation factor into discretizations of linear conservation laws. It has thusfar been unknown how to compute the precise value of this factor. This issue is resolved herein for Arnoldi-based Krylov subspace methods.}}, author = {{Linders, Viktor and Birken, Philipp}}, issn = {{1617-7061}}, language = {{eng}}, month = {{05}}, number = {{1}}, publisher = {{John Wiley & Sons Inc.}}, series = {{PAMM - Proceedings in Applied Mathematics and Mechanics}}, title = {{On the Consistency of Arnoldi-Based Krylov Methods for Conservation Laws}}, url = {{http://dx.doi.org/10.1002/pamm.202200157}}, doi = {{10.1002/pamm.202200157}}, volume = {{23}}, year = {{2023}}, }