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On the Consistency of Arnoldi-Based Krylov Methods for Conservation Laws

Linders, Viktor LU and Birken, Philipp LU (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)
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author
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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}},
}