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Domain decomposition in time for PDE-constrained optimization
Abstract
Here, PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal with the very large linear systems. We then illustrate the performance of our method on a variety of problems.
- Authors:
-
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg (Germany)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1249138
- Report Number(s):
- LLNL-JRNL-652253
Journal ID: ISSN 0010-4655
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Computer Physics Communications
- Additional Journal Information:
- Journal Volume: 197; Journal Issue: C; Journal ID: ISSN 0010-4655
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PDE-constrained optimization; space–time methods; preconditioning; domain decomposition; parallel computing
Citation Formats
Barker, Andrew T., and Stoll, Martin. Domain decomposition in time for PDE-constrained optimization. United States: N. p., 2015.
Web. doi:10.1016/j.cpc.2015.08.025.
Barker, Andrew T., & Stoll, Martin. Domain decomposition in time for PDE-constrained optimization. United States. https://doi.org/10.1016/j.cpc.2015.08.025
Barker, Andrew T., and Stoll, Martin. 2015.
"Domain decomposition in time for PDE-constrained optimization". United States. https://doi.org/10.1016/j.cpc.2015.08.025. https://www.osti.gov/servlets/purl/1249138.
@article{osti_1249138,
title = {Domain decomposition in time for PDE-constrained optimization},
author = {Barker, Andrew T. and Stoll, Martin},
abstractNote = {Here, PDE-constrained optimization problems have a wide range of applications, but they lead to very large and ill-conditioned linear systems, especially if the problems are time dependent. In this paper we outline an approach for dealing with such problems by decomposing them in time and applying an additive Schwarz preconditioner in time, so that we can take advantage of parallel computers to deal with the very large linear systems. We then illustrate the performance of our method on a variety of problems.},
doi = {10.1016/j.cpc.2015.08.025},
url = {https://www.osti.gov/biblio/1249138},
journal = {Computer Physics Communications},
issn = {0010-4655},
number = C,
volume = 197,
place = {United States},
year = {Fri Aug 28 00:00:00 EDT 2015},
month = {Fri Aug 28 00:00:00 EDT 2015}
}
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