Domain decomposition in time for PDE-constrained optimization

Barker, Andrew T.; Stoll, Martin

doi:10.1016/j.cpc.2015.08.025

Title: 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:

Barker, Andrew T. ^[1]; Stoll, Martin ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg (Germany)

Publication Date:: Fri Aug 28 00:00:00 EDT 2015

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:: 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.

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                    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

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                    Barker, Andrew T., and Stoll, Martin. Fri .  
"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.

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@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},

  journal      = {Computer Physics Communications},

  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}

}

Copy to clipboard

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Title: Domain decomposition in time for PDE-constrained optimization

Abstract

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