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Title: Optimization-based additive decomposition of weakly coercive problems with applications

Abstract

In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem, our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.

Authors:
;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
OSTI Identifier:
1631359
Alternate Identifier(s):
OSTI ID: 1237674; OSTI ID: 1441100
Report Number(s):
SAND-2015-5656J
Journal ID: ISSN 0898-1221; S0898122115006008; PII: S0898122115006008
Grant/Contract Number:  
FWP# 14-017511; AC04-94AL85000
Resource Type:
Published Article
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford) Journal Volume: 71 Journal Issue: 11; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; optimization; additive decomposition; weakly coercive problems; Oseen’s equations; finite elements

Citation Formats

Bochev, Pavel, and Ridzal, Denis. Optimization-based additive decomposition of weakly coercive problems with applications. United Kingdom: N. p., 2016. Web. doi:10.1016/j.camwa.2015.12.032.
Bochev, Pavel, & Ridzal, Denis. Optimization-based additive decomposition of weakly coercive problems with applications. United Kingdom. https://doi.org/10.1016/j.camwa.2015.12.032
Bochev, Pavel, and Ridzal, Denis. Wed . "Optimization-based additive decomposition of weakly coercive problems with applications". United Kingdom. https://doi.org/10.1016/j.camwa.2015.12.032.
@article{osti_1631359,
title = {Optimization-based additive decomposition of weakly coercive problems with applications},
author = {Bochev, Pavel and Ridzal, Denis},
abstractNote = {In this study, we present an abstract mathematical framework for an optimization-based additive decomposition of a large class of variational problems into a collection of concurrent subproblems. The framework replaces a given monolithic problem by an equivalent constrained optimization formulation in which the subproblems define the optimization constraints and the objective is to minimize the mismatch between their solutions. The significance of this reformulation stems from the fact that one can solve the resulting optimality system by an iterative process involving only solutions of the subproblems. Consequently, assuming that stable numerical methods and efficient solvers are available for every subproblem, our reformulation leads to robust and efficient numerical algorithms for a given monolithic problem by breaking it into subproblems that can be handled more easily. An application of the framework to the Oseen equations illustrates its potential.},
doi = {10.1016/j.camwa.2015.12.032},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 11,
volume = 71,
place = {United Kingdom},
year = {Wed Jun 01 00:00:00 EDT 2016},
month = {Wed Jun 01 00:00:00 EDT 2016}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.camwa.2015.12.032

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Cited by: 3 works
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