An optimization based domain decomposition method for partial differential equations
type: Item
instance of: scholarly article
title: An optimization based domain decomposition method for partial differential equations
zbMATH Open document ID: 0941.65123
DOI: 10.1016/S0898-1221(99)00127-3
author: Max Gunzburger
author: Janet S. Peterson
author: Hyesuk Lee
publication date: 2000-01-20T00:00:00Z
review text: The authors present an optimization-based domain decomposition algorithm for solving boundary value problems. Finite element approximations to solutions of the optimality system are defined and analyzed. A parallelizable gradient method for the solution of the optimality system is studied. Some of the potential good features of the domain decomposition algorithm discussed in the paper are: (i) different finite element discretizations based on different grid sizes and different degree polynomials may be used in each subdomain; (ii) problems with discontinuous media which lead to partial differential equations with discontinuous coefficients can be easily treated. Results from some numerical experiments showing the good numerical properties of the proposed algorithm can be found. In their concluding remarks the authors declare that the method can be extended to nonlinear problems and that details concerning the development, analysis and implementation of such an extension is subject of a forthcoming paper.
reviewed by: Krassimir Georgiev
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1391568
zbMATH Keywords: finite element methods
zbMATH Keywords: domain decomposition
zbMATH Keywords: optimization techniques
zbMATH Keywords: parallel computation
zbMATH Keywords: algorithm
zbMATH Keywords: gradient method
zbMATH Keywords: discontinuous coefficients
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391568