Domain decomposition method for optimization problems for partial differential equations

M. D. Gunzburger, Jeehyun Lee

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A nonoverlapping domain decomposition method for optimization problems for partial differential equations is presented. The domain decomposition is effected through an auxiliary optimization problem. This results in an multiobjective optimization problem involving the given functional and the auxiliary functional. The existence of an optimal solution to the multiobjective optimization problem is proved as are convergence estimates as the parameters used to regularize the problem (penalty parameters) and to combine the two objective functionals tend to zero. An optimality system for the optimal solution is derived and used to define a gradient method. Convergence results are obtained for the gradient method and the results of some numerical experiments are obtained. Then, unregularized problems having vanishing penalty parameters are discussed.

Original languageEnglish
Pages (from-to)177-192
Number of pages16
JournalComputers and Mathematics with Applications
Volume40
Issue number2
DOIs
Publication statusPublished - 2000 Jan 1

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Domain decomposition methods
Gradient methods
Domain Decomposition Method
Multiobjective optimization
Partial differential equations
Partial differential equation
Gradient Method
Multiobjective Optimization Problems
Optimization Problem
Penalty
Optimal Solution
Nonoverlapping Domain Decomposition
Optimality System
Convergence Estimates
Domain Decomposition
Decomposition
Convergence Results
Numerical Experiment
Tend
Experiments

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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Domain decomposition method for optimization problems for partial differential equations. / Gunzburger, M. D.; Lee, Jeehyun.

In: Computers and Mathematics with Applications, Vol. 40, No. 2, 01.01.2000, p. 177-192.

Research output: Contribution to journalArticle

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