An optimization-based domain decomposition method for parabolic equations

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

An optimization-based, non-overlapping domain decomposition method for the solution of the heat equation is presented. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains. The existence of an optimal solution is proved as is convergence of optimal solutions. 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.

Original languageEnglish
Pages (from-to)1644-1656
Number of pages13
JournalApplied Mathematics and Computation
Volume175
Issue number2
DOIs
Publication statusPublished - 2006 Apr 15

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Domain decomposition methods
Gradient methods
Domain Decomposition Method
Parabolic Equation
Optimal Solution
Gradient Method
Optimization
Nonoverlapping Domain Decomposition
Optimality System
Constrained Minimization
Heat Equation
Convergence Results
Minimization Problem
Jump
Numerical Experiment
Dependent
Experiments
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

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An optimization-based domain decomposition method for parabolic equations. / Lee, Jeehyun.

In: Applied Mathematics and Computation, Vol. 175, No. 2, 15.04.2006, p. 1644-1656.

Research output: Contribution to journalArticle

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