An optimization-based domain decomposition method for parabolic equations

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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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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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