An optimization-based domain decomposition method for parabolic equations

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.