An optimization‐based domain decomposition method for numerical simulation of the incompressible Navier‐Stokes flows

This article is concerned about an optimization‐based domain decomposition method for numerical simulation of the incompressible Navier‐Stokes flows. Using the method, an classical domain decomposition problem is transformed into a constrained minimization problem for which the objective functional is chosen to measure the jump in the dependent variables across the common interfaces between subdomains. The Lagrange multiplier rule is used to transform the constrained optimization problem into an unconstrained one and that rule is applied to derive an optimality system from which optimal solutions may be obtained. The optimality system is also derived using “sensitivity” derivatives instead of the Lagrange multiplier rule. We consider a gradient‐type approach to the solution of domain decomposition problem. The results of some numerical experiments are presented to demonstrate the feasibility and applicability of the algorithm developed in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011