An optimization-based domain decomposition method for a nonlinear problem

摘要

A nonoverlapping domain decomposition method for the solution of a nonlinear problem is presented. The method is based on optimization to seek the Neumann boundary conditions on the interfaces between subdomains. We show that solutions of the minimization problem exist and derive an optimality system from which these solutions may be determined. We also examine finite element approximations of the solutions of the optimality system. The domain decomposition method is then reformulated as a nonlinear least-squares problem and the results of numerical experiments are given.