An Iterative Non-overlapping Domain Decomposition Method for Optimal Boundary Control Problems Governed by Parabolic Equations

In this paper, we consider a numerical method for solving optimal boundary control problems governed by parabolic equations. In order to avoid large amounts of calculation produced by traditional numerical methods, we establish an iterative non-overlapping domain decomposition method. The whole domain is divided into many non-overlapping subdomains, and the optimal boundary control problem is decomposed into local problems in these subdomains. Robin conditions are used to communicate the local problems on the interfaces between subdomains. We build the iterative scheme for solving these local problems, and prove the convergence of the scheme. Finally, we present a numerical example to verify the validity of the iterative scheme.