We consider some elementary model problems that are taken to be representative of more important models on complex spatial structures. We discuss domain decomposition techniques from the point of view of optimal control in that coupling conditions are viewed as controllability constraints. This leads to the notion of virtual controls, which has been introduced by J.L. Lions. We pursue an augmented Lagrangian point of view. By this method the iterative coupling turns into a sequence of PDE control problems. We also provide extensions of the methods to elliptic problems on networked domains. This contribution is in honor of J.E. Lagnese, with whom the author collaborated over the past 15 years. Most of the results of this paper have been obtained in this collaboration.
展开▼
