Domain decomposition and homogenization of optimal control problems for partial differential equations on networked domains

We consider elliptic and hyperbolic PDEs on networked domains such as graphs and 2­d networks in threespace. We formulate corresponding optimal control problems and then consider iterative domain decomposition methods (DDM) based on socalled virtual controls. We further discuss homogenization procedures for such problems and discuss possible combinations of DDM and homogenization in the study of complex technological and infrastructural problems.