An iteration-by-subdomain overlapping Dirichlet/Robin domain decomposition method for advection–diffusion problems

We present a new overlapping Dirichlet/Robin Domain Decomposition method. The method uses Dirichlet and Robin transmission conditions on the interfaces of an overlapping partitioning of the computational domain. We derive interface equations to study the convergence of the method and show its properties through four numerical examples. The mathematical framework is general and can be applied to derive overlapping versions of all the classical nonoverlapping methods.