Strong Coupling Methods

We consider the procedure of computing the response of a coupled problem with a partitioned approach. Often we have existing procedures or even software to solve each sub-problem separately, and want to couple both. This setting seems to allow only the so-called weak coupling which is not sufficient for some problems. The so-called strong coupling --- a totally implicit formulation --- requires iteration in each time step. With the partitioned approach, one simple computational procedure is similar to a block-Gauss-Seidel iteration. We show why this approach may experience difficulties, and how they may be circumvented with block-Newton methods, still in the partitioned framework, by only using the solvers for the two sub-problems. We supply some examples from fluid-structure coupling.