Acceleration methods for the convergence of vector sequences applied to multi-physics problems

Partitioned solution approaches are well-known strategies to solve coupled problems and have demonstrated their applicability in a wide range of multi-physical simulations. Applying a partitioned approach opens up numerous possibilities, such as connecting different solvers or combining non-matching meshes and time-step sizes. On the other hand such a procedure has the drawback of only conditional stability, leading to poor convergence rates or - as a worst case scenario - to divergent behavior. In this contribution, we will give an interpretation of the iterative coupling process as a sequence of vectors converging to an unknown limit, which indeed represents a solution to the coupled problem. In order to improve computational efficiency, there are several practicable methods to accelerate the convergence of vector sequences. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)