Quasi-Newton waveform iteration for partitioned surface-coupled multiphysics applications

We present novel coupling schemes for partitioned multiphysics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multirate time stepping, and higher-order convergence in time. To achieve this, we combine waveform relaxation-a known method to achieve higher-order in applications with split time stepping based on continuous representations of coupling variables in time- with interface quasi-Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black-box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic testcases-a heat transfer scenario and a fluid-structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first-order-in-time coupling.