A Comparison of Different Quasi-Newton Acceleration Methods for Partitioned Multi-Physics Codes

In many cases, different physical systems interact, which translates to coupled mathematical models. We only focus on methods to solve (strongly) coupled problems with a partitioned approach, i.e. where each of the physical problems is solved with a specialized code that we consider to be a black box solver. Running the black boxes one after another, until convergence is reached, is a standard but slow solution technique, known as non-linear Gauss-Seidel iteration. A recent interpretation of this approach as a root-finding problem has opened the door to acceleration techniques based on Quasi-Newton methods that can be “strapped onto” the original iteration loop without modification to the underlying code. In this paper, we analyze the performance of different acceleration techniques on different multi-physics problems.