Coupling of Partitioned Physics Codes with Quasi-Newton Methods

Many physics problems can only be studied by coupling various numerical codes, each modeling a subaspect of the physics problem that is addressed. Often, each of these codes needs to be considered as a black box, either because the codes were written by different programmers, are proprietary software or are legacy code that can only be modified with major effort. Running these black boxes one after another, until convergence is reached, is a standard solution technique. It is easy to implement but comes at the cost of slow or even conditional convergence. A recent interpretation of this approach as a root-finding problem has opened the door to acceleration techniques based on quasi-Newton methods. These quasi-Newton methods can easily be “strapped onto” the original iterative loop without the need to modify the underlying code and with little extra computational cost. In this paper we analyze the performance of ten acceleration techniques that can be applied to accelerate the convergence of a non-linear Gauss-Seidel iteration, on three different multi-physics problems. The methods range from the very well known Broyden method to the arcane Eirola-Nevanlinna method. A switching strategy that was mooted a number of years ago for Broyden’s method, and was claimed to give promising results, but then fell by the wayside, is also considered. For the first time, this idea has been generalized to a wider class of quasi-Newton methods.