Adapting optimization procedures for the solution of coupled problems

A robust and stable numerical solution for coupled PDE problems has been an active area of research. Though monolithic solution procedures for such problems have proven to be efficient and robust, treatment of the coupled problem in an iterative partitioned approach, using Gauss-Seidel pattern for exchange of data, in order to facilitate black box treatment of specialized solvers for respective PDEs is attractive and of practical importance. This approach together with update schemes like Interface Quasi-Newton schemes [2] and Aitken has shown good behavior in terms of robustness and stability in a wide range of applications. Though this approach reduces necessary iterations, the Gauss-Seidel pattern of exchange of data between the PDE solvers, which requires the PDEs to be solved one after the other, increases the total execution time for the simulation. In this work the findings of an investigation of an alternative coupling scheme based on treatment of the coupled problem as an optimization problem are presented.     «

A robust and stable numerical solution for coupled PDE problems has been an active area of research. Though monolithic solution procedures for such problems have proven to be efficient and robust, treatment of the coupled problem in an iterative partitioned approach, using Gauss-Seidel pattern for exchange of data, in order to facilitate black box treatment of specialized solvers for respective PDEs is attractive and of practical importance. This approach together with update schemes like Interf...     »