Anderson-Type Mixing Methods for the Convergence Acceleration of Partitioned Fluid-Structure Interaction (FSI) Algorithms

We present a stable second-order partitioned iterative scheme for solving low mass ratio FSI problems. This work generalizes the previously developed nonlinear interface force correction (NIFC) framework based on a dynamically stabilized Aitken's geometric extrapolation procedure. Similar to NIFC, which also employs an Arbitrary Lagrangian-Eulerian (ALE) finite element framework; in the present formulation, approximate interface force corrections are constructed through subiterations to account for the missing effects of off-diagonal Jacobian terms in the "black-box" partitioned staggered scheme. Specific to this work we progress the idea of nonlinear sequence transformations of the modified Shanks-kernel to derive a suite of Anderson-type mixing (ATM) methods for iterative coupling. The main feature of the ATM strategy is that it combines the independent interface vectorial information of the two domain "sequences" to obtain a better acceleration procedure. Using the numeric properties of these sequence transformations we additionally demonstrate the ability to derive data-driven filtering and preconditioning methodologies to further accelerate the convergence of highly non-linear and strongly coupled partitioned Multiphysics simulations. To critically evaluate the comparative success of our proposed iterative scheme against the presently popular interface quasi-newton inverse least-squares (IQN-ILS) and inverse multi-vector Jacobian (IQN-IMVJ) methods, we parametrically measure the fixed-point iterative convergence and solution stability properties of each of the methods mentioned for three industry-standard benchmark problems of increasing complexity.