An investigation of Interface-GMRES(R) for fluid-structure interaction problems with flutter and divergence

The basic subiteration method for solving fluid–structure interaction problems consists of an iterative process in which the fluid and structure subsystems are alternatingly solved, subject to complementary partitions of the interface conditions. The main advantages of the subiteration method are its conceptual simplicity and its modularity. The method has several deficiencies, however, including a lack of robustness and efficiency. To bypass these deficiencies while retaining the main advantages of the method, we recently proposed the Interface-GMRES(R) solution method, which is based on the combination of subiteration with a Newton–Krylov approach, in which the Krylov space is restricted to the interface degrees-of-freedom. In the present work, we investigate the properties of the Interface-GMRES(R) method for two distinct fluid–structure interaction problems with parameter-dependent stability behaviour, viz., the beam problem and the string problem. The results demonstrate the efficiency and robustness of the Interface-GMRES(R) method. Keywords: Fluid–structure interaction – Subiteration – Newton–Krylov method – GMRES – Interface-GMRES – Reuse of Krylov vectors