Extrapolation vs. projection methods for linear systems of equations
Journal of Computational and Applied Mathematics
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Efficient implementation of minimal polynomial and reduced rank extrapolation methods
Journal of Computational and Applied Mathematics
Computer Methods in Applied Mechanics and Engineering
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
On the Nonnormality of Subiteration for a Fluid-Structure-Interaction Problem
SIAM Journal on Scientific Computing
Space/time multigrid for a fluid--structure-interaction problem
Applied Numerical Mathematics
A non-conforming monolithic finite element method for problems of coupled mechanics
Journal of Computational Physics
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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.