In our work we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point problems and prove the uniform well-posedness of these formulations. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust block preconditioners for the discretized fluid-structure interaction systems. Numerical examples are presented to demonstrate the robustness of these preconditioners.

Researchers should cite this work as follows:

• Kai Yang (2016), "Stable Discretizations and Robust Block Preconditioners for Fluid-Structure Interaction Systems," https://nanohub.org/resources/23524.

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1. algorithms
2. Finite Element Method/Analysis (FEM)
3. Illinois
4. NanoBio Node at Illinois
5. preconditioners
6. systems