English

Well-posedness and Robust Preconditioners for the Discretized Fluid-Structure Interaction Systems

Numerical Analysis 2023-07-19 v2

Abstract

In this paper 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. 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 preconditioners for the discretized fluid-structure interaction systems. Numerical examples are presented to show the robustness and efficiency of these preconditioners.

Keywords

Cite

@article{arxiv.1403.0046,
  title  = {Well-posedness and Robust Preconditioners for the Discretized Fluid-Structure Interaction Systems},
  author = {Jinchao Xu and Kai Yang},
  journal= {arXiv preprint arXiv:1403.0046},
  year   = {2023}
}

Comments

1. Added two preconditioners into the analysis and implementation 2. Rerun all the numerical tests 3. changed title, abstract and corrected lots of typos and inconsistencies 4. added references

R2 v1 2026-06-22T03:18:14.210Z