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