TY - JOUR
T1 - Well-posedness and robust preconditioners for discretized fluid-structure interaction systems
AU - Xu, Jinchao
AU - Yang, Kai
N1 - Funding Information:
This work is supported in part by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials under contract number DE-SC0009249 . It is also supported in part by NSF Grant DMS-1217142 , and Yunan Provincial Science and Technology Department Research Award: Interdisciplinary Research in Computational Mathematics and Mechanics with Applications in Energy Engineering.
Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/8/1
Y1 - 2015/8/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.cma.2014.09.034
DO - 10.1016/j.cma.2014.09.034
M3 - Article
AN - SCOPUS:84929328707
SN - 0374-2830
VL - 292
SP - 69
EP - 91
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -