Stable discretization and robust preconditioning for fluid-structure interaction

Open Access
Author:
Yang, Kai
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 11, 2015
Committee Members:
  • Jinchao Xu, Committee Chair
  • Ludmil Tomov Zikatanov, Committee Member
  • Anna L Mazzucato, Committee Member
  • Chun Liu, Committee Member
  • Padma Raghavan, Committee Member
Keywords:
  • fluid-structure interaction
  • poroelasticity
  • block preconditioner
Abstract:
In the simulation of multiphysics systems, we often encounter large-scale linear systems arising from the implicit time discretizations of coupled PDEs. Although it is possible to utilize the existing solvers for each field, systematic study is necessary in order to design fast solvers for the coupled systems. For large-scale sparse linear systems, preconditioned Krylov subspace methods are usually the most efficient solvers. Preconditioning techniques are the key to ensuring that these iterative solvers perform in a robust way for various applications. In this dissertation, we study the well-posedness of linear systems, based on which we develop robust preconditioners. By using this procedure, we study the well-posedness of poroelasticity and fluid-structure interaction and propose robust block preconditioners. In addition to exploring preconditioning techniques, we also introduce a new arbitrary Lagrangian Eulerian method for fluid-structure interaction with structure undergoing large rotation and small deformation. This technique provides a new approach to modeling important applications such as hydroelectric power generators and artificial heart pumps.