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{\large Andrew Barker \\
{\bf Multilevel Schwarz preconditioning for fluid-structure interaction with application to blood flow}}

Department of Applied Mathematics \\ 526 UCB \\ University of Colorado \\ Boulder \\ CO 80309-0526
\\
{\tt andrew.barker@colorado.edu}\\
Xiao-Chuan Cai\\
{\em Department of Computer Science
University of Colorado, Boulder}\end{center}

Simulation of fluid-structure interaction is a complex problem that
involves modeling different physics for the fluid and the structure and
coupling them together in a stable and efficient manner, and developing
scalable numerical methods for this highly nonlinear problem is a
computational challenge. Here we develop and test parallel, scalable
techniques in the multilevel Newton-Krylov-Schwarz family for solving the
nonlinear, monolithically coupled fluid-structure interaction system on
dynamic moving finite element meshes in the arbitrary Lagrangian-Eulerian
framework. We develop and numerically evaluate parallel nonlinear and
linear grid-sequencing techniques and linear multilevel preconditioners
for the monolithically coupled problem with fully implicit time-stepping,
compare these results to the corresponding one-level algorithm, and
present applications of the method to the simulation of blood flow.


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