@Article{NMTMA-7-473,
author = {Qinghai Zhang, Robert D. Guy and Bobby Philip},
title = {A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2014},
volume = {7},
number = {4},
pages = {473--498},
abstract = {<p style="text-align: justify;">This paper presents a method for solving the linear semi-implicit
immersed boundary equations which avoids the severe time step restriction
presented by explicit-time methods. The Lagrangian variables are
eliminated via a Schur complement to form a purely Eulerian saddle
point system, which is preconditioned by a projection operator and
then solved by a Krylov subspace method. From the viewpoint of
projection methods, we derive an ideal preconditioner for the
saddle point problem and compare the efficiency of a number of simpler
preconditioners that approximate this perfect one.
For low Reynolds number and high stiffness,
 one particular projection preconditioner
 yields an efficiency improvement of the explicit IB method
 by a factor around thirty.
Substantial speed-ups over explicit-time method are
 achieved for Reynolds number below 100.
This speedup increases as the Eulerian grid size and/or the Reynolds number are further reduced.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2014.1304si},
url = {http://global-sci.org/intro/article_detail/nmtma/5885.html}
}