TY - JOUR
T1 - A Projection Preconditioner for Solving the Implicit Immersed Boundary Equations
AU - Qinghai Zhang, Robert D. Guy & Bobby Philip
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 473
EP - 498
PY - 2014
DA - 2014/07
SN - 7
DO - http://doi.org/10.4208/nmtma.2014.1304si
UR - https://global-sci.org/intro/article_detail/nmtma/5885.html
KW - Fluid-structure interaction, immersed boundary method, projection method, preconditioning.
AB - <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>