@Article{NMTMA-7-473, author = {}, 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 = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2014.1304si}, url = {http://global-sci.org/intro/article_detail/nmtma/5885.html} }