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The immersed boundary (IB) method is a widely used approach to simulatingfluid-structure interaction (FSI). Although explicit versions of the IB methodcan suffer from severe time step size restrictions, these methods remainpopular because of their simplicity and generality. In prior work (Guy et al.,Adv Comput Math, 2015), some of us developed a geometric multigridpreconditioner for a stable semi-implicit IB method under Stokes flowconditions; however, this solver methodology used a Vanka-type smoother thatpresented limited opportunities for parallelization. This work extends thisStokes-IB solver methodology by developing smoothing techniques that aresuitable for parallel implementation. Specifically, we demonstrate that anadditive version of the Vanka smoother can yield an effective multigridpreconditioner for the Stokes-IB equations, and we introduce an efficient Schurcomplement-based smoother that is also shown to be effective for the Stokes-IBequations. We investigate the performance of these solvers for a broad range ofmaterial stiffnesses, both for Stokes flows and flows at nonzero Reynoldsnumbers, and for thick and thin structural models. We show here that linearsolver performance degrades with increasing Reynolds number and materialstiffness, especially for thin interface cases. Nonetheless, the proposedapproaches promise to yield effective solution algorithms, especially at lowerReynolds numbers and at modest-to-high elastic stiffnesses.

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations