A central-line coarse preconditioner for Stokes flows in artery-like domains

We consider numerical simulation of blood flows in the artery using multilevel domain decomposition methods. Because of the complex geometry, the construction and the solve of the coarse problem take a large percentage of the total compute time in the multilevel method. In this paper, we introduce a one-dimensional central-line model of the blood flow and use its stabilized finite element discretization to construct a coarse preconditioner. With suitable restriction and extension operators, we obtain a two-level additive Schwarz preconditioner for two- and three-dimensional problems. We present some numerical experiments with different arteries to show the efficiency and robustness of the new coarse preconditioner whose computational cost is considerably lower than other coarse preconditioners constructed using the two- or three-dimensional geometry of the artery.