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.

我们考虑使用多级域分解方法对动脉血流进行数值模拟。由于几何形状复杂，因此在多级方法中，构造和求解粗略问题会占用总计算时间的很大一部分。在本文中，我们介绍了一个一维的血流中心线模型，并使用其稳定的有限元离散化构造了一个粗糙的预处理器。使用合适的限制和扩展算子，我们获得了针对二维和三维问题的两级加性Schwarz预调节器。