We present a novel preconditioning technique for Krylov subspace algorithms to solve fluid‐structure interaction (FSI) linearized systems arising from finite element discretizations. An outer Krylov subspace solver preconditioned with a geometric multigrid (GMG) algorithm is used, where for the multigrid level subsolvers, a field‐split (FS) preconditioner is proposed. The block structure of the FS preconditioner is derived using the physical variables as splitting strategy. To solve the subsystems originated by the FS preconditioning, an additive Schwarz (AS) block strategy is employed. The proposed FS preconditioner is tested on biomedical FSI applications. Both 2D and 3D simulations are carried out considering aneurysm and venous valve geometries. The performance of the FS preconditioner is compared with that of a second preconditioner of pure domain decomposition type.

中文翻译：

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一种现场分裂预处理技术，用于流体-结构相互作用问题及其在生物力学中的应用。

我们为Krylov子空间算法提出了一种新颖的预处理技术，以解决有限元离散化引起的流固耦合（FSI）线性化系统。使用通过几何多重网格（GMG）算法进行预处理的外部Krylov子空间求解器，其中对于多重网格级别的子求解器，提出了场分割（FS）预处理器。FS预调节器的块结构是使用物理变量作为拆分策略得出的。为了解决由FS预处理引发的子系统，采用了附加的Schwarz（AS）块策略。拟议的FS预处理器已在生物医学FSI应用中进行了测试。考虑到动脉瘤和静脉瓣膜的几何形状，都进行了2D和3D模拟。