In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid--structure interaction (FSI) problems using a matrix-free finite element method in arbitrary Lagrangian--Eulerian (ALE) frame of reference. We derive a semi-implicit time integration scheme which improves the geometry-convective explicit (GCE) scheme for problems involving the interaction between incompressible hyperelastic solids and incompressible fluids. The proposed algorithm relies on the reformulation of the time-discrete problem as a generalized Stokes problem with strongly variable coefficients, for which optimal preconditioners have recently been developed. The resulting algorithm is scalable, optimal, and robust: we test our implementation on model problems that mimic classical Turek benchmarks in two and three dimensions, and investigate timing and scalability results.

翻译：本文开发了一种新算法，用于在任意拉格朗日-欧拉（ALE）参考系下，采用无矩阵有限元方法求解大规模不可压缩时变流固耦合（FSI）问题。我们推导出一种半隐式时间积分方案，该方案改进了几何-对流显式（GCE）方案，适用于不可压缩超弹性固体与不可压缩流体相互作用的问题。所提出的算法基于将时间离散问题重新表述为具有强变系数的广义斯托克斯问题，而该问题的最优预处理器已在近期得到发展。该算法具有可扩展性、最优性和鲁棒性：我们通过模拟经典Turek基准测试的二维和三维模型问题来测试实现，并研究了计时和可扩展性结果。