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：本文提出了一种新算法，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格式，该格式改进了几何-对流显式（GCE）格式在处理不可压缩超弹性固体与不可压缩流体相互作用问题时的性能。所提出算法基于将时间离散问题重新表述为系数强变化的广义Stokes问题，近期已针对此类问题发展了最优预条件子。该算法具有可扩展性、最优性和鲁棒性：我们在模拟经典Turek基准测试的二维和三维模型问题上检验了实现效果，并分析了计时与可扩展性结果。