The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem, consisting of the non-stationary Stokes equations, is discretized in space by $\mathcal{Q}_2$-$\mathcal{P}_1$ finite elements, whereas the structure subproblem, consisting of the linear or finite incompressible elasticity equations, is discretized in space by $\mathcal{Q}_1$ finite elements. A first order semi-implicit finite difference scheme is employed for time discretization. The resulting linear system at each time step is solved by a parallel GMRES solver, accelerated by block diagonal or triangular preconditioners. The parallel implementation is based on the PETSc library. Several numerical tests have been performed on Linux clusters to investigate the effectiveness of the proposed FSI solver.

翻译：本文旨在提出一种并行求解器，用于求解基于虚拟区域法思想、采用分布式拉格朗日乘子的流固耦合（FSI）问题公式。流体子问题由非定常斯托克斯方程描述，空间上采用$\mathcal{Q}_2$-$\mathcal{P}_1$有限元离散；而结构子问题则由线性或有限不可压缩弹性方程描述，空间上采用$\mathcal{Q}_1$有限元离散。时间离散采用一阶半隐式有限差分格式。每个时间步生成的线性系统通过并行GMRES求解器求解，并采用块对角或三角预条件子加速。并行实现基于PETSc库。在Linux集群上进行了多项数值测试，以验证所提出FSI求解器的有效性。