论文标题
与拉格朗日乘数的流体结构相互作用问题的并行求解器
A parallel solver for fluid structure interaction problems with Lagrange multiplier
论文作者
论文摘要
这项工作的目的是提出一个平行求解器，以表达流体结构相互作用（FSI）问题，该问题利用虚拟域方法的精神利用分布式的Lagrange乘数。 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元素。一阶半米差差差方案用于时间离散。每个时间步骤的生成线性系统通过平行的GMRE求解器求解，该求解器通过块对角线或三角前预处理加速。并行实现基于PETSC库。已经对Linux簇进行了几项数值测试，以研究所提出的FSI求解器的有效性。
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.
