A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D
A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D
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DOI：
10.1016/j.jcp.2017.03.043
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发表时间：
2017-07
期刊：
影响因子：
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通讯作者：
F. Kong;X. Cai
中科院分区：
文献类型：
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作者：
F. Kong;X. Cai
三维非结构网格上的非线性流固耦合问题在科学和工程中有着广泛的应用，如飞机的振动分析和心血管疾病的特定诊断。在这项工作中，我们为由非线性流体系统和非线性固体系统组成的整体耦合的FSI问题开发了一个高度可扩展的并行算法和软件框架。FSI系统在空间上采用稳定化有限元方法离散，在时间上采用全隐式后向差分格式。为了在每个时间步长求解大型稀疏的非线性代数方程组，我们提出了一种不精确的牛顿-Krylov方法和一个多层光滑的Schwarz预条件，其中等距粗网格由一个保持几何的粗化算法生成。这里的“几何”包括计算区域的边界和流体与固体之间的湿界面。数值结果表明，对于数亿个未知数的问题，在具有10,000个以上处理器核的超级计算机上，所提出的算法和实现在线性和非线性迭代次数以及总计算时间方面具有很高的可扩展性。
Nonlinear fluid–structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton–Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here “geometry” includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.