SIAM Journal on Scientific Computing, Volume 42, Issue 6, Page C359-C383, January 2020.
We present an approach to the numerical solution of steady Navier--Stokes equations. Approximation by the finite element method (FEM) leads to a nonlinear saddle-point system. The system is linearized by the Picard iteration, which leads to a sequence of linear saddle-point systems with nonsymmetric matrices. In this paper, we study the application of Balancing Domain Decomposition based on Constraints (BDDC) to these systems. In particular, we formulate the multilevel BDDC method and explore its applicability for the benchmark problem of lid-driven cavity. Another contribution of the paper is describing the development and application of our BDDC solver to real-world problems of oil flow in hydrostatic bearings.

中文翻译：

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不可压缩Navier-Stokes方程的多层BDDC

SIAM科学计算杂志，第42卷，第6期，第C359-C383页，2020年1月。
我们提出了一种稳定的Navier-Stokes方程数值解的方法。通过有限元方法（FEM）进行逼近会生成非线性鞍点系统。该系统通过Picard迭代进行线性化，这导致了具有非对称矩阵的一系列线性鞍点系统。在本文中，我们研究了基于约束的平衡域分解（BDDC）在这些系统中的应用。特别是，我们制定了多层BDDC方法，并探讨了其在盖驱动腔基准问题中的适用性。本文的另一个贡献是描述了BDDC求解器的开发和在流体静压轴承中油流的实际问题中的应用。