Title: Adaptive and frugal BDDC coarse spaces for virtual element discretizations of a Stokes problem with heterogeneous viscosity Show Chinese title

Title: 自适应且经济的BDDC粗空间用于具有异质粘度的Stokes问题的虚拟元离散化

Abstract: The virtual element method (VEM) is a family of numerical methods to discretize partial differential equations on general polygonal or polyhedral computational grids. However, the resulting linear systems are often ill-conditioned and robust preconditioning techniques are necessary for an iterative solution. Here, a balancing domain decomposition by constraints (BDDC) preconditioner is considered. Techniques to enrich the coarse space of BDDC applied to a Stokes problem with heterogeneous viscosity are proposed. In this framework a comparison between two adaptive techniques and a computationally cheaper heuristic approach is carried out. Numerical results computed on a physically realistic model show that the latter approach in combination with the deluxe scaling is a promising alternative. Show Chinese abstract

Abstract: 虚拟单元方法（VEM）是一类在一般多边形或多面体计算网格上离散偏微分方程的数值方法。 然而，得到的线性系统通常病态，为了迭代求解需要稳健的预处理技术。 这里考虑了一种基于约束的平衡域分解（BDDC）预处理器。 提出了用于具有异质粘度的斯托克斯问题的BDDC粗空间增强技术。 在此框架下，对两种自适应技术与一种计算成本更低的启发式方法进行了比较。 在物理上现实的模型上计算的数值结果表明，后者与豪华尺度结合是一种有前景的替代方案。