论文标题
在多绘制等几何分析中，用于Stokes系统的稳定离散和IETI-DP求解器
Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis
论文作者
论文摘要
我们对stokes方程的快速求解器感兴趣，该方程将通过多块同几何分析进行离散。在过去的几年中，已经提出了一些针对Stokes问题的INF-SUP稳定离散化，通常将分析仅限于单点域。我们专注于最简单的方法之一，即等几何泰勒元素。我们展示了如何将单点域域的稳定性结果传递到多斑块域。尽管这是可能的，但稳定性在很大程度上取决于几何形状。我们构建了双重的等几何撕裂和互连（IETI-DP）求解器，该求解器不会遭受该效果。我们提供收敛分析并提供数值测试。
We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the Stokes problem have been proposed, often the analysis was restricted to single-patch domains. We focus on one of the simplest approaches, the isogeometric Taylor--Hood element. We show how stability results for single-patch domains can be carried over to multi-patch domains. While this is possible, the stability strongly depends on the shape of the geometry. We construct a Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solver that does not suffer from that effect. We give a convergence analysis and provide numerical tests.
