论文标题
用于iSOGEOMETRIT多斑点问题的域分解方法与不精确的本地求解器
A domain decomposition method for Isogeometric multi-patch problems with inexact local solvers
论文作者
论文摘要
在等几何分析中，计算域通常被描述为多斑块，其中每个贴片由张量产品样条/NURBS参数化给出。在这项工作中，我们提出了一个类似feti的求解器，其中局部不进行的求解器在斑块水平上利用张量产品结构。为此，我们扩展到iSOOGEOMETRIC框架所谓的FETI的所有浮动变体，这使我们能够在斑块级别使用快速的对角线化方法。然后，我们为整个系统构建了一个预处理，并证明了其相对于本地网格大小的$ h $和贴片大小的$ h $（即，我们具有可扩展性）。我们的数值测试证实了这一理论，并且还显示了从样条度度$ p $中对该方法的计算成本的有利依赖性。
In Isogeometric Analysis, the computational domain is often described as multi-patch, where each patch is given by a tensor product spline/NURBS parametrization. In this work we propose a FETI-like solver where local inexact solvers exploit the tensor product structure at the patch level. To this purpose, we extend to the isogeometric framework the so-called All-Floating variant of FETI, that allows us to use the Fast Diagonalization method at the patch level. We construct then a preconditioner for the whole system and prove its robustness with respect to the local mesh-size $h$ and patch-size $H$ (i.e., we have scalability). Our numerical tests confirm the theory and also show a favourable dependence of the computational cost of the method from the spline degree $p$.
