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 quasi-robustness with respect to the local mesh-size $h$ and patch-size $H$: precisely the condition number of the preconditioned system is bounded by the square of the logarithm of $H∕h$. Our numerical tests confirm the theory and also show a favourable dependence of the computational cost of the method from the spline degree $p$.

在等几何分析中，计算域通常被描述为多面体，其中每个面体由张量积样条/ NURBS参数化给出。在这项工作中，我们提出了类似FETI的求解器，其中局部不精确的求解器在补丁级别利用张量积结构。为此，我们将等距几何框架扩展到FETI的所谓全浮动变体，该变体允许我们在补丁程序级别使用快速对角线化方法。然后，我们为整个系统构造一个前置条件，并证明其相对于局部网格大小的拟稳性$H$ 和补丁大小 $H$：精确地，预处理系统的条件数由的对数的平方限制 $H∕H$。我们的数值测试证实了该理论，并且还显示了该方法的计算成本与样条度的良好相关性$p$。