Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type basis functions, that are able to hold a global smoothness and allow to exactly capture a wide set of common geometries. The current rise of this approach has encouraged the search of fast solvers for isogeometric discretizations and nowadays this topic is receiving a lot of attention. In this framework, a desired property of the solvers is the robustness with respect to both the polynomial degree p and the mesh size h. For this task, in this paper we propose a two-level method such that a discretization of order p is considered in the first level whereas the second level consists of a linear or quadratic discretization. On the first level, we suggest to apply one single iteration of a multiplicative Schwarz method. The choice of the block-size of such an iteration depends on the spline degree p, and is supported by a local Fourier analysis (LFA). At the second level one is free to apply any given strategy to solve the problem exactly. However, it is also possible to get an approximation of the solution at this level by using an h-multigrid method. The resulting solver is efficient and robust with respect to the spline degree p. Finally, some numerical experiments are given in order to demonstrate the good performance of the proposed solver.

等几何分析 (IGA) 是一种用于偏微分方程 (PDE) 数值近似的计算技术。这种技术基于使用样条类型的基函数，它能够保持全局平滑并允许准确地捕获广泛的常见几何形状。目前这种方法的兴起鼓励了对等几何离散化的快速求解器的搜索，现在这个主题受到了很多关注。在这个框架中，求解器的一个理想属性是关于多项式次数p和网格大小h的鲁棒性。对于这个任务，在本文中，我们提出了一种两级方法，使得p阶离散化在第一级考虑，而第二级由线性或二次离散化组成。在第一级，我们建议应用乘法 Schwarz 方法的一次迭代。这种迭代的块大小的选择取决于样条度p，并由局部傅立叶分析 (LFA) 支持。在第二级，可以自由地应用任何给定的策略来准确地解决问题。但是，也可以通过使用h多重网格方法在此级别获得解的近似值。由此产生的求解器对于样条度p是有效且稳健的。最后，给出了一些数值实验，以证明所提出的求解器的良好性能。