Nonuniform rational B‐splines (NURBS) are the most common representation form in isogeometric analysis. In this article, we study the spectral behavior of discretization matrices arising from isogeometric Galerkin and collocation methods based on d‐variate NURBS of degrees (p₁,…,p_d), and applied to general second‐order partial differential equations defined on a d‐dimensional domain. The spectrum of these matrices can be compactly and accurately described by means of a so‐called symbol. We compute this symbol and show that it is the same as in the case of isogeometric discretization matrices based on d‐variate polynomial B‐splines of degrees (p₁,…,p_d). The theoretical results are confirmed with a selection of numerical examples.

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等几何离散化方法中的NURBS：频谱分析

非均匀有理B样条（NURBS）是等几何分析中最常见的表示形式。在本文中，我们研究了基于等距Galerkin的离散化矩阵的频谱行为以及基于度数d变量NURBS （p ₁，…，p _d）的搭配方法，并将其应用于在a上定义的一般二阶偏微分方程。d维域。这些矩阵的光谱可以通过所谓的符号紧凑而准确地描述。我们计算出该符号并表明它与基于度数的d变量多项式B样条的等几何离散化矩阵的情况相同（p ₁，…，p _d）。理论结果通过一系列数值实例得到证实。