We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded hierarchical meshes. By exploiting a local tensor-product structure, we extend the construction of weighted rules from the tensor-product to the hierarchical spline setting. The proposed algorithm has a computational cost proportional to the number of degrees of freedom and advantageous properties with increasing spline degree. To illustrate the performance of the method and confirm the theoretical estimates, a selection of 2D and 3D numerical tests is provided.

翻译：我们提出B级结构的加权二次曲线,以解决采用适当分级的等离子线的适应性等离子测量Galerkin方法产生的系统矩阵快速形成的问题。我们通过利用本地的高压产品结构,将加权规则的构建从高压产品扩大到等级样条设置。提议的算法的计算成本与自由度和有利特性的数量成正比,并增加样条度。为了说明该方法的性能并证实理论估计,我们提供了2D和3D数字测试的选择。