Hierarchical B-splines that allow local refinement have become a promising tool for developing adaptive isogeometric methods. Unfortunately, similar to tensor-product B-splines, the computational cost required for assembling the system matrices in isogeometric analysis with hierarchical B-splines is also high, particularly if the spline degree is increased. To address this issue, we propose an efficient matrix assembly approach for bivariate hierarchical B-splines based on the previous work (Pan, Jüttler and Giust, 2020). The new algorithm consists of three stages: approximating the integrals by quasi-interpolation, building three compact look-up tables and assembling the matrices via sum-factorization. A detailed analysis shows that the complexity of our method has the order $\mathcal{O}\left(N{p}^3\right)$ under a mild assumption about mesh admissibility, where $N$ and $p$ denote the number of degrees of freedom and spline degree respectively. Finally, several experimental results are demonstrated to verify the theoretical results and to show the performance of the proposed method.

允许局部细化的分层B样条已成为开发自适应等几何方法的有前途的工具。不幸的是，类似于张量积B样条曲线，在等价几何分析中使用分层B样条曲线组装系统矩阵所需的计算成本也很高，尤其是如果增加样条曲线度。为了解决这个问题，我们基于先前的工作（Pan，Jüttler和Giust，2020）提出了一种用于二元分层B样条的有效矩阵装配方法。新算法包括三个阶段：通过准插值逼近积分，构建三个紧凑的查找表以及通过求和分解来组装矩阵。详细分析表明，我们方法的复杂性具有阶$\mathcal{Ø}（ñp^3）$ 在关于网格可采性的温和假设下， $ñ$ 和 $p$分别表示自由度数和样条度数。最后，通过一些实验结果验证了理论结果并证明了该方法的性能。