This paper attempts to merge the concept of hierarchical finite element analysis (FEA) into isogeometric analysis (IGA). The proposed methodology replaces the traditional grid refinement of IGA with custom enrichment functions. The enrichment functions are properly designed B-Spline wavelets tailored to eliminate scale-coupling terms in the stiffness matrix. In this way, the refined solution is synthesized from contributions of smaller independent problems. The proposed approach has two obvious benefits: (1) the calculations performed at each resolution are not discarded when proceeding to a finer one, and (2) it has less computational requirements since the solution is divided into smaller systems. Numerical results on an elasticity problem demonstrate superior performance and accuracy compared to traditional FEA and IGA schemes.

本文尝试将层次有限元分析（FEA）的概念合并到等几何分析（IGA）中。所提出的方法用自定义扩展功能代替了IGA的传统网格优化。富集功能是经过适当设计的B样条小波，旨在消除刚度矩阵中的比例耦合项。这样，细化的解决方案是由较小的独立问题的贡献综合而成的。所提出的方法有两个明显的好处：（1）在进行更精细的计算时，不会放弃在每种分辨率下执行的计算；（2）由于将解决方案分为多个较小的系统，因此对计算的要求较少。与传统的FEA和IGA方案相比，关于弹性问题的数值结果显示出卓越的性能和准确性。