Isogeometric Analysis with Enriched Subdivision Space

Inspired by the partition of unity method, this paper proposes a general enrichment function augmentation strategy for isogeometric analysis based on subdivision surfaces to construct an isogeometric solver with optimal convergence. For any given subdivision surface, besides the original subdivision basis functions, we define a fixed number of locally defined enrichment functions for each extraordinary point. And then we theoretically prove that the new subdivision space equipped with enrichment functions remedies the approximation deficiencies inherent to conventional subdivision spaces. Extensive numerical examples verify that the proposed method achieves optimal convergence order for second-order elliptic problems. Compared with existing approaches, our method is applicable to arbitrary subdivision surfaces to achieve the optimal convergence rates without modifying the geometric representation.