Durkbin Cho

TL;DR: Based on the local refinement algorithm addressed in Sederberg et al. (2004) [17], the linear independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes is analyzed.

TL;DR: It is proved that Analysis-Suitable (AS) T-splines are Dual-Compatible, and it is shown that the classical construction of a dual basis for tensor-product T- Splines easily generalizes to DC T-Spline spaces.

TL;DR: An an overlapping Schwarz preconditioner for elliptic problems discretized with isogeometric analysis is constructed, showing in particular that the resulting algorithm is scalable and its convergence rate depends linearly on the ratio between subdomain and „overlap sizes” for fixed polynomial degree $p$ and regularity of the basis functions.

TL;DR: The proof that the proposed isogeometric BDDC preconditioner is scalable in the number of subdomains and quasi-optimal in the ratio of subdomain and element sizes is proved.

TL;DR: In this article, the approximation error of mapped NURBS spaces, such as those used in isogeometric analysis in accordance to the isoparametric paradigm, is investigated.