Hierarchical analysis-suitable T-splines: Formulation, B\'{e}zier extraction, and application as an adaptive basis for isogeometric analysis

摘要

In this paper hierarchical analysis-suitable T-splines (HASTS) are developed.The resulting spaces are a superset of both analysis-suitable T-splines andhierarchical B-splines. The additional flexibility provided by the hierarchy ofT-spline spaces results in simple, highly localized refinement algorithms whichcan be utilized in a design or analysis context. A detailed theoreticalformulation is presented including a proof of local linear independence foranalysis-suitable T-splines, a requisite theoretical ingredient for HASTS.B\'{e}zier extraction is extended to HASTS simplifying the implementation ofHASTS in existing finite element codes. The behavior of a simple HASTSrefinement algorithm is compared to the local refinement algorithm foranalysis-suitable T-splines demonstrating the superior efficiency and localityof the HASTS algorithm. Finally, HASTS are utilized as a basis for adaptiveisogeometric analysis.