Multi‐level Bézier extraction of truncated hierarchical B‐splines for isogeometric analysis

Abstract Multivariate basis splines (B‐splines) and Non‐uniform rational B‐splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical (THB‐splines) provide a solution for this. THB‐splines organize the parameter space into structure, which enables efficient approximation representation of functions with different levels detail. The truncation mechanism ensures partition unity property defines more scattered set without overlapping on multi‐level spline space. Transferring these Bézier elements facilitates straightforward incorporation existing finite element (FE) codes. By separating extraction from standard extraction, general independent framework applicable any sequence nested spaces is created. operators structure are constructed in local approach. Adjusting an point view multiplying those elements, direct map between obtained. presented implementation involves use open‐source Octave/MATLAB isogeometric analysis (IGA) code called GeoPDEs. A basic Poisson problem investigate performance compared THB‐spline