Isogeometric Analysis for 2D Magnetostatic Computations with Multi-level B\'{e}zier Extraction for Local Refinement

Abstract

Local refinement is vital for efficient numerical simulations. In the context of Isogeometric Analysis (IGA), hierarchical B-splines have gained prominence. The work applies the methodology of truncated hierarchical B-splines (THB-splines) as they keep additional properties. The framework is further enriched with B\'{e}zier extraction, resulting in the multi-level B\'{e}zier extraction method. We apply this discretization method to 2D magnetostatic problems. The implementation is based on an open-source Octave/MATLAB IGA code called GeoPDEs, which allows us to compare our routines with globally refined spline models as well as locally refined ones where the solver does not rely on B\'{e}zier extraction.