Isogeometric Analysis for 2D Magnetostatic Computations with Multi-level Bézier Extraction for Local Refinement
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Local refinement is vital for efficient numerical simulations. In the context of CAD- based discretization methods such as Isogeometric Analysis (IGA), hierarchical B-splines have gained prominence. The work extends the methodology to truncated hierarchical B-splines (THB-splines) as they keep additional properties. The framework is further enriched with Bézier extraction, resulting in the Multi-level Bézier extraction method. Converting these hierarchical splines into the representation of Bézier elements simplifies their seamless integration into existing finite element (FE) codes. 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 Bézier extraction.
