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

TL;DR

This paper introduces a multi-level Bézier extraction method within Isogeometric Analysis for efficient 2D magnetostatic simulations, enabling local refinement while maintaining key properties of hierarchical B-splines.

Contribution

It develops a novel multi-level Bézier extraction framework for IGA, enhancing local refinement capabilities in magnetostatic computations.

Findings

Effective local refinement in 2D magnetostatics

Comparison with global and local refinement models

Implementation within open-source GeoPDEs code

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.