Adaptive Isogeometric Analysis with THB-Splines and Multi-Level Bézier Extraction for Coupled Magnetostatics

Adaptive refinement in isogeometric analysis (IGA) provides a flexible way to improve accuracy while controlling computational effort. This work builds on spline basis functions, used both for geometry representation and numerical discretization, and extends them with truncated hierarchical B-splines (THB-splines) to enable local mesh refinement with structured flexibility. To support standard finite element assembly, multi-level Bézier extraction is applied, allowing THB-spline bases to be expressed in terms of local Bernstein polynomials. Refinement is driven by a least-squares a posteriori error estimator integrated into the spline discretization. A unified formulation is presented that couples this estimator with the harmonic mortaring of the rotor–stator, ensuring consistency of the interface while guiding refinement in the coupled problem. The method is demonstrated with 2-D magnetostatic simulations involving a permanent magnet synchronous machine (PMSM).