Computational Homogenization in Three‐Dimensional Magnetostatics Using Empirically Corrected Cluster Cubature (E3C) Hyper‐Reduction

ABSTRACT The recently published hyper‐reduction method “Empirically Corrected Cluster Cubature” (E3C) is applied for the first time in three dimensions (here magnetostatics). The method is verified to give accurate results even for a small number of integration points, such as 15 for 3D microstructure simulations. The influence of the number of snapshots and modes, as well as the number of integration points, is investigated and the set with the best performance is selected, showing hyper‐reduction errors of less than 1%. Exemplary simulations, including a two‐scale simulation are considered illustrating the performance of the E3C method for 3D simulations.