Computational Homogenization in 3D Magnetostatics using E3C Hyper-Reduction

TL;DR

This paper applies the E3C hyper-reduction method to 3D magnetostatics, demonstrating accurate and efficient simulations with minimal integration points and low error rates, advancing computational homogenization techniques.

Contribution

First application of E3C hyper-reduction in 3D magnetostatics, showing high accuracy with few integration points and detailed analysis of parameter effects.

Findings

Accurate results with as few as 15 integration points in 3D microstructure simulations.

Hyper-reduction errors below 1% with optimal parameter selection.

Successful 3D two-scale simulation demonstrating method effectiveness.

Abstract

The recently published hyper-reduction method "Empirically Corrected Cluster Cubature" (E3C) is for the first time applied 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.