# Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems

arXiv: https://arxiv.org/abs/1607.05429 · HTML: https://mlsanity.com/paper/1607.05429/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2016.

## Built on by (most cited first, 1 of 1)

- [Accounting for Hysteresis and Eddy Currents in Finite Element Simulations of Ferromagnetic Laminated Cores using a Recurrent Neural Network](https://mlsanity.com/paper/2607.14321/) (2026)

## Abstract (arXiv)

This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton--Raphson scheme. The resolution of many mesoscale problems per Gauss point allows to compute the homogenized constitutive law and its derivative by finite differences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauss point.