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This paper proposes the application of the waveform relaxation method to thehomogenization of multiscale magnetoquasistatic problems. In the monolithicheterogeneous multiscale method, the nonlinear macroscale problem is solvedusing the Newton--Raphson scheme. The resolution of many mesoscale problems perGauss point allows to compute the homogenized constitutive law and itsderivative by finite differences. In the proposed approach, the macroscaleproblem and the mesoscale problems are weakly coupled and solved separatelyusing the finite element method on time intervals for several waveformrelaxation iterations. The exchange of information between both problems isstill carried out using the heterogeneous multiscale method. However, thepartial derivatives can now be evaluated exactly by solving only one mesoscaleproblem per Gauss point.

Waveform Relaxation for the Computational Homogenization of Multiscale Magnetoquasistatic Problems