O. Ouchetto, S. Zouhdi, A. Bossavit, G. Griso, B. Miara et al., Homogenization of Structured Electromagnetic Materials and metamaterials, Journal of Materials Processing Technology, vol.181, issue.1, 2007.

M. Fiebig, Revival of the magnetoelectric effect, Journal Physics D: Applied Physics, vol.38, pp.123-152, 2005.

V. E. Wood and A. E. Austin, Possible applications for magnetoelectric materials, Int. Journal Magn, vol.5, pp.303-315, 1974.

M. I. Bichurin, V. M. Petrov, S. V. Averkin, and E. Liverts, Present status of theoretical modeling the magnetoelectric effect in magnetostrictivepiezoelectric nanostructures. Part I: Low frequency and electromechanical resonance ranges, Journal of Applied Physics, vol.107, 2010.

R. Corcolle, L. Daniel, and F. Bouillault, Generic formalism for homogenization of coupled behavior: Application to magnetoelectroelastic behavior, Physical Review B, vol.78, p.0, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00354428

C. Nan, M. I. Bichurin, S. Dong, D. Viehland, and G. Srinivasan, Multiferroic magnetoelectric composites: Historical perspective, status, and future directions, Journal of Applied Physics, vol.103, 2008.

N. Galopin, X. Mininger, F. Bouillault, and L. Daniel, Finite Element Modelling of Magnetoelectric Sensors, IEEE Trans. on Magn, vol.44, issue.6, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00352289

X. Mininger, N. Galopin, Y. Dennemont, and F. Bouillault, 3D finite element model for magnetoelectric sensors, Eur. Phys. J. Appl. Phys, vol.52, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00623577

N. Galopin, Finite Element Modeling of Magnetoelectric Composites with Interdigitated Electrodes, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01174743

Y. X. Liu, J. G. Wan, J. Liu, and C. W. Nan, Effect of magnetic bias field on magnetoelectric coupling in magnetoelectric composites, Journal of Applied Physics, vol.94, 2003.

T. T. Nguyen, X. Mininger, L. Daniel, and F. Bouillault, Influence of Mechanical Boundary Conditions on Magnetolectric Sensors, IEEE Trans. on Magn, vol.49, issue.5, 2013.

T. T. Nguyen, F. Bouillault, L. Daniel, and X. Mininger, Finite element modeling of magnetic field sensors based on nonlinear magnetoelectric effect, Journal of Applied Physics, vol.109, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00711554

D. T. Giang and N. H. Duc, Magnetoelectric sensor for microtesla magnetic-fields based on (Fe 80Co20)78Si12B10/PZT laminates, Sensors and Actuators A: Physical, vol.149, 2009.

J. Lou, D. Reed, M. Liu, and N. X. Sun, Electrostatically tunable magnetoelectric inductors with large inductance tenability, Applied Physics Letters, vol.94, 2009.

T. Lafont, L. Gimeno, J. Delamare, G. A. Lebedev, D. I. Zakharov et al., Magnetostrictive-piezoelectric composite structures for energy harvesting, Journal of Micromechanics and Microengineering, vol.22, p.94009, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00766924

H. Talleb, Z. Ren, J. Jiao, L. Liu, W. Di et al., Finite element modeling of magnetoelectric laminate composites in considering nonlinear and load effects for energy harvesting, Journal of Alloys and Compounds, vol.615, pp.65-74, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01025058

D. Guyomar, A. Badel, E. Lefeuvre, and C. Richard, Toward energy harvesting using active materials and conversion improvement by nonlinear processing, Ultrasonics, Ferroelectrics and Frequency Control, vol.52, issue.4, pp.584-595, 2010.

R. Corcolle, E. Salaün, F. Bouillault, Y. Bernard, C. Richard et al., Modeling of a beam structure with piezoelectric materials: introduction to SSD techniques, vol.27, pp.205-214, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00336752

H. Talleb and Z. Ren, Finite Element Modeling of a Magnetoelectric Energy Transducer Including the Load Effect, IEEE Trans. on Magn, vol.51, issue.3, pp.1-5
URL : https://hal.archives-ouvertes.fr/hal-00960967

F. Chinesta, R. Keunings, and A. Leyguel, The Proper Generalized Decomposition for Advanced Numerical Simulations, A. Primer, 2014.

E. Pruliere, F. Chinesta, and A. Ammar, On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition, Numerical Methods in Engineering, Mathematics and Computers in Simulation, vol.81, issue.4, pp.791-810, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00704427

L. Tamellini, O. Le-maître, and A. Nouy, Model Reduction Based on Proper Generalized Decomposition for the Stochastic Steady Incompressible Navier-Stokes Equations, SIAM J. Sci. Comput. vol, vol.36, issue.3, pp.1089-1117, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00733733

P. Alotto, M. Guarnieri, F. Moro, and A. Stella, A proper generalized decomposition approach for modeling fuel cell polymeric membranes, IEEE Trans. Mag, vol.47, issue.5, pp.1462-1465, 2011.

T. Henneron, A. Benabou, and S. Clénet, Nonlinear Proper Generalized Decomposition Method Applied to the Magnetic Simulation of a SMC Microstructure, IEEE Trans. Mag, vol.48, issue.11, pp.3242-3245, 2012.

T. Henneron and S. Clénet, Application of the PGD and DEIM to Solve a 3-D Non-Linear Magnetostatic Problem Coupled With the Circuit Equations, IEEE Trans. Magn, vol.52, issue.3, p.7202104, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01273222

M. Pineda-sanchez, Simulation of skin effect via separated representations, COMPEL, vol.29, issue.4, pp.919-929, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01008914

T. Henneron and S. Clénet, Model order reduction of quasi-static problems based on POD and PGD approaches, Eur. Phys. J. Appl. Phys, vol.64, issue.2, p.7, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00851978

T. Henneron and S. Clénet, Proper generalized decomposition method applied to solve 3D magnetoquasi-static field problems coupling with external electric circuits, IEEE Trans. Magn, vol.51, issue.6, p.7208910, 2015.

Z. Qin, H. Talleb, and Z. Ren, A proper generalized decomposition based solver for nonlinear magneto-thermal problems, IEEE Trans. Magn, vol.52, issue.2, p.7400209, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01229635

Z. Qin, H. Talleb, S. Yan, and Z. Ren, Application of the PGD in Parametric Finite Element Simulation of a Piezoelectric Energy Harvester, 10th International Symposium on Electric and Magnetic Fields, 2016.

X. Mininger, UPMC, 11 rue Joliot Curie, Plateau de Moulon, 91192 Gif sur Yvette Cedex, France, Tel. +33169851658, xavier.mininger@geeps.centralesupelec.fr Hakeim Talleb, Sorbonne Universités, UPMC Univ Paris 06, UR2, L2E, F-75005

T. Henneron and U. Lille1, Laboratory of electrical engineering and power electronics (L2EP), EA 2697, bat. P2, cité scientifique, 59655 Villeneuve d'ascq, France, Tel. +3320434865, thomas.henneron@univ-lille1.fr The authors are from the organizing laboratories of Compumag, 2019.