Comparison of DEIM and BPIM to Speed up a POD-based Nonlinear Magnetostatic Model

Thomas Henneron (1) , Laurent Montier (1) , Antoine Pierquin (1) , Stephane Clenet (1)

1 L2EP - Laboratoire d’Électrotechnique et d’Électronique de Puissance - ULR 2697

Proper Orthogonal Decomposition (POD) has been successfully used to reduce the size of linear Finite Element (FE) problems, and thus the computational time associated with. When considering a nonlinear behavior law of the ferromagnetic materials, the POD is not so efficient due to the high computational cost associated to the nonlinear entries of the full FE model. Then, the POD approach must be combined with an interpolation method to efficiently deal with the nonlinear terms, and thus obtaining an efficient reduced model. An interpolation method consists in computing a small number of nonlinear entries and interpolating the other terms. Different methods have been presented to select the set of nonlinear entries to be calculated. Then, the (Discrete) Empirical Interpolation method ((D)EIM) and the Best Points Interpolation Method (BPIM) have been developed. In this article, we propose to compare two reduced models based on the POD-(D)EIM and on the POD-BPIM in the case of nonlinear magnetostatics coupled with electric equation.

Mots clés: Best Points Interpolation Method; Empirical Interpolation Method; Proper Orthogonal Decomposition

Domaines: Analyse numérique [math.NA]; Electromagnétisme

Thomas Henneron, Laurent Montier, Antoine Pierquin, Stephane Clenet. Comparison of DEIM and BPIM to Speed up a POD-based Nonlinear Magnetostatic Model. IEEE Transactions on Magnetics, 2017, 53 (1), pp.1-4. ⟨10.1109/TMAG.2017.2660243⟩. ⟨hal-01519746⟩