Application of the Proper Generalized Decomposition to Solve Magnetoelectric Problem

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Among the model order reduction techniques, the Proper Generalized Decomposition (PGD) has shown its efficiency to solve a large number of engineering problems. In this article, the PGD approach is applied to solve a multi-physics problem based on a magnetoelectric device. A reduced model is developed to study the device in its environment based on an Offline/Online approach. In the Offline step, two specific simulations are performed in order to build a PGD reduced model. Then, we obtain a model very well fitted to study in the Online stage the influence of parameters like the frequency or the load. The reduced model of the device is coupled with an electric load (R-L) to illustrate the possibility offered by the PGD.Index Terms-Finite element method, Magnetoelectric problem, Proper Generalized Decomposition.

Fast Computation of Multi-Parametric Electromagnetic Fields in Synchronous Machines by Using PGD-Based Fully Separated Representations

“…where arctg is the inverse trigonometric function arctangent. Then, a second mapping is used to transform the resulting non-fully separable domain into a prismatic, easily separable one, (s, t), such as s ∈ [1,7] and t ∈ [0, 2π), using the following transformation, for i = 2, . .…”

“…PGD was previously applied in electromagnetics, such as, for instance, the computation of impedance in industrial busbar systems [6], the analysis of magnetoelectric devices [7] or batteries [8]. However, the complex non-separable geometry of electric motors limited its use for efficiently expressing the solution by separating the space coordinates.…”

Constrained Algorithm for the Selection of Uneven Snapshots in Model Order Reduction of a Bearingless Motor

“…In another work, Henneron and Clénet (2018) showed the efficiency of PGD along with an online/offline approach to study a multiphysics problem of a magnetoelectric device. In the offline stage, the reduced model of the problem without any electrical load was built via PGD.…”

Comparison of Model Order Reduction Methods for a Switched Reluctance Machine Characterization

“…This model, which is more economical in terms of calculation time, must offer acceptable accuracy. Among many MOR techniques that have been used to solve electromagnetic problems are the Proper Orthogonal Decomposition (POD) [4]- [8], the Proper Generalized Decomposition (PGD) [9]- [12], the Discrete Empirical Interpolation Method (DEIM) [13]- [16], the Best Point Interpolation Method (BPIM) [17] and the Orthogonal Interpolation Method (OIM) [18]. A POD approach for solving multiple-input problems is also presented in [19] and [20].…”