Reduction of model dimension in nonlinear finite element approximations of electromagnetic systems

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

“…Eigenvalue-based and POD methods are capable of reducing the dimension of nonlinear systems (Rutenkroger et al, 2004;Zhai & Vu-Quoc, 2007;Schmidthausler & Clemens, 2012;Sato & Igarashi, 2013a). Nevertheless, the corresponding reduced models have two major technical bottlenecks due to the nonlinear nature of the problem.…”

Error estimation of a proper orthogonal decomposition reduced model of a permanent magnet synchronous machine

“…Then, the reduced model is solved for the other remaining time steps. In computational electromagnetics, the POD method combined with the snapshot technique has been developed in order to study linear and non-linear problems, magnetostatic and quasi-static problems [3][4][5][6][7]. In the case of a rotating electrical machine, the snapshots correspond to the solution of the original model for different positions of the rotor [8,9].…”

Model Reduction of Three-Dimensional Eddy Current Problems Based on the Method of Snapshots

“…The basis vectors for the reduced model are then obtained from the eigenvectors of the variance-covariance matrix. It is shown that the model reduction based on method of snapshots is effective for fluid analysis [7], [8] and for quasi-static electromagnetic analysis in two dimensions [9], [10]. This method has also been shown effective for three dimensional quasi-static electromagnetic problems [11].…”

“…However, it seems uneasy to extend these methods to non-linear problems. On the other hand, the method of snapshots based on principal component analysis has been shown effective for the non-linear problems [6][7][8][9][10][11]. This method is also called the proper orthogonal decomposition [6].…”