Model order reduction techniques applied to magnetodynamic T-Ω-formulation

Abstract

Purpose The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated. Design/methodology/approach The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort. Findings Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown. Originality/value In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

A hybrid enrichment strategy for the efficient construction of reduced order models by the proper generalized decomposition

“…The subscript U denotes to which potential the function R and S belong. Other parameters such as the excitation in electrical machines, given by permanent magnet remanence or current angle and amplitude in the dq-frame can be introduced into the decomposition as well, which enables the fast study of the machine behavior by model order reduction techniques (Müller et al , 2020a, 2020b, 2021, 2022).…”

“…If non-linearities have to be considered a similar approach, i.e. the Discrete Empirical Interpolation Method (DEIM), can be used together with the POD and PGD (Chaturantabut and Sorensen, 2010; Henneron and Clénet, 2016, 2017, Müller et al , 2020a, 2020b, 2021, 2022). It collects the non-linearity in a second snapshot matrix, which is analogously decomposed as in the POD.…”

“…given by permanent magnet remanence or current angle and amplitude in the dq-frame can be introduced into the decomposition as well, which enables the fast study of the machine behavior by model order reduction techniques (Müller et al, 2020a(Müller et al, , 2020b(Müller et al, , 2021(Müller et al, , 2022. 2.2.1 Proper orthogonal decomposition.…”

Nonlinear parametric simulation by proper generalized decomposition on the example of a synchronous machine

“…MOR techniques are based on the approach that the unknown potentials can be decomposed into products of functions that depend on only one variable such as space or time (equation 2) (Nouy, 2010; Henneron and Clénet, 2016a, 2017; Müller et al , 2020a, 2020b). By approximating the unknown solution only in a subspace, the DOFs and the computational effort can be reduced.…”

“…In combination with the degrees of freedom (DOF) resulting from the spatial discretization of the finite element method (FEM), the computational effort increases quickly associated with the parameter variations. Model order reduction (MOR) techniques decrease the DOF to cope with this problem, by using approximations of the solution in a reduced subspace (Chaturantabut and Sorensen, 2010; Chinesta et al , 2013; Henneron and Clénet, 2016a, 2016b; Krimm et al , 2019; Müller et al , 2020a, 2020b). The modeling and analysis of electrical machines in the FEM can be distinguished into a combination of different problem families.…”