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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 paper, 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. [ABSTRACT FROM AUTHOR]

Among the model-order reduction techniques, the proper orthogonal decomposition (POD) has shown its efficiency to solve magnetostatic and magnetoquasistatic problems in the time domain. However, the POD is intrusive in the sense that it requires the extraction of the matrix system of the full model to build the reduced model. To avoid this extraction, nonintrusive approaches like the data-driven (DD) methods enable to approximate the reduced model without the access to the full matrix system. In this paper, the DD-POD method is applied to build a low-dimensional system to solve a magnetostatic problem coupled with electric circuit equations. [ABSTRACT FROM AUTHOR]

The proper generalized decomposition (PGD) is a model order reduction method which allows to reduce the computational time of a numerical problem by seeking for a separated representation of the solution. The PGD has been already applied to study an electrical machine but at standstill without accounting the motion of the rotor. In this paper, we propose a method to account for the rotation in the PGD approach in order to build an efficient metamodel of an electrical machine. Then, the machine metamodel will be coupled to its electrical and mechanical environment in order to obtain accurate results with an acceptable computational time on a full simulation. [ABSTRACT FROM AUTHOR]

Among the model order reduction techniques, the proper generalized decomposition (PGD) has shown its efficiency to solve static and quasistatic problems in the time domain. However, the introduction of non-linearity due to ferromagnetic materials, for example, has never been addressed. In this paper, the PGD technique combined with the discrete empirical interpolation method (DEIM) is applied to solve a non-linear magnetostatic problem coupled with the circuit equations. To evaluate the reduction technique, the transient state of a three-phase transformer at no load is studied using the full finite-element model and the PGD–DEIM model. [ABSTRACT FROM AUTHOR]

To face the curse of dimensionality met in uncertainty quantification problems when the model has a high number of random parameters, methods based on sparse approximation, such as the least angle regression (LAR) method, should be used. In this paper, we propose an extension of the LAR method, and we apply it to quantify the impact of uncertainties on the characteristics of the material on the magnetoelectric sensor performance. The sensor response is represented by a 2-D finite-element model with ten random parameters. A global sensitivity analysis is carried out in order to determine the most influential parameters. [ABSTRACT FROM AUTHOR]

To solve stochastic static field problems, a discretization by the finite-element method can be used. A system of equations is obtained with the unknowns (scalar potential at nodes, for example) being random variables. To solve this stochastic system, the random variables can be approximated in a finite-dimension functional space—a truncated polynomial chaos expansion. The error between the exact solution and the approximated one depends not only on the spatial mesh, but also on the discretization along the stochastic dimension. In this paper, we propose an a posteriori estimation of the error due to the discretization along the stochastic dimension. [ABSTRACT FROM AUTHOR]

To solve stochastic problems with geometric uncertainties, one can transform the original problem in a domain with stochastic boundaries and interfaces to a problem defined in a deterministic domain with uncertainties in the material behavior. The latter problem is then discretized. There exist infinitely many random mappings that lead to identical results in the continuous domain but not in the discretized domain. In this paper, an a priori error indicator is proposed for electromagnetic problems with scalar and vector potential formulations. This leads to criteria for selecting random mappings that reduce the numerical error. In an illustrative numerical example, the proposed a priori error indicator is compared with an a posteriori estimator for both potential formulations. [ABSTRACT FROM AUTHOR]