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The calculation of electromagnetic fields can involve many degrees of freedom (DOFs) to achieve accurate results. The DOFs are directly related to the computational effort of the simulation. The effort is decreased by using the proper generalized decomposition (PGD) and proper orthogonalized decomposition (POD). The purpose of this study is to combine the advantages of both methods. Therefore, a hybrid enrichment strategy is proposed and applied to different electromagnetic formulations.

The POD is an a-priori method, which exploits the solution space by decomposing reference solutions of the field problem. The disadvantage of this method is given by the unknown number of solutions necessary to reconstruct an accurate field representation. The PGD is an a-priori approach, which does not rely on reference solutions, but require much more computational effort than the POD. A hybrid enrichment strategy is proposed, based on building a small POD model and using it as a starting point of the PGD enrichment process.

The hybrid enrichment process is able to accurately approximate the reference system with a smaller computational effort compared to POD and PGD models. The hybrid enrichment process can be combined with the magneto-dynamic T-Ω formulation and the magnetic vector potential formulation to solve eddy current or non-linear problems.

The PGD enrichment process is improved by exploiting a POD. A linear eddy current problem and a non-linear electrical machine simulation are analyzed in terms of accuracy and computational effort. Further the PGD-AV formulation is derived and compared to the PGD-T-Ω reduced order model.

Magnetic hysteresis holds significant technical and physical importance in the design of electromagnetic components. Despite extensive research in this area, modeling magnetic hysteresis remains a challenging task that is yet to be fully resolved. The purpose of this paper is to study vector hysteresis play models for anisotropic ferromagnetic materials in a physical, thermodynamical approach.

In this work, hysteresis play models are implemented to interpret magnetic properties, drawing upon classical rate-independent plasticity principles derived from continuum mechanics theory. By conducting qualitative and quantitative verification and validation, various aspects of ferromagnetic vector hysteresis were thoroughly examined. By directly incorporating the hysteresis play models into the primal formulations using fixed point method, the proposed model is validated with measurements in a finite element (FE) environments.

The proposed vector hysteresis play model is verified with fundamental properties of hysteresis effects. Numerical analysis is performed in an FE environment. Measured data from a rotational single sheet tester (RSST) are validated to the simulated results.

The results of this work demonstrates that the essential properties of the hysteresis effects by electrical steel sheets can be represented by the proposed vector hysteresis play models. By incorporation of hysteresis play models into the weak formulations of the magnetostatic problem in the h-based magnetic scalar potential form, magnetic properties of electrical steel sheets can be locally analyzed and represented.

The goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects. Incorporating the vector hysteresis model in the magnetic vector potential formulation has encountered difficulties. One of the reasons is that the Newton method is very sensitive regarding the starting point and states distinct requirements for the nonlinear function in terms of monotony and smoothness. The other reason is that the differential reluctivity tensor of the material model is discontinuous due to the properties of the stop operators. In this work, line search methods to overcome these difficulties are discussed.

To stabilize the Newton iteration, line search methods are studied. The first method computes an error-oriented search direction. The second method is based on the Wolfe-Powell rule using the Armijo condition and curvature condition.

In this paper, the differentiation of the vector stop model, used to evaluate the Jacobian matrix, is studied. Different methods are applied for this nonlinear problem to ensure reliable and stable finite element simulations with consideration of vector hysteresis effects.

In this paper, two different line search Newton methods are applied to solve the magnetic field problems with consideration of vector hysteresis effects and ensure a stable convergence successfully. A comparison of these two methods in terms of robustness and efficiency is presented.

The present study aimed to develop the competencies of 21st-century learners by considering the characteristics of the education element in the curricula.

The study employed a qualitative research design and a content analysis technique. The research population consisted of 20 curriculum design professors selected via a snowball sampling method until data saturation was reached. The research instrument was semistructured interviewing. The content validity of the interview questions was determined according to 5 curriculum design experts' opinions. Four credibility, transferability, dependability and confirmability criteria were used to increase the accuracy of qualitative data. The findings were analyzed using thematic analysis (structural-interpretive) through open, axial and selective coding.

Education characteristics in competency-based curricula were categorized into knowledge, skills, attitude and educational values. Knowledge includes pedagogical knowledge, content knowledge, pedagogical content knowledge and pedagogical technological knowledge; teaching skills include organization, facilitation, care and flexibility; educational attitudes consist of educational and pedagogical attitudes; and educational values include individual and group-social values.

The present research put three critical dimensions together: the competencies of the new-age learners from the perspective of the curriculum, which is the heart of the education process and is aimed at sustainable development, which is the priority of the countries today.