Conference Agenda

The electromagnetic tomography of nonlinear materials is a quite new topic in literature. The lack of results can be ascribed to the complexity in dealing with the inverse problem, which is highly nonlinear and ill-posed even in the presence of linear materials.

Despite this, nonlinear materials find application in a large variety of different contexts, where tomographic inspection techniques are also needed.

In this contribution, the work of the research group is summarized starting from the mathematical formulation for the inverse problem in the nonlinear scenario ending up to a real-time inversion method based on the Monotonicity Principle.

In the context of digital twins, projection-based model order reduction (MOR) plays a crucial role in real-time control, fault diagnosis and performance prediction, particularly when accounting for multi-parameter variations in complex systems. However, traditional MOR techniques often exhibit limited robustness against parameter variations. In this work, a parameter-specific MOR approach is proposed for nonlinear multi-parameter electromagnetic problems based on tensor decomposition. The approach is compared with classical MOR as well as local MOR, typically reliant on clustering techniques, through two numerical examples: a four-parameter electrical motor and a three-parameter voice coil actuator. The numerical examples show that the proposed approach outperforms classical MOR and local MOR methods in terms of computational efficiency and accuracy.

The aim is to avoid expensive computations of eddy currents in nonlinear 3D problems which are large compared to the penetration depth. To this end a nonlinear effective surface impedance is introduced. The effective surface impedance is determined by solving a suitable cell problem for the case of a time-harmonic eddy current problem. With this effective surface impedance an equivalent

static magnetic field problem can be solved efficiently using a magnetic scalar potential in finite element models. The method with

the effective material is cheap and accurate compared to the eddy current problem as shown by numerical simulations.

For transformers under periodic non-sinusoidal excitation, the harmonic balance method is a widely adopted approach for solving the magnetic field. However, performing model order reduction (MOR) in harmonic-domain analysis is a problem, as traditional MOR methods which work in the time domain are ineffective in harmonic-domain analysis. To address this issue, this paper introduces a spectral proper orthogonal decomposition (spectral POD) within the harmonic balance scheme for magneto-quasi-static (MQS) field problems. This approach effectively reduces the degrees of freedoms (DoFs) for computation of each harmonic, and significantly improves computational efficiency. Additionally, the methodologies for selecting snapshots and processing samples are discussed in this paper. To demonstrate the implementation of this MOR approach, a transformer model with excitations containing 49 harmonic orders is presented as a case study. The correctness and accuracy of the proposed MOR approach are validated by comparing its results with those obtained from full-order harmonic balance computations.

We present a new geometrical numerical method that is able to deal with grids with curved (i.e., non-planar) faces. The fundamental problem with this kind of grids is that up-to-now no low-order convergent numerical method for diffusion-like problems is able to use only one discrete flux unknown for every curved face. Our new numerical schemes achieves exactly this result. The basic idea behind our method is to devise a new dual grid, which, contrary to standard approaches, is not constructed according to barycentric subdivision but instead is determined from the very geometry of curved faces. Once such a “generalized dual grid” is available, the methodology of our numerical method is exactly the same of the standard discrete geometric approaches, in the sense that the new dual grid is used in the scheme just like the standard barycentric one. Hence, all the solid foundations of geometric methods are immediately available also to our new numerical method.