arXiv subjects

Ruth V. Sabariego

Publications and source records attributed to Ruth V. Sabariego.

10 recordsLinked to original sources

arXiv2026

Magnetic Field Conforming Multiscale Formulations for Locally-Confined Nonlinear Eddy Current Problems Using the FE-HMM Method

Magnetic composites used for the conversion of electrical energy often incorporate ferromagnetic inclusions insulated from each other to mitigate eddy current losses. Numerical models for these composites must be robust enough to address potential convergence issues arising from the presence of nonlinear magnetic inclusions and presence of significant confined eddy currents in the cell. This paper introduces an $\mathbf{h}$-conforming multiscale formulation for magnetic composites in a periodic framework. The proposed method uses the Heterogeneous Multiscale Method (HMM) with two mesoscale problems: a magnetoquasistatic problem for upscaling the homogenized magnetic flux density $\mathbf{B}_M$ and a magnetostatic problem for upscaling the macroscale incremental reluctivity $(\partial \mathbf{B}_M/\partial \mathbf{H}_M)$. Additionally, the method uses relaxed Newton--Raphson schemes at both macro and mesoscale levels to mitigate the well-known NR convergence issue linked to nonlinear BH constitutive laws in $\mathbf{h}$-conforming formulations. The accuracy and performance of the formulation are evaluated using 2D and 3D idealized periodic soft magnetic composites with linear and nonlinear BH curves. Furthermore, the paper demonstrates that the magnetoquasistatic mesoscale problem can be replaced by a magnet a

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arXiv2026

A Multi-Scale ResNet-augmented Fourier Neural Operator Framework for High-Frequency Sequence-to-Sequence Prediction of Magnetic Hysteresis

Accurate modeling of magnetic hysteresis is essential for high-fidelity power electronics device simulations. The transient hysteresis phenomena such as the ringing effect and the minor loops are the bottleneck for the accurate hysteresis modeling and the core losses estimation. To capture the hysteresis loops with both the macro structure and the micro transient details, in this paper, we propose the multi-scale ResNet augmented Fourier Neural Operator (Res-FNO). The framework employs a hybrid input structure that combines sequential time-series data with scalar material labels through specialized feature engineering. Specifically, the time derivative of magnetic flux density ($\frac{dB}{dt}$) is incorporated as a critical physical feature to enhance the model sensitivity to high-frequency oscillations and minor loop triggers. The proposed architecture synergizes global spectral modeling with localized refinement by integrating a multi-scale ResNet path in parallel with the FNO blocks. This design allows the global operator path to capture the underlying physical evolution while the local refinement path, compensates for spectral bias and reconstructs fine-grained temporal details. Extensive experimental validation across diverse magnetic materials from 79 to Material 3C90 demonstrates the strong generalization capability of the proposed Res-FNO, proving its robust ability to model complex ringing effects and minor loops in realistic power electronic applications.

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arXiv2025

Dynamic hysteresis model of grain-oriented ferromagnetic material using neural operators

Accurately capturing the behavior of grain-oriented (GO) ferromagnetic materials is crucial for modeling the electromagnetic devices. In this paper, neural operator models, including Fourier neural operator (FNO), U-net combined FNO (U-FNO) and Deep operator network (DeepONet) are used to approximate the dynamic hysteresis models of GO steel. Furthermore, two types of data augmentation strategies including cyclic rolling augmentation and Gaussian data augmentation (GDA) are implemented to enhance the learning ability of models. With the inclusion of these augmentation techniques, the optimized models account for not only the peak values of the magnetic flux density but also the effects of different frequencies and phase shifts. The accuracy of all models is assessed using the L2-norm of the test data and the mean relative error (MRE) of calculated core losses. Each model performs well in different scenarios, but FNO consistently achieves the best performance across all cases.

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arXiv2021

Hyperbolic Basis Functions for Time-Transient Analysis of Eddy Currents in Conductive and Magnetic Thin Sheets

This paper presents a new time-domain finite-element approach for modelling thin sheets with hyperbolic basis functions derived from the well-known steady-state solution of the linear flux diffusion equation. The combination of solutions at different operating frequencies permits the representation of the time-evolution of field quantities in the magnetic field formulation. This approach is here applied to solve a planar shielding problem in harmonic and time-dependent simulations for materials with either linear or nonlinear characteristics. Local and global quantities show good agreement with the reference solutions obtained by the standard finite element method on a complete and representative discretization of the region exposed to a time-varying magnetic field.

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arXiv2019

Efficient simulation of DC-AC power converters using Multirate Partial Differential Equations

Switch-mode power converters are used in various applications to convert between different voltage (or current) levels. They use transistors to switch on and off the input voltage to generate a pulsed voltage whose arithmetic average is the desired output voltage of the converter. After smoothening by filters, the converter output is used to supply devices. The simulation of these switch-mode power converters by conventional time discretization is computationally expensive since a high number of time steps is necessary to properly resolve the unknown state variables and detect switch events of the excitation. This paper proposes a multirate method based on the concept of Multirate Partial Differential Equations (MPDEs), which splits the solution into fast varying and slowly varying parts. The method is developed to work with pulse width modulated (PWM) excitation with a constant switching cycle and varying duty cycle. The important case of varying duty cycles in the MPDE framework is addressed for the first time. Switching event detection is no longer necessary and a much smaller number of time steps for a decent resolution are required, thus leading to a highly efficient method.

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arXiv2019

Multirate PWM balance method for the efficient field-circuit coupled simulation of power converters

The field-circuit coupled simulation of switch-mode power converters with conventional time discretization is computationally expensive since very small time steps are needed to appropriately account for steep transients occurring inside the converter, not only for the degrees of freedom (DOFs) in the circuit, but also for the large number of DOFs in the field model part. An efficient simulation technique for converters with idealized switches is obtained using multirate partial differential equations, which allow for a natural separation into components of different time scales. This paper introduces a set of new PWM eigenfunctions which decouple the systems of equations and thus yield an efficient simulation of the field-circuit coupled problem. The resulting method is called the multirate PWM balance method.

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arXiv2018

Efficient simulation of DC-DC switch-mode power converters by multirate partial differential equations

In this paper, Multirate Partial Differential Equations (MPDEs) are used for the efficient simulation of problems with 2-level pulsed excitations as they often occur in power electronics, e.g., DC-DC switch-mode converters. The differential equations describing the problem are reformulated as MPDEs which are solved by a Galerkin approach and time discretization. For the solution expansion two types of basis functions are proposed, namely classical Finite Element (FE) nodal functions and the recently introduced excitation-specific pulse width modulation (PWM) basis functions. The new method is applied to the example of a buck converter. Convergence, accuracy of the solution and computational efficiency of the method are numerically analyzed.

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arXiv2017

POD-based reduced-order model of an eddy-current levitation problem

The accurate and efficient treatment of eddy-current problems with movement is still a challenge. Very few works applying reduced-order models are available in the literature. In this paper, we propose a proper-orthogonal-decomposition reduced-order model to handle these kind of motional problems. A classical magnetodynamic finite element formulation based on the magnetic vector potential is used as reference and to build up the reduced models. Two approaches are proposed. The TEAM workshop problem 28 is chosen as a test case for validation. Results are compared in terms of accuracy and computational cost.

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arXiv2017

Solving nonlinear circuits with pulsed excitation by multirate partial differential equations

In this paper the concept of Multirate Partial Differential Equations (MPDEs) is applied to obtain an efficient solution for nonlinear low-frequency electrical circuits with pulsed excitation. The MPDEs are solved by a Galerkin approach and a conventional time discretization. Nonlinearities are efficiently accounted for by neglecting the high-frequency components (ripples) of the state variables and using only their envelope for the evaluation. It is shown that the impact of this approximation on the solution becomes increasingly negligible for rising frequency and leads to significant performance gains.

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arXiv2017

Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.

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