arXiv subjects

Merle Backmeyer

Publications and source records attributed to Merle Backmeyer.

5 recordsLinked to original sources

arXiv2026

A Reduced Magnetic Vector Potential Approach with Higher-Order Splines

This work presents a high-order isogeometric formulation for magnetoquasistatic eddy-current problems based on a decomposition into Biot-Savart-driven source fields and finite-element reaction fields. Building upon a recently proposed surface-only Biot-Savart evaluation, we generalize the reduced magnetic vector potential framework to the quasistatic regime and introduce a consistent high-order spline discretization. The resulting method avoids coil meshing, supports arbitrary winding paths, and enables high-order field approximation within a reduced computational domain. Beyond establishing optimal convergence rates, the numerical investigation identifies the requirements necessary to recover high-order accuracy in practice, including geometric regularity of the enclosing interface, accurate kernel quadrature, and compatible trace spaces for the source-reaction coupling.

math.NA↗

arXiv2026

Gradient-Informed Machine Learning in Electromagnetics

Simulation techniques such as the finite element method are essential for designing electrical devices, but their computational cost can be prohibitive for repeated or real-time computations. Projection-based model order reduction techniques mitigate this by reducing the model size and complexity, yet face challenges when extended to nonlinear or non-affine parametric models. In this work, Isogeometric Analysis (IGA) is combined with proper orthogonal decomposition and Gaussian process regression to construct a non-intrusive surrogate model of a parametric nonlinear model of a permanent magnet synchronous machine. The differentiable nature of IGA allows for computationally efficient extraction of parametric sensitivities, which are leveraged for gradient-enhanced surrogate modeling.

cs.CE↗

arXiv2025

Learning electromagnetic fields based on finite element basis functions

Parametric surrogate models of electric machines are widely used for efficient design optimization and operational monitoring. Addressing geometry variations, spline-based computer-aided design representations play a pivotal role. In this study, we propose a novel approach that combines isogeometric analysis, proper orthogonal decomposition and deep learning to enable rapid and physically consistent predictions by directly learning spline basis coefficients. The effectiveness of this method is demonstrated using a parametric nonlinear magnetostatic model of a permanent magnet synchronous machine.

cs.CE↗

arXiv2024

Solving Electromagnetic Scattering Problems by Isogeometric Analysis with Deep Operator Learning

We present a hybrid approach combining isogeometric analysis with deep operator networks to solve electromagnetic scattering problems. The neural network takes a computer-aided design representation as input and predicts the electromagnetic field in a de Rham conforming B-spline basis such that for example the tangential continuity of the electric field is respected. The physical problem is included in the loss function during training. Our numerical results demonstrate that a trained network accurately predicts the electric field, showing convergence to the analytical solution with optimal rate. Additionally, training on a variety of geometries highlights the network's generalization capabilities, achieving small error increases when applied to new geometries not included in the training set.

cs.CE↗

arXiv2023

Modeling non-planar coils in a full-scale stellarator

Design and modeling of a stellarator fusion reactor is a multidisciplinary effort that requires a tight integration between simulation of highly nonlinear multi-physics and representation of non-planar complex geometries. The critical current calculation and the design of the mechanical structures are among the most crucial aspects as they set size, cost, and time to build the stellarator. Because of the asymmetric and non-planar nature of its components the modeling of such figures of merit needs to be carried out at large scale, without the possibility of taking advantage of any particular symmetry. In this work we develop a three-dimensional model for the analysis of the magnetic field and forces, necessary for such considerations, for complex coil geometries, such as stellarators, where a two-dimensional approach can not provide accurate analyses and verification of assumptions. Moreover, this method can quickly generate a large amount of critical modeling data (e.g. Lorentz load, displacement and stresses) that could be integrated into a workflow for coil design optimization based on machine learning or other recent optimization tools.

physics.plasm-ph↗