arXiv subjects

Michael Wiesheu

Publications and source records attributed to Michael Wiesheu.

10 recordsLinked to original sources

arXiv2026

Efficient Pareto-Front Generation for Electric Machines using IGA and Second Order Derivatives

The multiobjective optimization of electric machines always involves a trade-off caused by various competing objectives such as performance and cost. A suitable design is usually determined by comparing variants from the Pareto front, which has been generated by a large number of simulation runs. This paper addresses the efficient generation of the Pareto front using a continuation method based on a homotopy method that exploits second-order derivative information to achieve superlinear convergence, enabling the fast generation of new Pareto-optimal points within only a few iterations. A key contribution is the derivation of formulas to compute the Hessian with respect to geometry parameters and shape, thus enabling direct modifications of the motor geometry in the context of Isogeometric Analysis. We apply our method to nonlinear 2D magnetostatic simulations of a permanent magnet synchronous motor and demonstrate its effectiveness by optimizing the cost, mean torque and torque ripple of the motor. Compared to a first-order optimization method, this approach reduces the number of iterations and function evaluations needed, making the pareto optimization fast and efficient.

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↗

arXiv2026

A Comparison of Multirate Co-Simulation Techniques for Field-Circuit Coupled Problems

This paper compares three different multirate splitting approaches for the application on field-circuit coupled magnetoquasistatic simulations. For these methods, again three different variants for exchanging values between the field and circuit are tested, namely voltages, currents and flux correction terms. All scenarios are applied on two different benchmark problems, i.e. a coil inductor and transformer model coupled to different circuits. The convergence behavior of different time steppers (Implicit Euler and Trapezoidal Rule) is determined for all possible settings, and guidelines for practical applications are derived.

math.NA↗

arXiv2026

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↗

arXiv2025

Combined Parameter and Shape Optimization of Electric Machines with Isogeometric Analysis

In structural optimization, both parameters and shape are relevant for the model performance. Yet, conventional optimization techniques usually consider either parameters or the shape separately. This work addresses this problem by proposing a simple yet powerful approach to combine parameter and shape optimization in a framework using Isogeometric Analysis (IGA). The optimization employs sensitivity analysis by determining the gradients of an objective function with respect to parameters and control points that represent the geometry. The gradients with respect to the control points are calculated in an analytical way using the adjoint method, which enables straightforward shape optimization by altering of these control points. Given that a change in a single geometry parameter corresponds to modifications in multiple control points, the chain rule is employed to obtain the gradient with respect to the parameters in an efficient semi-analytical way. The presented method is exemplarily applied to nonlinear 2D magnetostatic simulations featuring a permanent magnet synchronous motor and compared to designs, which were optimized using parameter and shape optimization separately. It is numerically shown that the permanent magnet mass can be reduced and the torque ripple can be eliminated almost completely by simultaneously adjusting rotor parameters and shape. The approach allows for novel designs to be created with the potential to reduce the optimization time substantially.

math.OC↗

arXiv2025

An Air-Gap Element for the Isogeometric Space-Time-Simulation of Electric Machines

Space-time methods promise more efficient time-domain simulations, in particular of electrical machines. However, most approaches require the motion to be known in advance so that it can be included in the space-time mesh. To overcome this problem, this paper proposes to use the well-known air-gap element for the rotor-stator coupling of an isogeometric machine model. First, we derive the solution in the air-gap region and then employ it to couple the rotor and stator. This coupling is angle dependent and we show how to efficiently update the coupling matrices to a different angle, avoiding expensive quadrature. Finally, the resulting time-dependent problem is solved in a space-time setting. The spatial discretization using isogeometric analysis is particularly suitable for coupling via the air-gap element, as NURBS can exactly represent the geometry of the air-gap. Furthermore, the model including the air-gap element can be seamlessly transferred to the space-time setting. However, the air-gap element is well known in the literature. The originality of this work is the application to isogeometric analysis and space-time.

math.NA↗

arXiv2025

Isogeometric Analysis for 2D Magnetostatic Computations with Multi-level Bézier Extraction for Local Refinement

Local refinement is vital for efficient numerical simulations. In the context of Isogeometric Analysis (IGA), hierarchical B-splines have gained prominence. The work applies the methodology of truncated hierarchical B-splines (THB-splines) as they keep additional properties. The framework is further enriched with Bézier extraction, resulting in the multi-level Bézier extraction method. We apply this discretization method to 2D magnetostatic problems. The implementation is based on an open-source Octave/MATLAB IGA code called GeoPDEs, which allows us to compare our routines with globally refined spline models as well as locally refined ones where the solver does not rely on Bézier extraction.

cs.CE↗

arXiv2024

A magnetic oriented approach to the systematic coupling of field and circuit equations

A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which explicitly encodes the energy storage, dissipation, and transfer mechanisms. This implies a power balance on the continuous level which can be preserved under appropriate discretization in space and time. The models and main results are presented in detail for linear constitutive models, but the extension to nonlinear elements and more general coupling mechanisms is possible. The theoretical findings are demonstrated by numerical results.

math.NA↗

arXiv2024

Spline-Based Rotor and Stator Optimization of a Permanent Magnet Synchronous Motor

This work features the optimization of a Permanent Magnet Synchronous Motor using 2D nonlinear simulations in an Isogeometric Analysis framework. The rotor and stator designs are optimized for both geometric parameters and surface shapes via modifications of control points. The scaling laws for magnetism are employed to allow for axial and radial scaling, enabling a thorough optimization of all critical machine parameters for multiple operating points. The process is carried out in a gradient-based fashion with the objectives of lowering motor material cost, torque ripple and losses. It is shown that the optimization can be efficiently conducted for many optimization variables and all objective values can be reduced.

math.OC↗

arXiv2023

How to Build the Optimal Magnet Assembly for Magnetocaloric Cooling: Structural Optimization with Isogeometric Analysis

In the search for more efficient and less environmentally harmful cooling technologies, the field of magnetocalorics is considered a promising alternative. To generate cooling spans, rotating permanent magnet assemblies are used to cyclically magnetize and demagnetize magnetocaloric materials, which change their temperature under the application of a magnetic field. In this work, an axial rotary permanent magnet assembly, aimed for commercialization, is computationally designed using topology and shape optimization. This is efficiently facilitated in an isogeometric analysis framework, where harmonic mortaring is applied to couple the rotating rotor-stator system of the multipatch model. Inner, outer and co-rotating assemblies are compared and optimized designs for different magnet masses are determined. These simulations are used to homogenize the magnetic flux density in the magnetocaloric material. The resulting torque is analyzed for different geometric parameters. Additionally, the influence of anisotropy in the active magnetic regenerators is studied in order to guide the magnetic flux. Different examples are analyzed and classified to find an optimal magnet assembly for magnetocaloric cooling.

math.NA↗