Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.31032

On the Application of Hybrid Mixed Domain Decomposition Methods to Permanent Magnet Synchronous Machines

Timon Seibel·Sebastian Schöps·Kersten Schmidt
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this work, we study the application of a hybrid mixed domain decomposition(HMDD) method for the rotor-stator coupling of a permanent magnet synchronous machine. For this, we derive a variational formulation on the electric machine inspired by hybridized discontinuous Galerkin methods using a mixed magnetostatics problem, an affine material law and boundary conditions respecting the symmetry of the motor. We are then able to locate the resulting finite element method within the HMDD framework. This enables us naturally to transfer the well-posedness results and error estimates for the HMDD method to the finite element method considered in this work. Lastly, as a proof of concept, we consider an academic example and compare the resulting magnetic flux density and potential lines to their counterparts obtained by a well-established in-house code using iso-geometric analysis.

Explore related subjects

cs.CEcs.NAmath.NA

Keep this discovery

BibTeXRIS

Timon Seibel, Sebastian Schöps, Kersten Schmidt. 2026-09-01. On the Application of Hybrid Mixed Domain Decomposition Methods to Permanent Magnet Synchronous Machines. https://arxiv.org/abs/2605.31032

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

cs.CE subjectcs.NA subjectmath.NA subject

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

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

A non-intrusive approach to index-aware learning

We present a non-intrusive version of the index-aware learning framework introduced in arXiv:2309.00958. Index-aware learning itself is an approach for learning the time and parameter dependent solutions of differential-algebraic equations (DAEs), in particular those describing electric circuits. A central feature of the approach is that it ensures the learned solutions to fulfill the inherent constraints of the DAE, such as e.g. Kirchhoff's laws in the case of electric circuits. This is achieved by leveraging a decoupling of the DAE into its differential and algebraic parts, with the non-intrusive version of the approach additionally relying on results from arXiv:2604.20475 and arXiv:2107.07755. We illustrate the approach using a filtered buck converter as an example and compare both the intrusive and non-intrusive versions. The code for the example is openly available.

cs.CE↗
arXiv2026

A meshfree solver for coupled bulk-surface problems with self-organizing surface geometry

In many systems, the interaction between a deformable surface or interface and the surrounding bulk fluid is coupled with intrinsic spatiotemporal dynamics within the moving surface. Examples include tumor growth, biological tissue morphogenesis, cardiac mechanics, multi-phase surfactant chemistry, additive manufacturing, clothing wear-and-tear, and reactive combustion flows. Solving such problems requires both geometric computing algorithms to track and resolve the surface and numerical methods to solve the coupled governing equations in the surface and the surrounding bulk phase. Here, we present a fully meshfree numerical solver for such coupled bulk-surface problems with deformable interfaces. The presented solver tracks the surface implicitly, solving for the dynamic surface geometry based on stress balance coupled to surrounding fluid phases. We show convergence for a mass-conserving case on a growing sphere and solve bulk-surface problems with incompressible Navier-Stokes fluids coupled to in-surface nonlinear reaction-diffusion dynamics. Finally, we show a model of biological morphogenesis, solving simultaneously for the dynamic surface shape and the fields on the curved surface with two-way coupling.

cs.CE↗