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To propose trigonometric interpolation in combination with the sliding‐surface technique for modeling rotation in electrical machine models discretised by the finite integration technique (FIT).

Locked‐step, linear and trigonometric interpolation techniques are developed for coupling the stator and rotor model parts of an electrical machine model.

Linear and trigonometric interpolation should be preferred over the locked‐step approach. Three‐machine models with sliding‐surface coupling discretised by the FIT result in efficient and reliable models.

The introduction of sliding‐surface techniques in the FIT, the trigonometric interpolation used in combination, the application of the FIT for simulating electrical machines.

To propose an air‐gap element for electrical machine simulation which accounts for static and dynamic rotor eccentricity.

The air‐gap element technique is extended to account for a non‐centered rotor. The consistency, stability and convergence of the discretisation error are studied. A specialized efficient solution technique combining the conjugate gradient algorithm with fast Fourier transforms is developed.

The eccentric air‐gap technique offers better discretisation properties than the classical techniques based on remeshing. Thanks to the specialized solver, the computation times remain comparable.

The introduction of eccentricity in the air‐gap element used for finite element electrical machine simulation is a new development.

To propose trigonometric interpolation in combination with both sliding‐surface and moving‐band techniques for modelling rotation in finite‐element electrical machine models. To show that trigonometric interpolation is at least as accurate and efficient as standard stator‐rotor coupling schemes.

Trigonometric interpolation is explained concisely and put in a historical perspective. Characteristic drawbacks of trigonometric interpolation are alleviated one by one. A comparison with the more common locked‐step linear‐interpolation and mortar‐element approaches is carried out.

Trigonometric interpolation offers a higher accuracy and therefore can outperform standard stator‐rotor coupling techniques when equipped with an appropriate iterative solver incorporating Fast Fourier Transforms to reduce the higher computational cost.

The synthetic interpretation of trigonometric interpolation as a spectral‐element approach in the machine's air gap, the efficient iterative solver combining conjugate gradients with Fast Fourier Transforms. The unified application to both sliding‐surface and moving‐band techniques.

The purpose of this paper is to review the mutual coupling of electromagnetic fields in the magnetic vector potential formulation with electric circuits in terms of (modified) nodal and loop analyses. It aims for an unified and generic notation.

The coupled formulation is derived rigorously using the concept of winding functions. Strong and weak coupling approaches are proposed and examples are given. Discretization methods of the partial differential equations and in particular the winding functions are discussed. Reasons for instabilities in the numerical time domain simulation of the coupled formulation are presented using results from differential-algebraic-index analysis.

This paper establishes a unified notation for different conductor models, e.g. solid, stranded and foil conductors and shows their structural equivalence. The structural information explains numerical instabilities in the case of current excitation.

The presentation of winding functions allows to generically describe the coupling, embed the circuit equations into the de Rham complex and visualize them by Tonti diagrams. This is of value for scientists interested in differential geometry and engineers that work in the field of numerical simulation of field-circuit coupled problems.

Transient eddy current formulations based on the Finite Integration Technique (FIT) for the magneto‐quasistatic regime are extended to include motional induction effects of moving conductors with simple geometries by different approaches. A new regularization of the formulation using discrete grad‐div augmentation of the curlcurl formulation is presented and tested. To improve the implicit time integration process, several schemes for an error controlled variable time step selection are presented and for the repetitive solution of the arising large sparse systems of equations a sparse direct solver is compared to iterative methods such as a preconditioned conjugate gradient method and a new algebraic multigrid solver, which is aware of the curlcurl nullspace.

To provide a numerical technique for the quick and simple determination of the switching time instants for field‐circuit coupled problems with switching elements.

3D magnetic vector potential formulation coupled to an electrical circuit with switching elements, for example, diodes, is presented. The change of the state of the switching elements is implemented as a modification of the model topology.

Since every step of the singly diagonally implicit Runge‐Kutta methods delivers not only the solution of this time step but also its stage derivatives, they can be efficiently employed to construct a dense‐output‐based interpolation polynomial, with their roots approximating the switching time instants.

This paper presents a computationally cheap interpolation approach for quick and accurate determination of switching time instances for field‐circuit coupled problems with switching elements. The proposed technique can be successfully incorporated into software packages designed to model coupled problems of different nature, where sudden changes of quality may take place.

This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromagnetic field problems in nonlinear media. The hybrid technique is based on new theoretical results regarding the similarities between the Picard‐Banach fixed‐point (polarization) method and the Newton method. At each iteration, the solution is obtained as a linear combination of the old solution, and the new Picard‐Banach and Newton solutions. The numerical solutions are calculated through a “triangle” (bidimensional) minimization of the residual or of the energy functional. The goal of this combination is to increase the robustness of the iterative method, without losing the quadratic speed of convergence in the vicinity of the solution. The proposed method generalizes and unifies in a single algorithm the overrelaxed Picard‐Banach and the underrelaxed Newton methods.

The coupling between a 3D modified magnetic vector potential formulation discretized by the finite integration technique and an electrical circuit that includes solid and stranded conductors is presented. This paper describes classical time integration methods and the implicit Runge‐Kutta methods, the latter being an appropriate alternative to the first ones to solve effectively index 1 differential‐algebraic equations arising from combined simulation of electromagnetic fields and electrical circuits.

The purpose of this paper is to present and apply a parasitic extraction approach for the calculation of DC busbar inductances.

A computational approach based on the finite integration technique and computed magnetic energy is developed to extract parasitic inductances. The finite integration analysis is conducted via the magnetoquasistatic solver of CST EM Studio^® capturing the 3D geometrical effects of the design, as well as the skin and proximity effects.

The method is applied successfully to evaluate the leakage inductances of two printed circuit boards structures; a backplane sample for the verification purpose and a real DC bus employed in a three‐phase pulse width modulation inverter.

The paper demonstrates that the method calculates the loop inductances accurately. It does not, however, verify the used technique to split loop inductances into partial inductances.

The extraction method is easy‐to‐use and able to handle complex geometries within acceptable computation time and accuracy.

The paper introduces a way to compute the parasitic inductances from the results of a numerical electromagnetic field solver.

Improved numerical calculation techniques for low‐frequency current density distributions within high‐resolution anatomy models caused by ambient electric or magnetic fields or direct contact to potential drops using the finite integration technique (FIT).

The methodology of calculating low‐frequency electromagnetic fields within high‐resolution anatomy models using the FIT is extended by a local grid refinement scheme using a non‐matching‐grid formulation domain. Furthermore, distributed computing techniques are presented. Several numerical examples are analyzed using these techniques.

Numerical simulations of low‐frequency current density distributions may now be performed with a higher accuracy due to an increased local grid resolution in the areas of interest in the human body voxel models when using the presented techniques.

The local subgridding approach is introduced to reduce the number of unknowns in the very large‐scale linear algebraic systems of equations that have to be solved and thus to reduce the required computational time and memory resources. The use of distributed computation techniques such as, e.g. the use of a parallel solver package as PETSc follows the same goals.