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To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal decomposition (POD) and centroidal Voronoi tessellation (CVT) have been used to solve many engineering problems. The purpose of this paper is to investigate the computational principle, accuracy and efficiency of the POD-based and the CVT-based reduced-order method when dealing with quasi-magnetostatic problems.

The paper investigates computational features of the reduced-order method based on POD and CVT methods for quasi-magnetostatic problems. Firstly the construction method for the POD and the CVT reduced-order basis is introduced. Then, a reduced model is constructed using high-fidelity finite element solutions and a Galerkin projection. Finally, the transient quasi-magnetostatic problem of the TEAM 21^a model is studied with the proposed reduced-order method.

For the TEAM 21^a model, the numerical results show that both POD-based and CVT-based reduced-order approaches can greatly reduce the computational time compared with the full-order finite element method. And the results obtained from both reduced-order models are in good agreement with the results obtained from the full-order model, while the computational accuracy of the POD-based reduced-order model is a little higher than the CVT-based reduced-order model.

The CVT method is introduced to construct the reduced-order model for a quasi-magnetostatic problem. The computational accuracy and efficiency of the presented approaches are compared.

New analytical approximation for the frequency‐dependent impedance matrix components of symmetric VLSI interconnect on lossy silicon substrate are derived. The results have been obtained by using an approximate quasi‐magnetostatic analysis of symmetric coupled microstrip on‐chip interconnects on silicon. We assume that the magnetostatic field meets the boundary conditions of a single isolated infinite line; therefore, the boundary conditions for the conductors in the structure are approximately satisfied. The derivation is based on the approximate solution of quasi‐magnetostatic equations in the structure (dielectric and silicon semi‐space), and takes into account the substrate skin‐effect. Comparisons with published data from circuit modeling or full‐wave numerical analyses are presented to validate the inductance and resistance expressions derived for symmetric coupled VLSI interconnects. The analytical characterization presented in this paper is well situated for inclusion into CAD codes in the design of RF and mixed‐signal integrated circuits on silicon.

The LF magnetic field (50 Hz‐100 kHz) generated in the air by electrical appliances is characterised using multipoles. The maximum likelihood estimation of an equivalent multipolar source is computed using a genetic algorithm. The choice of the position and the number of measurement points are discussed.

System contains units which are the tools for the actuators designs, optimization and steady‐states or transients simulation. Design and optimization process has been based on the equivalent circuit model with “field” procedures for concentrated circuit parameters calculation. For the optimization the penalty function method combined with the conjugate gradients method has been adopted. In the steady‐states simulation, the entirely 2D or 3D field formulation has been employed. Whereas in transients, it is assumed that the field is produced under the time‐varying voltage constraints, so the combined field‐circuit formulation has been applied.

This study aims to enhance the parallel performance of a parallel-in-space-and-time (PinST) finite-element method (FEM) using time step overlapping. The effectiveness of the developed method is clarified in a magnet eddy-current loss analysis of a practical interior permanent magnet synchronous motor (IPMSM) using a massively parallel computing environment.

The developed PinST FEM is a combination of the domain decomposition method as a parallel-in-space (PinS) method and a parallel time-periodic explicit error correction (PTP-EEC) method, which is one of the parallel-in-time (PinT) approaches. The parallel performance of the PinST FEM is further improved by overlapping the time steps with different processes in the PTP-EEC method.

By applying the overlapping PTP-EEC method, the convergence of the transient solution to its steady state can be accelerated drastically. Consequently, the good parallel performance of the PinST FEM is achieved in magnetic field analyses of the practical IPMSM using a massively parallel computing environment, in which over 10,000 processes are used.

In this study, the PinST FEM based on time step overlapping is newly developed and its effectiveness is demonstrated in a massively parallel computing environment, in which using either the PinS or PinT method alone cannot achieve sufficient parallel performance. This finding implies a new direction of parallel computing approaches for electromagnetic field computation.

To propose a novel 3D hybrid approach, based on a discrete formulation of Maxwell equations (the cell method – CM), suitable for solving eddy current problems in unbounded domains.

Field equations for magnetodynamics are expressed directly in algebraic form thanks to the CM. The eddy current problem inside bulk conductors is formulated in terms of discrete modified vector potential, whereas magnetic scalar potential is used in order to model the free space. The CM is coupled to the boundary element method by using a surface boundary operator, which maps the surface magnetic fluxes to the surface magnetic scalar potentials. This leads to a unique set of linear equations to be solved in terms of discrete potentials. The eddy currents in bulk conductors are then obtained from discrete potentials.

It is shown that formulation of hybrid approaches can be simplified by expressing field equations directly in algebraic form without need of weighted residual techniques. An original strategy, based on Green's formula for the magnetic scalar potential, is proposed in order to couple conducting parts to the exterior domain.

Conducting bodies with multiply connected parts cannot be modelled by the proposed approach, since it is based on the magnetic scalar potential. The resulting global matrix is partially dense and non‐symmetric; therefore, standard iterative solvers such as GMRES have to be used.

The proposed approach can be suitably used for analyzing eddy current problems involving models with high degree of complexity, large air domains and moving parts. These are typical of induction heating processes.

This paper proposes a new 3D hybrid approach, based on a discrete formulation of Maxwell equations. A novel coupling strategy relying on integral electromagnetic variables, i.e. magnetic fluxes and magnetic scalar potentials, is devised in order to solve uniquely for eddy currents inside conducting bodies.