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This paper aims to develop an automated domain decomposition strategy that is based on the presence of nonlinear field grading material, in the context of model order reduction for transient strongly nonlinear electro-quasistatic (EQS) field problems.

The paper provides convincing empirical insights to support the proposed domain decomposition algorithm, a numerical investigation of the performance of the algorithm for different snapshots and model order reduction experiments.

The proposed method successfully decomposes the computational domain, while the resulting reduced models are highly accurate. Further, the algorithm is computationally efficient and robust, while it can be embedded in black-box model reduction implementations.

This paper fulfills the demand to effectively perform model order reduction for transient strongly nonlinear EQS field problems.

The purpose of this paper is to present the embedding of linear and nonlinear order reduction methods in a theoretical framework for handling hierarchically interconnected dynamical systems.

Based on the component connection modeling (CCM), a modified framework called mCCM for describing interconnected dynamic systems especially with hierarchical structures is introduced and used for order reduction purposes. The balanced truncation method for linear systems and the trajectory piecewise linear reduction scheme are used for the order reduction of systems described within the mCCM framework.

It is shown that order reduction methods can be embedded into the context of interconnected dynamical systems with the benefit of having a further degree of freedom in form of the hierarchical level, on which the order reduction is performed.

The aspect of hierarchy within system descriptions is exploited for order reduction purposes. This distinguishes the presented approach from common methods, which already start with single large-scale systems without explicitly considering hierarchical structures.

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.

To simulate large parasitic resistive networks, one must reduce the size of the circuit models through methods that are accurate and preserve terminal connectivity and network sparsity. The purpose here is to present such a method, which exploits concepts from graph theory in a systematic fashion.

The model order reduction problem is formulated for parasitic resistive networks through graph theory concepts and algorithms are presented based on the notion of vertex cut in order to reduce the size of electronic circuit models. Four variants of the basic method are proposed and their respective merits discussed.

The algorithms proposed enable the production of networks that are significantly smaller than those produced by earlier methods, in particular the method described in the report by Lenaers entitled “Model order reduction for large resistive networks”. The reduction in the number of resistors achieved through the algorithms is even more pronounced in the case of large networks.

The paper seems to be the first to make a systematic use of vertex cuts in order to reduce a parasitic resistive network.

The purpose of this paper is to determine the broadband frequency response of the impedance matrix of wireless power transfer (WPT) systems comprising litz wire coils.

A finite-element (FE)-based method is proposed which treats the microstructure of litz wires by an auxiliary cell problem. In the macroscopic model, litz wires are represented by a block with a homogeneous, artificial material whose properties are derived from the cell problem. As the frequency characteristics of the material closely resemble a Debye relaxation, it is possible to convert the macroscopic model to polynomial form, which enables the application of model reduction techniques of moment-matching type.

FE-based model-order reduction using litz wire homogenization provides an efficient approach to the broadband analysis of WPT systems. The error of the reduced-order model (ROM) is comparable to that of the underlying original model and can be controlled by varying the ROM dimension.

Since the present model does not account for displacement currents, the operating frequency of the system must lie well below its first self-resonance frequency.

The proposed method is well-suited for the computer-aided design of WPT systems. It outperforms traditional FE analysis in computational efficiency.

The presented homogenization method employs a new formulation for the cell problem which combines the benefits of several existing approaches. Its incorporation into an order-reduction method enables the fast computation of broadband frequency sweeps.

The purpose of this paper is to use different model order reduction techniques to cope with the computational effort of solving large systems of equations. By appropriate decomposition of the electromagnetic field problem, the number of degrees of freedom (DOF) can be efficiently reduced. In this contribution, the Proper Generalized Decomposition (PGD) and the Proper Orthogonal Decomposition (POD) are used in the frame of the T-Ω-formulation, and the feasibility is elaborated.

The POD and the PGD are two methods to reduce the model order. Particularly in the context of eddy current problems, conventional time-stepping algorithms can lead to many numerical simulations of the studied problem. To simulate the transient field, the T-Ω-formulation is used which couples the magnetic scalar potential and the electric vector potential. In this paper, both methods are studied on an academic example of an induction furnace in terms of accuracy and computational effort.

Using the proposed reduction techniques significantly reduces the DOF and subsequently the computational effort. Further, the feasibility of the combination of both methods with the T-Ω-formulation is given, and a fundamental step toward fast simulation of eddy current problems is shown.

In this paper, the PGD is combined for the first time with the T-Ω-formulation. The application of the PGD and POD and the following comparison illustrate the great potential of these techniques in combination with the T-Ω-formulation in context of eddy current problems.

A mathematical description of temperature-dependent boundary conditions is crucial in manifold model-based control or prototyping applications, where accurate thermal simulation results are required. Estimation of boundary condition coefficients for complex geometries in complicated or unknown environments is a challenging task and often does not fulfill given accuracy limits without multiple manual adaptions and experiments. This paper aims to describe an efficient method to identify thermal boundary conditions from measurement data using model order reduction.

An optimization problem is formulated to minimize temperature deviation over time between simulation data and available temperature sensors. Convection and radiation effects are expressed as a combined heat flux per surface, resulting in multiple temperature-dependent film coefficient functions. These functions are approximated by a polynomial function or splines, to generate identifiable parameters. A formulated reduced order system description preserves these parameters to perform an identification. Experiments are conducted with a test-bench to verify identification results with radiation, natural and forced convection.

The generated model can approximate a nonlinear transient finite element analysis (FEA) simulation with a maximum deviation of 0.3 K. For the simulation of a 500 min cyclic cooling and heating process, FEA takes a computation time of up to 13 h whereas the reduced model takes only 7-11 s, using time steps of 2 s. These low computation times allow for an identification, which is verified with an error below 3 K. When film coefficient estimation from literature is difficult due to complex geometries or turbulent air flows, identification is a promising approach to still achieve accurate results.

A well parametrized model can be further used for model-based control approaches or in observer structures. To the knowledge of the authors, no other methodology enables model-based identification of thermal parameters by physically preserving them through model order reduction and therefore derive it from a FEA description. This method can be applied to much more complex geometries and has been used in an industrial environment to increase product quality, due to accurate monitoring of cooling processes.

The article aims to present an efficient numerical method for computing the far-fields of phased antenna arrays over broad frequency bands as well as wide ranges of steering and look angles.

The suggested approach combines finite-element analysis, projection-based model-order reduction, and empirical interpolation.

The reduced-order models are highly accurate but significantly smaller than the underlying finite-element models. Thus, they enable a highly efficient numerical far-field computation of phased antenna arrays. The frequency-slicing greedy method proposed in this paper greatly reduces the computational costs for constructing the reduced-order models, compared to state-of-the-art methods.

The frequency-slicing greedy method is intended for use with matrix factorization methods. It is not applicable when the underlying finite-element system is solved by iterative methods.

In contrast to conventional finite-element models of phased antenna arrays, reduced-order models are very cheap to evaluate. Hence, they provide an enabling technology for computing radiation patterns over broad frequency bands and wide ranges of steering angles.

The paper presents a two-step model-order reduction method for efficiently computing the far-field patterns of phased antenna arrays. The suggested frequency-slicing greedy method constructs the reduced-order models in a systematic fashion and improves computing times, compared to existing methods.

A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing.

The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM.

The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability.

The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated.

The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials.

Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

The finite element method (FEM) for 3D models needs heavy computational cost. The computational cost for FE analysis of moving objects, e.g. Vibration energy harvester, must be reduced to exploit the simulation of the dynamic system in its design. The paper aims to discuss these issues.

To reduce the computational time of FEM, the model order reduction (MOR) based on proper orthogonal decomposition has been proposed. For the moving systems, MOR is modified.

It is shown that proposed MOR makes it possible to drastically reduce the coupling analysis of the energy harvester in which the equations of motion, magnetostatics, and circuit are repeatedly solved.

To reduce the computational time of FEM, block-MOR is presented, in which the whole domain is subdivided into N-blocks. As a result computational cost for MOR can be reduced.