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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.

Model order reduction (MOR) has been widely used in the electric networks but little has been done to reduce higher index differential algebraic equations (DAEs). The paper aims to discuss these issues.

Most methods first do an index reduction before reducing a higher DAE but this can lead to a loss of physical properties of the system.

The paper presents a MOR method for DAEs called the index-aware MOR (IMOR) which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

MOR has been widely used to reduce large systems from electric networks but little has been done to reduce higher index DAEs. Most methods first do an index reduction before reducing a large system of DAEs but this can lead to a loss of physical properties of the system. The paper presents a MOR method for DAEs called the IMOR which can reduce a DAE while preserving its physical properties such as the index. The feasibility of this method is tested on real-life electric networks.

This paper proposes an algorithm for the extraction of reduced order models of MEMS switches, based on using a physics aware simplification technique.

The reduced model is built progressively by increasing the complexity of the physical model. The approach starts with static analyses and continues with dynamic ones. Physical phenomena are introduced sequentially in the reduced model whose order is increased until accuracy, computed by assessing forces that are kept in the reduced model, is acceptable.

The technique is exemplified for RF-MEMS switches, but it can be extended for any device where physical phenomena can be included one by one, in a hierarchy of models. The extraction technique is based on analogies that are carried out for both the multiphysics and the full-wave electromagnetic phenomena and their couplings. In the final model, the multiphysics electromechanical phenomena is reduced to a system with lumped components with nonlinear elastic and damping forces, coupled with a system with distributed and lumped components which represents the reduced model of the RF electromagnetic phenomena.

Contrary to the order reduction by projection methods, this approach has the advantage that the simplified model can be easily understood, the equations and variables have significance for the user and the algorithm starts with a model of minimal order, which is increased until the approximation error is acceptable. The novelty of the proposed method is that, being tailored to a specific application, it is able to keep physical interpretation inside the reduced model. This is the reason why, the obtained model has an extremely low order, much lower than the one achievable with general state-of-the-art procedures.

The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.

This paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.

It is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centers

The paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

The purpose of this paper is to demonstrate the applicability of the Discrete Empirical Interpolation method (DEIM) for simulating the swing dynamics of benchmark power system problems. The authors demonstrate that considerable savings in computational time and resources are obtained using this methodology. Another purpose is to apply a recently developed modified DEIM strategy with a reduced on-line computational burden on this problem.

On-line computational cost of the power system dynamics problem is reduced by using DEIM, which reduces the complexity of the evaluation of the nonlinear function in the reduced model to a cost proportional to the number of reduced modes. The on-line computational cost is reduced by using an approximate snap-shot ensemble to construct the reduced basis.

Considerable savings in computational resources and time are obtained when DEIM is used for simulating swing dynamics. The on-line cost implications of DEIM are also reduced considerably by using approximate snapshots to construct the reduced basis.

Applicability of DEIM (with and without approximate ensemble) to a large-scale power system dynamics problem is demonstrated for the first time.

Based on the framework of Krylov subspace-based model order reduction (MOR), compact models of the piezoelectric energy harvester devices can be generated. However, the stability of reduced piezoelectric model often cannot be preserved. In previous research studies, “MOR after Schur,” “Schur after MOR” and “multiphysics structure preserving MOR” methods have proven successful in obtaining stable reduced piezoelectric energy harvester models. Though the stability preservation of “MOR after Schur” and “Schur after MOR” methods has already been mathematically proven, the “multiphysics structure preserving MOR” method was not. This paper aims to provide the missing mathematical proof of “multiphysics structure preserving MOR.”

Piezoelectric energy harvesters can be represented by system of differential-algebraic equations obtained by the finite element method. According to the block structure of its system matrices, “MOR after Schur” and “Schur after MOR” both perform Schur complement transformations either before or after the MOR process. For the “multiphysics structure preserving MOR” method, the original block structure of the system matrices is preserved during MOR. 

This contribution shows that, in comparison to “MOR after Schur” and “Schur after MOR” methods, “multiphysics structure preserving MOR” method performs the Schur complement transformation implicitly, and therefore, stabilizes the reduced piezoelectric model.

The stability preservation of the reduced piezoelectric energy harvester model obtained through “multiphysics structure preserving MOR” method is proven mathematically and further validated by numerical experiments on two different piezoelectric energy harvester devices.

The purpose of this paper is to describe reduced order modelling based on dynamic flexibility approximation and applied to transient analyses.

This work is based on a recently proposed flexibility‐based component modes synthesis (CMS) approach which was shown to be very efficient for solving large eigenvalue problems. The model reduction approach is based on partionning via the localized Lagrange multipliers method, which makes it very appropriate to handle coupled problems.

In particular, it is demonstrated in this paper how the utilised model reduction method can be applied only to one part of the structure and efficiently coupled to a full finite element model. The performance of the method is investigated on numerical examples of plate and 3D problems.

The proposed flexibility‐based CMS approach can be used as a very efficient tool for complex engineering structures under dynamic load where the mode superposition method applies. The efficiency of the computations is brought about by the model reduction.

The paper is concerned with interpolatory proper orthogonal decomposition (IPOD) methods for nonlinear transmission line circuits. This paper aims to examine several factors that must be considered when applying such model reduction techniques to this kind of circuit.

Two types of POD will be implemented. In each case, the choice of the order of the reduced model and the order of the interpolation space shall be considered. The stability of the models shall be explored.

The results indicate that the order for the reduced model to obtain accurate results depends on the chosen method when considering nonlinear transmission lines. The results also indicate that the structure of the nonlinear transmission line is crucial for determining the stability of the reduced models.

The work compares two IPOD methods and discusses the issues involved in achieving an accurate and stable reduced-order model for a nonlinear transmission line.

This paper aims to present a method for the efficient reduction of networks modelling parasitic couplings in very‐large‐scale integration (VLSI) circuits.

The parasitic effects are modelled by large RLC networks and current sources for the digital switching currents. Based on the determined behaviour of the digital modules, an efficient description of these networks is proposed, which allows for a more efficient model reduction than standard methods.

The proposed method enables a fast and efficient simulation of the parasitic effects. Additionally, an extension of the reduction method to elements, which incorporate some supply voltage dependence to model the internal currents more precisely than independent current sources is presented.

The presented method can be applied to large electrical networks, used in the modelling of parasitic effects, for reducing their size. A reduced model is created which can be used in investigations with circuit simulators requiring a lowered computational effort.

Contrary to existing methods, the presented method includes the knowledge of the behaviour of the sources in the model to enhance the model reduction process.

The purpose of this paper is to establish an intelligent framework to generate the data representatives in snapshot simulation in order to construct the online reduced-order model based on the generated data information. It could greatly reduce the computational time in snapshot simulation and accelerate the computational efficiency in the real-time computation of reduced-order modeling.

The snapshot simulation, which generates the data to construct reduced-order models (ROMs), usually is computationally demanding. In order to accelerate the snapshot generation, this paper presents a discrete element interpolaiton method (DEIM)-embedded hybrid simulation approach, in which the entire snapshot simulation is partitioned into multiple intervals of equal length. One of the three models: the full order model (FOM), local ROM, or local ROM-DEIM which represents a hierarchy of model approximations, fidelities and computational costs, will be adopted in each interval.

The outcome of the proposed snapshot simulation is an efficient ROM-DEIM applicable to various online simulations. Compared with the traditional FOM and the hybrid method without DEIM, the proposed method is able to accelerate the snapshot simulation by 54.4%–63.91% and 10.5%–27.85%, respectively. In the online simulation, ROM-DEIM only takes 4.81%–8.56% of the computational time of FOM, while preserving excellent accuracy (with relative error <1%).

1. A DEIM-embedded hybrid snapshot simulation methodology is proposed to accelerate snapshot data generation and reduced-order model (ROM)-DEIM development. 2. The simulation alternates among FOM, ROM and ROM-DEIM to adaptively generate snapshot data of salient subspace representation while minimizing computational load. 3. The DEIM-embedded hybrid snapshot approach demonstrates excellent accuracy (<1% error) and computational efficiency in both online snapshot simulation and online ROM-DEIM verification simulation.