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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.

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.

This paper describes an efficient reduced‐order method for the analysis of cylindrical dielectric resonators with an inhomogeneous dielectric medium. The field equations are formulated using the Laplace‐domain finite element method and are reduced to lower‐order models using the complex frequency hopping (CFH) technique. CFH is a moment matching technique which has been used successfully in the circuit simulation area for the solution of a large set of ordinary differential equations. The proposed technique is faster than the conventional approach by one to three orders of magnitude. The results are compared with those of other numerical methods available in the literature.

The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.

The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.

The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).

In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.

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.

This paper aims to describe a method for efficient frequency domain model order reduction. The method attempts to combine the desirable attributes of Krylov reduction and proper orthogonal decomposition (POD) and is entitled Krylov enhanced POD (KPOD).

The KPOD method couples Krylov’s moment-matching property with POD’s data generalization ability to construct reduced models capable of maintaining accuracy over wide frequency ranges. The method is based on generating a sequence of state- and frequency-dependent Krylov subspaces and then applying POD to extract a single basis that generalizes the sequence of Krylov bases.

The frequency response of a pre-stressed microelectromechanical system resonator is used as an example to demonstrate KPOD’s ability in frequency domain model reduction, with KPOD exhibiting a 44 per cent efficiency improvement over POD.

The results indicate that KPOD greatly outperforms POD in accuracy and efficiency, making the proposed method a potential asset in the design of frequency-selective applications.

This paper aims to present an efficient IMPES algorithm based on a global model order reduction method, proper orthogonal decomposition (POD), to achieve the fast solution and prediction of two-phase flows in porous media.

The key point of the proposed algorithm is to establish an accurate POD reduced-order model (ROM) for two-phase porous flows. To this end, two projection methods including projecting the original governing equations (Method I) and projecting the discrete form of original governing equations (Method II) are respectively applied to construct the POD-ROM, and their distinctions are compared and analyzed in detail. It is found the POD-ROM established by Method I is inapplicable to multiphase porous flows due to its failed introduction of fluid saturation and permeability that locate on the edge of grid cell, which would lead to unphysical results.

By using Method II, an efficient IMPES algorithm that can substantially speed up the simulation of two-phase porous flows is developed based on the POD-ROM. The computational efficiency and numerical accuracy of the proposed algorithm are validated through three numerical examples, and simulation results illustrate that the proposed algorithm displays satisfactory computational speed-up (one to two orders of magnitude) without sacrificing numerical accuracy obviously when comparing to the standard IMPES algorithm that without any acceleration technique. In addition, the determination of POD modes number, the relative errors of wetting phase pressure and saturation, and the influence of POD modes number on the overall performances of the proposed algorithm, are investigated.

1. Two projection methods are applied to establish the POD-ROM for two-phase porous flows and their distinctions are analyzed. The reason why POD-ROM is difficult to be applied to multiphase porous flows is clarified firstly in this study. 2. A highly efficient IMPES algorithm based on the POD-ROM is proposed to accelerate the simulation of two-phase porous flows. 3. Satisfactory computational speed-up (one to two orders of magnitude) and prediction accuracy of the proposed algorithm are observed under different conditions.

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.

In this paper, an effective method to calculate the reduced-order model (ROM) of high-order linear time-invariant system is elaborated; this is done by evaluating time moments of the original high-order model (HOM).

The developed method has been applied to a hydraulic actuator of antiroll bar mechanism dedicated to heavy vehicle semi-active suspension. And as the actuator is a large-scale system; and that in this case, the only control applied is a classical control and with trial and error procedure (like PID), the use of an order reduction method is necessary. Hence, the actuator that has an eighth-order transfer function with uncontrollable states has been approximated by fully controllable second-order model, which is suitable for feedback controllers (RST, LQR […]). The RST control is applied to control the roll angle of the actuator and simulations are carried out to show the effectiveness of the procedure.

It is clear that RST shows good tracking as compared to PID. For further work, the given RST controller has a discrete character and can be easily implemented on the real process and then as a further simulation, one can use another controller such as fractional adaptive controller.

In the recent years, the technological need of modeling order, thus the complexity of the systems, directed the researchers toward the reduction of order of these systems, not only to facilitate the analysis but also to find a suitable approximation of the high-order systems while keeping the same important characteristics as closely as possible. Several methods are available but they fail to give stable transfer functions or important characteristics of the original system.