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The purpose of this paper is the realization of Fast nonlinear finite element analysis (FEA).

Nonlinear magnetic field analysis is achieved by using Newton-Raphson method implemented by relaxed convergence criterion of Krylov subspace method.

This paper mathematically analyzes the reason why nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed.

The proposed method is essential to reduce the elapsed time in nonlinear magnetic field analysis of quasi-stationary field.

The proposed method is able to be extended to not only static field but also time domain FEA strongly coupled with circuit equation.

Because the speedup of performance evaluation of electrical machines would be achieved using proposed method, the work efficiency in manufacturing would be accelerated.

It can be seen that the nonlinear convergence can be achieved if the convergence criterion for linearized equation is relaxed. The verification of proposed method is demonstrated using practical nonlinear magnetic field problem.

Strategies for accelerated multi-objective optimization of aerodynamic surfaces are investigated, including the possibility of exploiting surrogate modeling techniques for computational fluid dynamic (CFD)-driven design speedup of such surfaces. The purpose of this paper is to reduce the overall optimization time.

An algorithmic framework is described that is composed of: a search space reduction, fast surrogate models constructed using variable-fidelity CFD models and co-Kriging, and Pareto front refinement. Numerical case studies are provided demonstrating the feasibility of solving real-world problems involving multi-objective optimization of transonic airfoil shapes and accurate CFD simulation models of such surfaces.

It is possible, through appropriate combination of surrogate modeling techniques and variable-fidelity models, to identify a set of alternative designs representing the best possible trade-offs between conflicting design objectives in a realistic time frame corresponding to a few dozen of high-fidelity CFD simulations of the respective surfaces.

The proposed aerodynamic design optimization algorithmic framework is novel and holistic. It proved useful for fast design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search space, which is extremely challenging when using conventional methods due to the excessive computational cost.

The purpose of this paper is the improvement of topology optimization. The scope of the paper is focused on the speedup of optimization.

To achieve the speedup, the method of moving asymptotes (MMA) with constrained condition of level set function is applied instead of solving the Hamilton–Jacobi equation.

The acceleration of convergence of objective function is drastically improved by the implementation of MMA.

Normally, the level set method is solved through the Hamilton–Jacobi equation. However, the possibility of introducing mathematical programming is clear by the constrained condition. Furthermore, the proposed method is suitable for efficiently solving the topology optimization problem in the magnetic field system.

The approximate factorisation‐conjugate gradient squared (AF‐CGS) method has been successfully demonstrated for unsteady turbulent aerofoil flows and transonic inviscid flows in two and three dimensions. The method consists of a conjugate gradient solution of the linear system at each step with the ADI approximate factorisation as a preconditioner. In the present paper the method is adapted to obtain rapid convergence for steady aerofoil flows when compared to the basic explicit method. Modifications to the original method are described, convergence criteria are examined and the method is demonstrated for transonic flow including AGARD test case 9 for the RAE2822 aerofoil.

The purpose of this paper is to reduce the overall computational time of aerodynamic shape optimization that involves accurate high-fidelity simulation models.

The proposed approach is based on the surrogate-based optimization paradigm. In particular, multi-fidelity surrogate models are used in the optimization process in place of the computationally expensive high-fidelity model. The multi-fidelity surrogate is constructed using physics-based low-fidelity models and a proper correction. This work introduces a novel correction methodology – referred to as the adaptive response prediction (ARP). The ARP technique corrects the low-fidelity model response, represented by the airfoil pressure distribution, through suitable horizontal and vertical adjustments.

Numerical investigations show the feasibility of solving real-world problems involving optimization of transonic airfoil shapes and accurate computational fluid dynamics simulation models of such surfaces. The results show that the proposed approach outperforms traditional surrogate-based approaches.

The proposed aerodynamic design optimization algorithm is novel and holistic. In particular, the ARP correction technique is original. The algorithm is useful for fast design of aerodynamic surfaces using high-fidelity simulation data in moderately sized search spaces, which is challenging using conventional methods because of excessive computational costs.

The purpose of this study is to account for a recent non-mainstream econometric approach using microdata and how it can inform research in business administration. More specifically, the paper draws from the applied microeconometric literature stances in favor of fitting Poisson regression with robust standard errors rather than the OLS linear regression of a log-transformed dependent variable. In addition, the authors point to the appropriate Stata coding and take into account the possibility of failing to check for the existence of the estimates – convergency issues – as well as being sensitive to numerical problems.

The author details the main issues with the log-linear model, drawing from the applied econometric literature in favor of estimating multiplicative models for non-count data. Then, he provides the Stata commands and illustrates the differences in the coefficient and standard errors between both OLS and Poisson models using the health expenditure dataset from the RAND Health Insurance Experiment (RHIE).

The results indicate that the use of Poisson pseudo maximum likelihood estimators yield better results that the log-linear model, as well as other alternative models, such as Tobit and two-part models.

The originality of this study lies in demonstrating an alternative microeconometric technique to deal with positive skewness of dependent variables.

The purpose of this paper is to present a method for analysis and optimization of morphing wing. Moreover, a numerical advantage of morphing airfoil wing, typically assessed in simplified two-dimensional analysis is found using higher fidelity methods.

Because of multi-point nature of morphing wing optimization, an approach for optimization by analysis is presented. Starting from naïve parametrization, multi-fidelity aerodynamic data are used to construct response surface model. From the model, many significant information are extracted related to parameters effect on objective; hence, design sensitivity and, ultimately, optimal solution can be found.

The method was tested on benchmark problem, with some easy-to-predict results. All of them were confirmed, along with additional information on morphing trailing edge wings. It was found that wing with morphing trailing edge has around 10 per cent lower drag for the same lift requirement when compared to conventional design.

It is demonstrated that providing a smooth surface on wing gives substantial improvement in multi-purpose aircrafts. Details on how this is achieved are described. The metodology and results presented in current paper can be used in further development of morphing wing.

Most of literature describing morphing airfoil design, optimization or calculations, performs only 2D analysis. Furthermore, the comparison is often based on low-fidelity aerodynamic models. This paper uses 3D, multi-fidelity aerodynamic models. The results confirm that this approach reveals information unavailable with simplified models.

The aim of this chapter is to examine the nominal and real convergence of Czechia. The importance of the convergence of Czechia with the euro area is linked to the future intention of joining the Economic and Monetary Union after the Maastricht criteria are met. This chapter covers the period from 2004 to 2021. We argue that nominal convergence is relative to the Maastricht criteria, when real convergence focuses on different areas: the Maastricht criteria, gross domestic product (GDP) per capita in purchasing power standards and real GDP growth rate, labour market (minimum labour costs and unemployment rates. Findings suggest that Czechia has reported the strongest real convergence in the area of relative economic level, moderate convergence of labour costs and divergence of unemployment. The nominal convergence analysis suggests that Czechia will not meet the Maastricht benchmarks in the near future and is not ready to join the euro area given its high inflation rate and the state of public finances.

Continuum‐atomistic modeling denotes a mixed approach combining the usual framework of continuum mechanics with atomistic features like e.g. interaction potentials. Thereby, the kinematics are typically characterized by the so called Cauchy‐Born rule representing atomic distance vectors in the spatial configuration as an affine mapping of the atomic distance vectors in the material configuration in terms of the local deformation gradient. The application of the Cauchy‐Born rule requires sufficiently homogeneous deformations of the underlying crystal. The model is no more valid if the deformation becomes inhomogeneous. By virtue of the Cauchy‐Born hypothesis, a localization criterion has been derived in terms of the loss of infinitesimal rank‐1 convexity of the strain energy density. According to this criterion, a numerical yield condition has been computed for two different interatomic energy functions. Therewith, the range of the Cauchy‐Born rule validity has been defined, since the strain energy density remains quasiconvex only within the computed yield surface. To provide a possibility to continue the simulation of material response after the loss of quasiconvexity, a relaxation procedure proposed by Tadmor et al. [1] leading necessarily to the development of microstructures has been used. Alternatively to the above mentioned criterion, a stability criterion has been applied to detect the critical deformation. For the study in the postcritical region, the path‐change procedure proposed by Wagner and Wriggers [2] has been adapted for the continuum‐atomistics and modified.

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.