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This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate derivatives of solutions outputs with respect to arbitrary solution input(s). A problem involving conduction in a plane wall with convection at its surfaces is used as a test problem, as it has an analytical solution, and the error can be evaluated directly.

The finite volume method is used to discretize the transient heat diffusion equation with constant thermophysical properties. The discretized problem is then linearized, which results in two linear systems; one for the primary solution field and one for the secondary field, representing the derivative of the primary field with respect to the selected input(s). Derivatives required in the formation of the secondary linear system are obtained by automatic differentiation using an operator overloading and templating approach in C++.

The temporal and spatial discretization error for the derivative solution follows the same order of accuracy as the primary solution. Second-order accuracy of the spatial and temporal discretization schemes is confirmed for both primary and secondary problems using both orthogonal and non-orthogonal grids. However, it has been found that for non-orthogonal cases, there is a limit to the error reduction, which is concluded to be a result of errors in the Gauss-based gradient reconstruction method.

The convergence and error properties of derivative solutions obtained by forward mode automatic differentiation of finite volume-based codes have not been previously investigated.

The purpose of this paper is to illustrate automatic differentiation (AD) as a new technology for the device sizing in electromagnetism by using gradient constrained optimization. Component architecture for the design of engineering systems (CADES) framework, previously described, is presented here with extended features.

The paper is subject to further usage for optimization of AD (also named algorithmic differentiation) which is a powerful technique that computes derivatives of functions described as computer programs in a programming language like C/C++, FORTRAN.

Indeed, analytical modeling is well suited regarding optimization procedure, but the modeling of complex devices needs sometimes numerical formulations. This paper then reviews the concepts implemented in CADES which aim to manage the interactions of analytical and numerical modeling inside of gradient‐based optimization procedure. Finally, the paper shows that AD has no limit for the input program complexity, or gradients accuracy, in the context of constrained optimization of an electromagnetic actuator.

AD is employed for a large and complex numerical code computing multidimensional integrals of functions. Thus, the paper intends to prove the AD capabilities in the context of electromagnetic device sizing by means of gradient optimization. The code complexity as also as the implications of AD usage may stand as a good reference for the researchers in this field area.

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.

Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).

Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.

In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.

The purpose of this paper is to develop surrogate models, using deep learning (DL), that can facilitate the application of EM analysis software. In the current status quo, electrical systems can be found in an ever-increasing range of products that are part of everyone’s daily live. With the advances in technology, industries such as the automotive, communications and medical devices have been disrupted with new electrical and electronic systems. The innovation and development of such systems with increasing complexity over time has been supported by the increased use of electromagnetic (EM) analysis software. Such software enables engineers to virtually design, analyze and optimize EM systems without the need for building physical prototypes, thus helping to shorten the development cycles and consequently cut costs.

The industry standard for simulating EM problems is using either the finite difference method or the finite element method (FEM). Optimization of the design process using such methods requires significant computational resources and time. With the emergence of artificial intelligence, along with specialized tools for automatic differentiation, the use of DL has become computationally much more efficient and cheaper. These advances in machine learning have ushered in a new era in EM simulations where engineers can compute results much faster while maintaining a certain level of accuracy.

This paper proposed two different models that can compute the magnetic field distribution in EM systems. The first model is based on a recurrent neural network, which is trained through a data-driven supervised learning method. The second model is an extension to the first with the incorporation of additional physics-based information to the authors’ model. Such a DL model, which is constrained by the laws of physics, is known as a physics-informed neural network. The solutions when compared with the ground truth, computed using FEM, show promising accuracy for the authors’ DL models while reducing the computation time and resources required, as compared to previous implementations in the literature.

The paper proposes a neural network architecture and is trained with two different learning methodologies, namely, supervised and physics-based. The working of the network along with the different learning methodologies is validated over several EM problems with varying levels of complexity. Furthermore, a comparative study is performed regarding performance accuracy and computational cost to establish the efficacy of different architectures and learning methodologies.

A research project is reported in which techniques for the automatic classification of book material were investigated. Attention was focussed on three fundamental issues, namely: the computer‐based surrogation of monographic material, the clustering of book surrogates on the basis of content association, and the evaluation of the resultant classifications. A test collection of 250 books, which was assembled on behalf of the project, is described together with its surrogation by means of the complete back‐of‐the‐book index, table of contents, title and Dewey classification code(s) of each volume. Some properties of hierarchic and non‐hierarchic automatic classifications of the test collection are discussed, followed by their evaluation with reference to a small set of queries and relevance judgements. Finally, a less formal evaluation of the classifications in terms of the logical appeal of the cluster membership is reported. The work has shown that, on a small experimental scale and in the context of the test data used, automatic classifications of book material represented by index list can be produced which are superior, on the basis of a generalized measure of effectiveness, to a conventional library classification of the same material.

Proposes a methodology for dealing with the problem of designing a material microstructure the best suitable for a given goal.

The chosen model problem for the design is a two‐phase material, with one phase related to plasticity and another to damage. The design problem is set in terms of shape optimization of the interface between two phases. The solution procedure proposed herein is compatible with the multi‐scale interpretation of the inelastic mechanisms characterizing the chosen two‐phase material and it is thus capable of providing the optimal form of the material microstructure. The original approach based upon a simultaneous/sequential solution procedure for the coupled mechanics‐optimization problem is proposed.

Several numerical examples show a very satisfying performance of the proposed methodology. The latter can easily be adapted to other choices of design variables.

Confirms that one can thus achieve the optimal design of the nonlinear behavior of a given two‐phase material with respect to the goal specified by a cost function, by computing the optimal form of the shape interface between the phases.

This paper aims to probe the limits of the empirical-normative divide as a conceptual framework in business ethics.

A systems theory perspective debunks this divide as a false distinction that cannot do justice to the conceptual complexity of the field of corporate social responsibility (CSR) scholarship.

Drawing on the systems-theoretic ideas of Niklas Luhmann and the “Laws of Form” by George Spencer Brown, the paper shows that the divide may be dissected into a four-cell matrix constituted by two other distinctions-descriptive vs prescriptive and categorical vs hypothetical-the latter of which was seminally suggested by Donaldson and Preston (1995).

The emerging four-cell matrix is shown to centrally embrace the multiplicity of normative, empirical and instrumental approaches to CSR. This multiplicity is exemplified by the application of these approaches to the phenomenon of CSR communication.

A more general implication of the proposed argument for the field of business ethics is in tracing the phenomena of moral diversity and moral ambivalence back to the regime of functional differentiation as the distinguishing feature of the modern society. This argument drives home the point that economic operations are as ethical or unethical as political operations, and that both economic and political perspectives on ethical issues are as important or unimportant as are religious, artistic, educational or scientific perspectives.

In contrast to the empirical-normative divide, the perspective is shown to centrally embrace the multiplicity of normative, empirical and instrumental approaches to CSR.

The aim of this paper is to investigate competitive pricing strategies of apparel brands and retailers.

The paper begins with a broad discussion of competition by examining Porter's five forces model, and narrows by examining price competition within price tiers in the retail apparel industry according to store format and brands. Included are case studies of apparel retailers and brands incorporating concepts of pricing strategies, brand positioning, and price competition, with a focus on retail channel relationships. The paper analyzes the impact of price competition on apparel retailers and brands, and further examines price tiers as a competitive strategy.

The study reveals that the concept of price tiers is applicable to apparel retailers and brands. Price tiering is a vehicle for market positioning for the retail apparel industry. Retailers are enacting a price tier strategy by branding their retail store formats or engaging store brands as a vehicle of differentiation for a tier. Retailers and brands can be successful with a price tier strategy, unless they fail to differentiate between tiers on factors other than on price alone.

The lack of relevant price competition literature, relating to the retailer apparel industry, forced the exploration of price competition literature from grocery and automotive sectors.

The paper provides useful information on the impact of price competition on apparel retailers and brands, and also price tiers as a competitive strategy.

The goal of this research is to investigate the convergence behavior of the Newton iteration, when solving the nonlinear problem with consideration of hysteresis effects. Incorporating the vector hysteresis model in the magnetic vector potential formulation has encountered difficulties. One of the reasons is that the Newton method is very sensitive regarding the starting point and states distinct requirements for the nonlinear function in terms of monotony and smoothness. The other reason is that the differential reluctivity tensor of the material model is discontinuous due to the properties of the stop operators. In this work, line search methods to overcome these difficulties are discussed.

To stabilize the Newton iteration, line search methods are studied. The first method computes an error-oriented search direction. The second method is based on the Wolfe-Powell rule using the Armijo condition and curvature condition.

In this paper, the differentiation of the vector stop model, used to evaluate the Jacobian matrix, is studied. Different methods are applied for this nonlinear problem to ensure reliable and stable finite element simulations with consideration of vector hysteresis effects.

In this paper, two different line search Newton methods are applied to solve the magnetic field problems with consideration of vector hysteresis effects and ensure a stable convergence successfully. A comparison of these two methods in terms of robustness and efficiency is presented.

This paper presents a shape optimization problem under acoustic, aerodynamic and geometric constraints. The acoustic specification concerns the generated sonic boom. The aim is to see the validity of incomplete sensitivities when a nonlinear CFD model is coupled with a nonlinear wave transport model to define pressure rise on the ground.