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Article
Publication date: 31 July 2019

Christopher DeGroot

This paper aims to investigate the convergence and error properties of a finite volume-based heat conduction code that uses automatic differentiation to evaluate…

Abstract

Purpose

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.

Design/methodology/approach

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++.

Findings

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.

Originality/value

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

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 11 September 2009

P. Enciu, F. Wurtz, L. Gerbaud and B. Delinchant

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 28 no. 5
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 5 February 2018

Ajay Vadakkepatt, Sanjay R. Mathur and Jayathi Y. Murthy

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…

Abstract

Purpose

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.

Design/methodology/approach

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).

Findings

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.

Originality/value

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 2
Type: Research Article
ISSN: 0961-5539

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Book part
Publication date: 30 August 2019

Joshua C. C. Chan, Liana Jacobi and Dan Zhu

Vector autoregressions (VAR) combined with Minnesota-type priors are widely used for macroeconomic forecasting. The fact that strong but sensible priors can substantially…

Abstract

Vector autoregressions (VAR) combined with Minnesota-type priors are widely used for macroeconomic forecasting. The fact that strong but sensible priors can substantially improve forecast performance implies VAR forecasts are sensitive to prior hyperparameters. But the nature of this sensitivity is seldom investigated. We develop a general method based on Automatic Differentiation to systematically compute the sensitivities of forecasts – both points and intervals – with respect to any prior hyperparameters. In a forecasting exercise using US data, we find that forecasts are relatively sensitive to the strength of shrinkage for the VAR coefficients, but they are not much affected by the prior mean of the error covariance matrix or the strength of shrinkage for the intercepts.

Details

Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A
Type: Book
ISBN: 978-1-78973-241-2

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Article
Publication date: 1 March 1985

P.G.B. ENSER

A research project is reported in which techniques for the automatic classification of book material were investigated. Attention was focussed on three fundamental issues…

Abstract

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.

Details

Journal of Documentation, vol. 41 no. 3
Type: Research Article
ISSN: 0022-0418

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Article
Publication date: 1 July 2005

Adnan Ibrahimbegović, Igor Grešovnik, Damijan Markovič, Sergiy Melnyk and Tomaž Rodič

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

Abstract

Purpose

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

Design/methodology/approach

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.

Findings

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

Originality/value

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.

Details

Engineering Computations, vol. 22 no. 5/6
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 15 January 2020

Steffen Roth, Vladislav Valentinov and Lars Clausen

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

Abstract

Purpose

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

Design/methodology/approach

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.

Findings

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).

Practical implications

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.

Social implications

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.

Originality/value

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

Details

Sustainability Accounting, Management and Policy Journal, vol. 11 no. 4
Type: Research Article
ISSN: 2040-8021

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Article
Publication date: 1 October 2006

Genessa M. Fratto, Michelle R. Jones and Nancy L. Cassill

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

Abstract

Purpose

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

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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.

Originality/value

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

Details

Journal of Fashion Marketing and Management: An International Journal, vol. 10 no. 4
Type: Research Article
ISSN: 1361-2026

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Article
Publication date: 1 October 2004

Bijan Mohammadi

This paper presents a shape optimization problem under acoustic, aerodynamic and geometric constraints. The acoustic specification concerns the generated sonic boom. The…

Abstract

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 14 no. 7
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 June 2003

Jaroslav Mackerle

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view…

Abstract

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

Details

Engineering Computations, vol. 20 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

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