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Abstract

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 12
Type: Research Article
ISSN: 0961-5539

Open Access
Article
Publication date: 3 June 2022

Peter Gangl, Stefan Köthe, Christiane Mellak, Alessio Cesarano and Annette Mütze

This paper aims to deal with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque while keeping low…

Abstract

Purpose

This paper aims to deal with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque while keeping low the amount of material used, by means of gradient-based free-form shape optimization.

Design/methodology/approach

The presented approach is based on the mathematical concept of shape derivatives and allows to obtain new motor designs without the need to introduce a geometric parametrization. This paper presents an extension of a standard gradient-based free-form shape optimization algorithm to the case of multiple objective functions by determining updates, which represent a descent of all involved criteria. Moreover, this paper illustrates a way to obtain an approximate Pareto front.

Findings

The presented method allows to obtain optimal designs of arbitrary, non-parametric shape with very low computational cost. This paper validates the results by comparing them to a parametric geometry optimization in JMAG by means of a stochastic optimization algorithm. While the obtained designs are of similar shape, the computational time used by the gradient-based algorithm is in the order of minutes, compared to several hours taken by the stochastic optimization algorithm.

Originality/value

This paper applies the presented gradient-based multi-objective optimization algorithm in the context of free-form shape optimization using the mathematical concept of shape derivatives. The authors obtain a set of Pareto-optimal designs, each of which is a shape that is not represented by a fixed set of parameters. To the best of the authors’ knowledge, this approach to multi-objective free-form shape optimization is novel in the context of electric machines.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 41 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Open Access
Article
Publication date: 14 December 2021

Phillip Baumann and Kevin Sturm

The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological…

Abstract

Purpose

The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.

Design/methodology/approach

The authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.

Findings

The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutz' method, the averaged adjoint method and Delfour's method.

Originality/value

In contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

Details

Engineering Computations, vol. 39 no. 1
Type: Research Article
ISSN: 0264-4401

Keywords

Open Access
Article
Publication date: 19 August 2020

Ahmed Berkane and Abdallah Bradji

We consider, as discretization in space, the nonconforming mesh developed in SUSHI (Scheme Using Stabilization and Hybrid Interfaces) developed in Eymard et al. (2010) for a…

Abstract

We consider, as discretization in space, the nonconforming mesh developed in SUSHI (Scheme Using Stabilization and Hybrid Interfaces) developed in Eymard et al. (2010) for a semi-linear heat equation. The time discretization is performed using a uniform mesh. We are concerned with a nonlinear scheme that has been studied in Bradji (2016) in the context of the general framework GDM (Gradient Discretization Method) (Droniou et al., 2018) which includes SUSHI. We provide sufficient conditions on the size of the spatial mesh and the time step which allow to prove a W1,(L2)-error estimate. This error estimate can be viewed as an improvement for the W1,2(L2)-error estimate proved in Bradji (2016). The W1,(L2)-error estimate we want to prove in this note was stated without proof in Bradji (2016, Remark 7.2, Page 1302). Its proof is based on a comparison with an appropriately chosen auxiliary finite volume scheme along with the derivation of some new estimates on its solution.

Details

Arab Journal of Mathematical Sciences, vol. 27 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Open Access
Article
Publication date: 5 April 2021

Samuel Ssekajja

The author considers an invariant lightlike submanifold M, whose transversal bundle tr…

Abstract

Purpose

The author considers an invariant lightlike submanifold M, whose transversal bundle tr(TM) is flat, in an indefinite Sasakian manifold M¯(c) of constant φ¯-sectional curvature c. Under some geometric conditions, the author demonstrates that c=1, that is, M¯ is a space of constant curvature 1. Moreover, M and any leaf M of its screen distribution S(TM) are, also, spaces of constant curvature 1.

Design/methodology/approach

The author has employed the techniques developed by K. L. Duggal and A. Bejancu of reference number 7.

Findings

The author has discovered that any totally umbilic invariant ligtlike submanifold, whose transversal bundle is flat, in an indefinite Sasakian space form is, in fact, a space of constant curvature 1 (see Theorem 4.4).

Originality/value

To the best of the author’s findings, at the time of submission of this paper, the results reported are new and interesting as far as lightlike geometry is concerned.

Details

Arab Journal of Mathematical Sciences, vol. 28 no. 1
Type: Research Article
ISSN: 1319-5166

Keywords

Open Access
Article
Publication date: 21 March 2024

Hedi Khedhiri and Taher Mkademi

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

Abstract

Purpose

In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

Design/methodology/approach

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2z2iw2z1+iw1, (z1,w1,z2,w2)C4.

Findings

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

Originality/value

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξHC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

Details

Arab Journal of Mathematical Sciences, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

Open Access
Article
Publication date: 8 August 2019

Karl Hollaus

The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by…

1038

Abstract

Purpose

The simulation of eddy currents in laminated iron cores by the finite element method (FEM) is of great interest in the design of electrical devices. Modeling each laminate by finite elements leads to extremely large nonlinear systems of equations impossible to solve with present computer resources reasonably. The purpose of this study is to show that the multiscale finite element method (MSFEM) overcomes this difficulty.

Design/methodology/approach

A new MSFEM approach for eddy currents of laminated nonlinear iron cores in three dimensions based on the magnetic vector potential is presented. How to construct the MSFEM approach in principal is shown. The MSFEM with the Biot–Savart field in the frequency domain, a higher-order approach, the time stepping method and with the harmonic balance method are introduced and studied.

Findings

Various simulations demonstrate the feasibility, efficiency and versatility of the new MSFEM.

Originality/value

The novel MSFEM solves true three-dimensional eddy current problems in laminated iron cores taking into account of the edge effect.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Abstract

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 11
Type: Research Article
ISSN: 0961-5539

Open Access
Article
Publication date: 14 March 2023

Svetlin Georgiev, Aissa Boukarou, Keltoum Bouhali and Khaled Zennir

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global…

Abstract

Purpose

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

Design/methodology/approach

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

Findings

This paper is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

Originality/value

This article is devoted to the generalized Kadomtsev–Petviashvili I equation. This study aims to propose a new approach for investigation for the existence of at least one global classical solution and the existence of at least two nonnegative global classical solutions. The main arguments in this paper are based on some recent theoretical results.

Details

Arab Journal of Mathematical Sciences, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

Content available
Article
Publication date: 31 October 2008

Luiz Moutinho and Kun-Huang Huarng

341

Abstract

Details

Journal of Modelling in Management, vol. 3 no. 3
Type: Research Article
ISSN: 1746-5664

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