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Article
Publication date: 1 August 2000

Gao‐Lian Liu

So far the literature on inverse shape design in aerodynamics is still confined to the single‐point (nominal design point) design and to steady flow. This situation cannot…

Abstract

So far the literature on inverse shape design in aerodynamics is still confined to the single‐point (nominal design point) design and to steady flow. This situation cannot cope with the modern development of internal and external aerodynamics and aerothermoelasticity, especially turbomachinery and aircraft flows. Accordingly, in recent years a new generation of inverse shape design problem has been suggested and investigated theoretically and computationally, consisting mainly of: unsteady inverse and hybrid problems; multipoint inverse and hybrid problems; and inverse problem in aerothermoelasticity. It opens a new area of research in fluid mechanics and aerothermoelasticity. An overview of its status and perspective is given herein, emphasizing the new concepts, theory and methods of solution involved.

Details

Aircraft Engineering and Aerospace Technology, vol. 72 no. 4
Type: Research Article
ISSN: 0002-2667

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Article
Publication date: 1 April 1995

Lorraine G. Olson and Robert D. Throne

We compare a recently proposed generalized eigensystem approach and anew modified generalized eigensystem approach to more widely used truncatedsingular value…

Abstract

We compare a recently proposed generalized eigensystem approach and a new modified generalized eigensystem approach to more widely used truncated singular value decomposition and zero‐order Tikhonov regularization for solving multidimensional elliptic inverse problems. As a test case, we use a finite element representation of a homogeneous eccentric spheres model of the inverse problem of electrocardiography. Special attention is paid to numerical issues of accuracy, convergence, and robustness. While the new generalized eigensystem methods are substantially more demanding computationally, they exhibit improved accuracy and convergence compared with widely used methods and offer substantially better robustness.

Details

Engineering Computations, vol. 12 no. 4
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 6 March 2017

Oleg M. Alifanov

The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author…

Abstract

Purpose

The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author and his colleagues to the solution to ill-posed inverse heat transfer problems (IHTPs) with their possible extension to a wider class of inverse problems of mathematical physics and, most importantly, to show the wide possibilities of this methodology by examples of aerospace applications. In this regard, this study can be seen as a continuation of those applications that were discussed in the lecture.

Design/methodology/approach

The application of the inverse method was pre-tested with experimental investigations on a special test equipment in laboratory conditions. In these studies, the author used the solution to the nonlinear inverse problem in the conjugate (conductive and convective) statement. The corresponding iterative algorithm has been developed and tested by a numerical and experimental way.

Findings

It can be stated that the theory and methodology of solving IHTPs combined with experimental simulation of thermal conditions is an effective tool for various fundamental and applied research and development in the field of heat and mass transfer.

Originality/value

With the help of the developed methods of inverse problems, the investigation was conducted for a porous cooling with a gaseous coolant for heat protection of the re-entry vehicle in the natural environment of hypersonic flight. Moreover, the analysis showed that the inverse methods can make a useful contribution to the study of heat transfer at the surface of a solid body under the influence of the hypersonic heterogeneous (dusty) gas stream and in many other aerospace applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 3
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 29 April 2014

Ahmed Abou-Elyazied Abdallh and Luc Dupré

Magnetic material properties of an electromagnetic device (EMD) can be recovered by solving a coupled experimental numerical inverse problem. In order to ensure the…

Abstract

Purpose

Magnetic material properties of an electromagnetic device (EMD) can be recovered by solving a coupled experimental numerical inverse problem. In order to ensure the highest possible accuracy of the inverse problem solution, all physics of the EMD need to be perfectly modeled using a complex numerical model. However, these fine models demand a high computational time. Alternatively, less accurate coarse models can be used with a demerit of the high expected recovery errors. The purpose of this paper is to present an efficient methodology to reduce the effect of stochastic modeling errors in the inverse problem solution.

Design/methodology/approach

The recovery error in the electromagnetic inverse problem solution is reduced using the Bayesian approximation error approach coupled with an adaptive Kriging-based model. The accuracy of the forward model is assessed and adapted a priori using the cross-validation technique.

Findings

The adaptive Kriging-based model seems to be an efficient technique for modeling EMDs used in inverse problems. Moreover, using the proposed methodology, the recovery error in the electromagnetic inverse problem solution is largely reduced in a relatively small computational time and memory storage.

Originality/value

The proposed methodology is capable of not only improving the accuracy of the inverse problem solution, but also reducing the computational time as well as the memory storage. Furthermore, to the best of the authors knowledge, it is the first time to combine the adaptive Kriging-based model with the Bayesian approximation error approach for the stochastic modeling error reduction.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 3
Type: Research Article
ISSN: 0332-1649

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Article
Publication date: 1 August 1996

M. RAUDENSKÝ, J. HORSKÝ, J. KREJSA and L. SLÁMA

Inverse problems deal with determining the causes on the basis of knowing their effects. The object of the inverse parameter estimation problem is to fix the thermal…

Abstract

Inverse problems deal with determining the causes on the basis of knowing their effects. The object of the inverse parameter estimation problem is to fix the thermal material parameters (the cause) on the strength of a given observation of the temperature history at one or more interior points (the effect). This paper demonstrates two novel approaches to the inverse problems. These approaches use two artificial intelligence mechanisms: neural network and genetic algorithm. Examples shown in this paper give a comparison of results obtained by both of these methods. The numerical technique of neural networks evolved from the effort to model the function of the human brain and the genetic algorithms model the evolutional process of nature. Both of the presented approaches can lead to a solution without having problems with the stability of the inverse task. Both methods are suitable for parallel processing and are advantageous for a multiprocessor computer architecture.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 September 2021

Alfredo Canelas and Jean Rodolphe Roche

In this paper the authors review the recent numerical techniques proposed to solve the forward and inverse problems concerning the electromagnetic casting and…

Abstract

Purpose

In this paper the authors review the recent numerical techniques proposed to solve the forward and inverse problems concerning the electromagnetic casting and electromagnetic levitation techniques of the metallurgical industry. In addition, the authors present a new topology optimization method to solve the inverse axisymmetric electromagnetic levitation problem.

Design/methodology/approach

The proposed method is based on an exact second-order topological expansion of a Kohn–Vogelius-like functional specially devised for this problem.

Findings

Through some examples the authors show that it can find suitable solutions efficiently.

Originality/value

The new method completes the set of efficient methods available to solve the inverse electromagnetic casting and the inverse axisymmetric electromagnetic levitation problems.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 17 June 2021

Lucas Fernandez and Ravi Prakash

The purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.

Abstract

Purpose

The purpose of this paper is to present topological derivatives-based reconstruction algorithms to solve an inverse scattering problem for penetrable obstacles.

Design/methodology/approach

The method consists in rewriting the inverse reconstruction problem as a topology optimization problem and then to use the concept of topological derivatives to seek a higher-order asymptotic expansion for the topologically perturbed cost functional. Such expansion is truncated and then minimized with respect to the parameters under consideration, which leads to noniterative second-order reconstruction algorithms.

Findings

In this paper, the authors develop two different classes of noniterative second-order reconstruction algorithms that are able to accurately recover the unknown penetrable obstacles from partial measurements of a field generated by incident waves.

Originality/value

The current paper is a pioneer work in developing a reconstruction method entirely based on topological derivatives for solving an inverse scattering problem with penetrable obstacles. Both algorithms proposed here are able to return the number, location and size of multiple hidden and unknown obstacles in just one step. In summary, the main features of these algorithms lie in the fact that they are noniterative and thus, very robust with respect to noisy data as well as independent of initial guesses.

Details

Engineering Computations, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 3 June 2020

Adam Basílio, Fran Sérgio Lobato and Fábio de Oliveira Arouca

The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually…

Abstract

Purpose

The study of heat transfer mechanisms is an area of great interest because of various applications that can be developed. Mathematically, these phenomena are usually represented by partial differential equations associated with initial and boundary conditions. In general, the resolution of these problems requires using numerical techniques through discretization of boundary and internal points of the domain considered, implying a high computational cost. As an alternative to reducing computational costs, various approaches based on meshless (or meshfree) methods have been evaluated in the literature. In this contribution, the purpose of this paper is to formulate and solve direct and inverse problems applied to Laplace’s equation (steady state and bi-dimensional) considering different geometries and regularization techniques. For this purpose, the method of fundamental solutions is associated to Tikhonov regularization or the singular value decomposition method for solving the direct problem and the differential Evolution algorithm is considered as an optimization tool for solving the inverse problem. From the obtained results, it was observed that using a regularization technique is very important for obtaining a reliable solution. Concerning the inverse problem, it was concluded that the results obtained by the proposed methodology were considered satisfactory, as even with different levels of noise, good estimates for design variables in proposed inverse problems were obtained.

Design/methodology/approach

In this contribution, the method of fundamental solution is used to solve inverse problems considering the Laplace equation.

Findings

In general, the proposed methodology was able to solve inverse problems considering different geometries.

Originality/value

The association between the differential evolution algorithm and the method of fundamental solutions is the major contribution.

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Article
Publication date: 1 February 2006

A. Rap, L. Elliott, D.B. Ingham, D. Lesnic and X. Wen

To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

Abstract

Purpose

To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

Design/methodology/approach

The proposed numerical technique is based on the boundary element method (BEM) combined with an iterative sequential quadratic programming (SQP) procedure. The governing convection‐diffusion equation is transformed into a Helmholtz equation and the ill‐conditioned system of equations that arises after the application of the BEM is solved using an iterative technique.

Findings

The iterative BEM presented in this paper is well‐suited for solving inverse source problems for convection‐diffusion equations with constant coefficients. Accurate and stable numerical solutions were obtained for cases when the number of sources is correctly estimated, overestimated, or underestimated, and with both exact and noisy input data.

Research limitations/implications

The proposed numerical method is limited to cases when the Péclet number is smaller than 100. Future approaches should include the application of the BEM directly to the convection‐diffusion equation.

Practical implications

Applications of the results presented in this paper can be of value in practical applications in both heat and fluid flow as they show that locations and strengths for an unknown number of point sources can be accurately found by using boundary measurements only.

Originality/value

The BEM has not as yet been employed for solving inverse source problems related with the convection‐diffusion equation. This study is intended to approach this problem by combining the BEM formulation with an iterative technique based on the SQP method. In this way, the many advantages of the BEM can be applied to inverse source convection‐diffusion problems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 16 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 1992

C.K. HSIEH, MEHDI AKBARI and HONGJUN LI

A method has been developed for the solution of inverse heat diffusion problems to find the initial condition, boundary condition, and the source and sink function in the…

Abstract

A method has been developed for the solution of inverse heat diffusion problems to find the initial condition, boundary condition, and the source and sink function in the heat diffusion equation. The method has been used in the development of a source‐and‐sink method to find the boundary conditions in inverse Stefan problems. Green's functions have been used in the solution, and the problems are solved by using two approaches: a series solution approach, and a time incremental approach. Both can be used to find the boundary conditions without reliance on the flux information to be supplied at both sides of the interface. The methods are efficient in that they require less equations to be solved for the conditions. The numerical results have shown to be accurate, convergent, and stable. Most of all, the results do not degrade with time as in other time marching schemes reported in the literature. Algorithms can also be easily developed for the solution of the conditions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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