Shape identification for natural convection problems using the adjoint variable method

Park, H. M.; Shin, Hyung-Ki

doi:10.1016/s0021-9991(03)00046-9

Cited by 33 publications

(14 citation statements)

References 11 publications

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“…Research on shape design in heat convection fields based on the gradient method and adjoint variables has been conducted by Momose et al (2009), Park and Ku (2001), Park and Shin (2003), Morimoto et al (2010), and Aounallah et al (2013). The adjoint variable method has advantageous calculation efficiency in its solutions of optimization problems.…”

Section: Introductionmentioning

confidence: 99%

“…Momose et al (2009) have proposed a shape sensitivity analysis method that seeks to maximize the velocity in the sub-domain in natural convection fields; however, this method was limited to steady-state problems. Park and Ku (2001) and Park and Shin (2003) used the adjoint variable method for shape identification problems in unsteady natural convection fields. They proposed the limiting of design variables that express boundary shapes to the minimum number of variables required for the steady-state problem.…”

Section: Introductionmentioning

confidence: 99%

“…They conducted an analysis using Bezier curves, which facilitate expressions of smooth boundary shapes with a minimal number of design variables. This method is similar to that of Park and Ku (2001) and Park and Shin (2003). As described above, many methods were shape optimization methods using parametric design variables for design boundaries.…”

Section: Introductionmentioning

confidence: 99%

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Shape design of heat convection fields based on the adjoint method

Katamine

2018

Mechanical Engineering Reviews

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The utilization of shape design to improve heat transfer characteristics in heat convection fields is an important subject in engineering. This review paper explains a numerical solution for the shape design problems involving steady and unsteady heat convection fields. Reshaping for the shape design is carried out by traction method, which is proposed as an approach to solving shape optimization problems. The traction method is a shape optimization method with some advantages such as deformation analysis of pseudo-elastic bodies can be used in the shape update analysis and smoothness in shape update can be maintained. In steady-state heat convection fields, shape design problems that control the temperature distribution in the sub-domains of the heat convection field are introduced. The square integration error between the actual temperature distribution and the target temperature distribution in the specified sub-domains is employed as the objective functional for the shape design. In unsteady heat convection fields, two shape design problems are shown; these problems also involve control of the temperature distribution in sub-domains of the field. In the first problem, in a manner similar to the steady-state problem, the square integration error of the sub-domains during the specified period of time is used as the objective functional. In the second problem, a multi-objective shape design problem that utilizes a normalized objective functional is formulated for the problem to prescribe the temperature distribution and the total dissipated energy minimization problem. The shape gradient of these shape design problems for steady and unsteady fields is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Numerical analysis programs for shape design problems using the traction method are developed, and the validity of the demonstrated method is confirmed by results of 2D numerical analyses.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shape design of heat convection fields based on the adjoint method

Katamine

2018

Mechanical Engineering Reviews

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“…Park (Park and Ku, 2001), (Park and Shin, 2003) Yan (Yan and Gao, 2013), (Yan et al, 2015) Yaji (Yaji et al, 2015) Alexandersen (Alexandersen et al, 2014) Yaji (Yaji et al, 2015) Alexandersen (Alexandersen et al, 2014) Yan Gauss-Newton (Yan et al, 2014) (Yan et al, 2017) (…”

mentioning

confidence: 99%

Solution to shape design problems of unsteady forced heat-convection fields

Katamine¹,

Okada²

2017

Transactions of the JSME (In Japanese)

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This paper presents numerical solution to two shape design problems of unsteady forced heat-convection fields to control temperature to a prescribed distribution. In the first problem, the square error integral between the actual temperature distributions and the prescribed temperature distributions on the prescribed sub-domains during the specified period of time is used as the objective functional. In the second problem, a multi-objective shape optimization problem using normalized objective functional is formulated for the temperature distribution prescribed problem and the total dissipated energy minimization problem in the unsteady forced heat-convection fields. Shape gradient of these shape design problems is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems. Numerical analyses program for the shape design is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses.

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“…A similar BIE-based treatment of shape-material sensitivity has been recently proposed [47] for optical tomography featuring the scalar Helmholtz equation with a complex wavenumber, while e.g. [3,37] present other applications of adjoint-based shape sensitivity analyses.…”

mentioning

confidence: 99%

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

Bonnet

Guzina

2009

Journal of Computational Physics

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This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous "reference" solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm.

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Shape identification for natural convection problems using the adjoint variable method

Cited by 33 publications

References 11 publications

Shape design of heat convection fields based on the adjoint method

Shape design of heat convection fields based on the adjoint method

Solution to shape design problems of unsteady forced heat-convection fields

Elastic-wave identification of penetrable obstacles using shape-material sensitivity framework

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