An Optimum Design Problem in Magnetostatics

Henrot, Antoine; Villemin, Grégory

doi:10.1051/m2an:2002012

Cited by 5 publications

(8 citation statements)

References 9 publications

(11 reference statements)

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“…On note i?o I'aimant, FQ son bord, S la sonde, K^ (resp. A"^) designe la roue Ce probleme a ete I'objet d'une these industrielle, le lecteur interesse pourra consulter les resultats dans [167].…”

Section: O P T I M I S a T I O N D'un A I M A N Tunclassified

Variation et optimisation de formes

Henrot

Pierre

2005

Mathématiques &Amp; Applications

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749

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Section: O P T I M I S a T I O N D'un A I M A N Tunclassified

Variation et optimisation de formes

Henrot

Pierre

2005

Mathématiques &Amp; Applications

Self Cite

516

749

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“…The proposed implementation takes advantage of the analytic structure of the governing equations. While boundary-integral techniques have been used for shape optimization of elliptic PDEs, this was typically done in the discrete setting (i.e., "discretize-then-differentiate") with or without the adjoint equations used to evaluate the shape sensitivities as in [33,34,35,36,37,38].…”

Section: Review Of Computational Methods For Shape Optimization Of Elmentioning

confidence: 99%

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

Peng¹,

Niakhai²,

Protas³

2013

SIAM J. Sci. Comput.

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This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a onedimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shapedifferential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the solution and does not require grids adapted to the contour. This approach is thoroughly validated and optimization results obtained in different test problems exhibit nontrivial shapes of the computed optimal contours.

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“…A related approach for gradient flows involving Laplacian type PDE constraints can be found in [35,36]. Other approaches using level sets can be found in [37][38][39][40][41], as well as boundary integral methods in [42][43][44]. See [45,31,29,34,46,47] for other methods.…”

Section: Optimization Algorithmmentioning

confidence: 99%