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An optimum design problem in magnetostatics

Antoine HenrotGrégory Villemin — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.

Optimization of the shape and the location of the actuators in an internal control problem

Antoine HenrotHervé Maillot — 2001

Bollettino dell'Unione Matematica Italiana

Consideriamo un corpo Ω sottomesso ad una forza esterna data e del quale vogliamo controllare lo spostamento. Cerchiamo un rinforzo per minimizzare un funzionale che dipende dallo spostamento del corpo. L'insieme delle configurazioni ammissibili è un insieme di funzioni caratteristiche di sottodomini (un rinforzo ammissibile è un sottodominio con una rigidezza uguale ad uno) di volume prescritto. In tal caso, si ha bisogno di una versione rilassata del problema di ottimizzazione e si cerca una densità...

An Optimum Design Problem in Magnetostatics

Antoine HenrotGrégory Villemin — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we are interested in finding the optimal shape of a magnet. The criterion to maximize is the jump of the electromagnetic field between two different configurations. We prove existence of an optimal shape into a natural class of domains. We introduce a quasi-Newton type algorithm which moves the boundary. This method is very efficient to improve an initial shape. We give some numerical results.

Eliciting harmonics on strings

Steven J. CoxAntoine Henrot — 2008

ESAIM: Control, Optimisation and Calculus of Variations

One may produce the th harmonic of a string of length by applying the 'correct touch' at the node π / q during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their 'touch' is a damper of magnitude concentrated at π / q . The 'correct touch' is that for which the modes, that do not vanish at π / q , are maximally damped. We here examine the associated spectral problem. We find the spectrum to be periodic and determined by a polynomial of degree q - 1 . We...

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