Hadamard incomplete sensitivity and shape optimization
Bijan Mohammadi (2010)
Control and Cybernetics
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Bijan Mohammadi (2010)
Control and Cybernetics
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G. Allaire, C. Dapogny, G. Delgado, G. Michailidis (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves...
Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader (2005)
Control and Cybernetics
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Dalibor Lukáš (2004)
Applications of Mathematics
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In this paper we present theoretical, computational, and practical aspects concerning 3-dimensional shape optimization governed by linear magnetostatics. The state solution is approximated by the finite element method using Nédélec elements on tetrahedra. Concerning optimization, the shape controls the interface between the air and the ferromagnetic parts while the whole domain is fixed. We prove the existence of an optimal shape. Then we state a finite element approximation to the optimization...
Timo Tiihonen (1997)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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(2005)
Control and Cybernetics
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Tao Liao, Hao-Chih Lee, Ge Yang, Yongjie Jessica Zhang (2015)
Molecular Based Mathematical Biology
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The functionality of biomolecules depends on their flexible structures, which can be characterized by their surface shapes. Tracking the deformation and comparing biomolecular shapes are essential in understanding their mechanisms. In this paper, a new spectral shape correspondence analysis method is introduced for biomolecules based on volumetric eigenfunctions. The eigenfunctions are computed from the joint graph of two given shapes, avoiding the sign flipping and confusion in the...