Structural optimization using topological and shape sensitivity via a level set method
Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader (2005)
Control and Cybernetics
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Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader (2005)
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...
Bijan Mohammadi (2010)
Control and Cybernetics
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Jan Sokołowski, Tomasz Lewiński (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...
Xu Guo, Kang Zhao, Michel Wang (2005)
Control and Cybernetics
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Q. Haxhibeqiri (1985)
Matematički Vesnik
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Zhanheng Gao, Reihaneh Rostami, Xiaoli Pang, Zhicheng Fu, Zeyun Yu (2016)
Molecular Based Mathematical Biology
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Novel approaches for generating and comparing flexible (non-rigid) molecular surface meshes are developed. The mesh-generating method is fast and memory-efficient. The resulting meshes are smooth and accurate, and possess high mesh quality. An isometric-invariant shape descriptor based on the Laplace- Beltrami operator is then explored for mesh comparing. The new shape descriptor is more powerful in discriminating different surface shapes but rely only on a small set of signature values....