论文信息 - Shape Optimization and Applications

Shape Optimization and Applications

This part mainly deals with the existence (and uniqueness, if possible) of optimal shapes and their regularity. The topics have been marked by the pioneering work of Caffarelli and Alt [2], and presently are intensively developed, in particular by French and Italian schools. In general, the problem of the existence of an optimal shape is complex and difficult due to the lack of appropriate compactness in the set of domains and to poor behavior of the shape functionals with respect to the topology in the set of domains [3].

Arian Novruzi | A. Novruzi

[1] Jan Sokolowski,et al. On the Topological Derivative in Shape Optimization , 1999 .

[2] A. Novruzi,et al. Shape optimization of the hydrogen fuel cell cathode air channels , 2012 .

[3] Arian Novruzi,et al. Structure of shape derivatives , 2002 .

[4] L. Caffarelli,et al. Existence and regularity for a minimum problem with free boundary. , 1981 .

[5] J. Simon. Differentiation with Respect to the Domain in Boundary Value Problems , 1980 .

[6] M. Pierre,et al. Regularity and Singularities of Optimal Convex Shapes in the Plane , 2011, 1112.3054.

[7] Grégoire Allaire,et al. Coupling the Level Set Method and the Topological Gradient in Structural Optimization , 2006 .

[8] J. Roche,et al. Newton's Method in Shape Optimisation: A Three-Dimensional Case , 2000 .

[9] A one-shot inpainting algorithm based on the topological asymptotic analysis , 2006 .

[10] Dorin Bucur,et al. Variational Methods in Shape Optimization Problems , 2005, Progress in Nonlinear Differential Equations and Their Applications.