We consider some elliptic PDEs with Dirichlet and Neumann data prescribed on some portion of the boundary of the domain and we obtain rigidity results that give a classification of the solution and of the domain. In particular, we find mild conditions under which a partially overdetermined problem is, in fact, globally overdetermined: this enables to use several classical results in order to cl...

This work deals with the development and application of reduction strategies for real-time and many query problems arising in fluid dynamics, such as shape optimization, shape registration (reconstruction), and shape parametrization. The proposed strategy is based on the coupling between reduced basis methods for the reduction of computational complexity and suitable shape parametrizations – su...

The structure of data is important to the recognition of data. It is a fundamental question how measures and complements the structure of multi-features, because the fusion structure of multi-features is more complete than that of the single feature. To settle the question, we propose three methods for feature structure fusion in feature vectors or feature vector spaces. Firstly, the applicabil...

Fatigue describes the damage or failure of material under cyclic loading. Activation and deactivation operations of technical units are important examples in engineering where fatigue and especially low-cycle fatigue (LCF) play an essential role. A significant scatter in fatigue life for many materials results in the necessity of advanced probabilistic models for fatigue. Moreover, structural s...

Abstract: The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier–Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equat...

this paper is about discrete sensitivity analysis. a triangular bending element with constant moment and six degrees of freedom is used. the required derivatives for sensitivity analysis are calculated explicitly. these formulations, finite element method and sequential linear programming are utilized to find shape optimization of plate bending structures. the numerical examples, which show the...

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove ...

We consider the problem of placing a Dirichlet region made by n small balls of given radius in a given domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look for the Γ−limit of suitably scaled functionals, in order to get informations on the asymptotical distribution of the centres of the balls. This problem is both linked t...

We describe ADJIFOR, an automated adjoint code generator for Fortran, and present preliminary results from the application of ADJIFOR to augment the CFL3D ow solver. Based on these initial results with CFL3D, we argue that, even in its infancy, ADJIFOR can deliver derivatives accurately and eeciently for use in aerodynamic shape optimization problems with 200 to 500 independent design variables.

We focus here on the analysis of the regularity or singularity of solutions Ω0 to shape optimization problems among convex planar sets, namely: J(Ω0) = min{J(Ω), Ω convex, Ω ∈ Sad}, where Sad is a set of 2-dimensional admissible shapes and J : Sad → R is a shape functional. Our main goal is to obtain qualitative properties of these optimal shapes by using first and second order optimality condi...