Shape derivative of discretized problems

2006 ◽  
pp. 209-228
Author(s):  
M. Souli ◽  
J. P. Zolesio
Keyword(s):  
Shape Derivative

scholarly journals Shape derivative of cost function for singular point: Evaluation by the generalized J integral

JSIAM Letters ◽  
2014 ◽  
Vol 6 (0) ◽  
pp. 29-32 ◽  
Author(s):  
Hideyuki Azegami ◽  
Kohji Ohtsuka ◽  
Masato Kimura
Keyword(s):  
Singular Point ◽  
Cost Function ◽  
Shape Derivative ◽  
J Integral ◽  
Point Evaluation

Derivation of shape derivative for the nanoelasticity problem

2020 ◽  
pp. 601-602
Author(s):  
Timon Rabczuk ◽  
Jeong-Hoon Song ◽  
Xiaoying Zhuang ◽  
Cosmin Anitescu
Keyword(s):  
Shape Derivative

scholarly journals On the Second-Order Shape Derivative of the Kohn-Vogelius Objective Functional Using the Velocity Method

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Jerico B. Bacani ◽  
Julius Fergy T. Rabago
Keyword(s):  
Free Boundary ◽  
Shape Optimization ◽  
Optimization Technique ◽  
Velocity Fields ◽  
Second Order ◽  
Shape Derivative ◽  
State Variables ◽  
Derivatives Of ◽  
Objective Functional ◽  
Perturbation Of Identity

The exterior Bernoulli free boundary problem was studied via shape optimization technique. The problem was reformulated into the minimization of the so-called Kohn-Vogelius objective functional, where two state variables involved satisfy two boundary value problems, separately. The paper focused on solving the second-order shape derivative of the objective functional using the velocity method with nonautonomous velocity fields. This work confirms the classical results of Delfour and Zolésio in relating shape derivatives of functionals using velocity method and perturbation of identity technique.

An energy gap functional: Cavity identification in linear elasticity

2017 ◽  
Vol 25 (5) ◽  
pp. 573-595 ◽  
Author(s):  
Amel Ben Abda ◽  
Emna Jaïem ◽  
Sinda Khalfallah ◽  
Abdelmalek Zine
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Shape Optimization ◽  
Least Squares ◽  
Level Set ◽  
Linear Elasticity ◽  
Optimization Problem ◽  
Energy Gap ◽  
Shape Derivative ◽  
Steepest Descent Algorithm

AbstractThe aim of this work is an analysis of some geometrical inverse problems related to the identification of cavities in linear elasticity framework. We rephrase the inverse problem into a shape optimization one using an energetic least-squares functional. The shape derivative of this cost functional is combined with the level set method in a steepest descent algorithm to solve the shape optimization problem. The efficiency of this approach is illustrated by several numerical results.

scholarly journals Optimization of the first Steklov eigenvalue in domains with holes: a shape derivative approach

2006 ◽  
Vol 186 (2) ◽  
pp. 341-358 ◽  
Author(s):  
Julián Fernández Bonder ◽  
Pablo Groisman ◽  
Julio D. Rossi
Keyword(s):  
Shape Derivative ◽  
Steklov Eigenvalue
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