Chapter 15: Dynamic Regularization, Level Set Shape Optimization, and Computed Myography

2012 ◽  
pp. 315-326 ◽  
Author(s):  
Kees van den Doel ◽  
Uri M. Ascher
Keyword(s):  
Shape Optimization ◽  
Level Set

scholarly journals Driving force profile design in comb drive electrostatic actuators using a level set-based shape optimization method

2014 ◽  
Vol 51 (2) ◽  
pp. 369-383 ◽  
Author(s):  
Takayo Kotani ◽  
Takayuki Yamada ◽  
Shintaro Yamasaki ◽  
Makoto Ohkado ◽  
Kazuhiro Izui ◽  
...  
Keyword(s):  
Shape Optimization ◽  
Level Set ◽  
Driving Force ◽  
Optimization Method ◽  
Comb Drive ◽  
Electrostatic Actuators ◽  
Force Profile ◽  
Profile Design

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 A Level Set Method in Shape and Topology Optimization for Variational Inequalities

2007 ◽  
Vol 17 (3) ◽  
pp. 413-430 ◽  
Author(s):  
Piotr Fulmański ◽  
Antoine Laurain ◽  
Jean-Francois Scheid ◽  
Jan Sokołowski
Keyword(s):  
Topology Optimization ◽  
Variational Inequalities ◽  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Energy Functional ◽  
Optimization Techniques ◽  
Shape And Topology Optimization ◽  
And Topology ◽  
Topological Derivatives

A Level Set Method in Shape and Topology Optimization for Variational InequalitiesThe level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed for the topology variations in the form of small holes. The derivation of topological derivatives is performed within the framework proposed in (Sokołowski and Żochowski, 2003). Numerical results confirm that the method is efficient and gives better results compared with the classical shape optimization techniques.

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