Shape Optimization of Conductor-Ferromagnetic Material Interface in Eddy Current System Using Continuum Sensitivity With Level-Set Method

2019 ◽  
Author(s):  
Jun Hyeong Wang ◽  
Kyung Sik Seo ◽  
Il Han Park
Keyword(s):  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Eddy Current ◽  
Current System ◽  
Ferromagnetic Material ◽  
Material Interface ◽  
Continuum Sensitivity

Adaptive level set method for accurate boundary shape in optimization of electromagnetic systems

2014 ◽  
Vol 33 (3) ◽  
pp. 809-820 ◽  
Author(s):  
Kang Hyouk Lee ◽  
Seung Geon Hong ◽  
Myung Ki Baek ◽  
Hong Soon Choi ◽  
Young Sun Kim ◽  
...  
Keyword(s):  
Shape Optimization ◽  
Level Set Method ◽  
Level Set ◽  
Numerical Technique ◽  
Computational Time ◽  
Heaviside Function ◽  
Interface Problem ◽  
Shape Variation ◽  
Material Interface ◽  
Content Type

Purpose – The purpose of this paper is to present a new numerical technique, called adaptive level set method, for use with the finite element method. Design/methodology/approach – A conventional level set method using the smeared Heaviside function has been employed for shape and topology optimizations. The smeared Heaviside function yields an indistinct interface boundary, and so can increase computational time and cause numerical errors. The adaptive level set method does not use the smeared Heaviside function. To coincide with the material interface, it processes the zero level as the boundary data of element meshing. Findings – Usefulness and accuracy of shape optimization using the adaptive level set method are shown by comparison to the conventional level set method. A shape optimization procedure using the adaptive level set method is introduced. Numerical examples are employed to explain how the adaptive level set method is applied. Originality/value – The adaptive level set method is proposed to relieve the interface problem of the conventional level set method. Shape variation in the optimization is calculated from the continuum sensitivity analysis.

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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