.png){kind=icon}
Return
A LEVEL SET BASED SHAPE OPTIMIZATION METHOD FOR AN ELLIPTIC OBSTACLE PROBLEM
.png){kind=icon}
PRE
AI
DOI：10.1142/S0218202511005155.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
In this paper, we construct a level set method for an elliptic obstacle problem, which can be reformulated as a shape optimization problem. We provide a detailed shape sensitivity analysis for this reformulation and a stability result for the shape Hessian at the optimal shape. Using the shape sensitivities, we construct a geometric gradient flow, which can be realized in the context of level set methods. We prove the convergence of the gradient flow to an optimal shape and provide a complete analysis of the level set method in terms of viscosity solutions. To our knowledge this is the first complete analysis of a level set method for a nonlocal shape optimization problem. Finally, we discuss the implementation of the methods and illustrate its behavior through several computational experiments.
Keywords:
Level set methods
free boundary problems
obstacle problem
Journal
IF:
3
Papers:
2.2K
Citations:
4.6K
Organization
Cited Papers
.png){kind=icon}
ShareSaveShareSaveShareSaveShareSaveDetermination of available transfer capability with implication of cascading collapse uncertainty
OAAI
OAAIShareSave
View more