Analysis of a level set method for topology optimization

Abstract

A level set method for the topological optimization of domains is proposed and analysed in this paper. The framework of the analysis is that of elliptic optimal control problems with a binary control acting as a source term of the state equation. The main ingredient of the algorithm is the concept of topological derivative. Convergence results are proven and illustrated by some numerical experiments.

Keywords:

• topology optimization
• level set method
• topological sensitivity
• topological derivative

AMS Subject Classification :

• 49K20
• 49M05
• 49M25
• 49Q10
• 49Q12