A new fictitious domain method in shape optimization
- Eppler, Karsten
- Harbrecht, Helmut
- Mommer, Mario
2010 Mathematics Subject Classification
- 49Q10 49M15 65N30 65K10 49K20
- Ficticious domain method, shape optimization, least square solution, Quasi--Newton method
The present paper is concerned with investigating the capability of the smoothness preserving fictitious domain method from  to shape optimization problems. We consider the problem of maximizing the Dirichlet energy functional in the class of all simply connected domains with fixed volume, where the state equation involves an elliptic second order differential operator with non-constant coefficients. Numerical experiments in two dimensions validate that we arrive at a fast and robust algorithm for the solution of the considered class of problems. The proposed method keeps applicable for three dimensional shape optimization problems.